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2918 publications that use or cite Magma, spanning 1973 to 2011.
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arXiv:0904.3908. The authors gratefully acknowledge the hospitality of the Magma group at the University of Sydney for their hospitality and would like to thank Lassina Dembélé Steve Donnelly, Benjamin Linowitz, and Ron Livné for their helpful comments
Failure of the Hasse principle for Enriques surfaces
arXiv:1008.0596
arXiv:0909.0062
More on superstring chiral measures
On the diophantine equation $x^2+5^a11^b=y^n $
arXiv:1001.2525
arXiv:0905.2737v2
Remarks on proficient groups
for calculations
arXiv:0905.0380v1 [math.DG]
arXiv:0710.1149
Replaces NR1003105
We obtain the following statement (via Magma).
All computation in this paper is done by using a computer algebra system Magma
A new semifield of order $2^10$
Look up paper
arXiv:0902.1738
arXiv:1002.4228v2 [math.NT]
IACR eprint:2006:372. Used for computations
See also http://www.nku.edu/~christensen/SMS420jeremy.pdf
Algorithmic enumeration of ideal classes for quaternion orders
READ ALLAN We also benchmark the DFS variant against the powerful computer algebra system MAGMA
Implementation of F4 which is compared with Magma. The Cabarcas version is about 4 times slower and uses more memory
Although one can compute exactly in a finite, non-perturbative manner in AP Theory,using, e.g., the computer algebra system magma, ([W1], [W2], [W3], [C], [C1], [CW]), the only quantitative prediction AP Theory makes at this point is: if the Higgs boson appears experimentally, it will be somehow related to Poincare's homology 3-sphere and representations of its fundamental group, the binary icosahedral group, I(120), of order 120.
Replaces NR1003104 One may compute directly, by hand or by Magma that in fact the automorphism group is defined already over F7.
Automorphisms of hyperelliptic modular curves $X_0(N)$ in positive characteristic
Automorphisms of hyperelliptic modular curves $X_0(N)$ in positive characteristic
arXiv:0811.0876
Blackbox computation of $A_$-algebras
arXiv:0807.3869v1
Character degrees of normally monomial maximal class 5-groups
CODE
A Magma program for the explicit evaluation of the formula of Corollary 7.6 can be obtained from the authors.
Codes associated with triangular graphs, and permutation decoding
Replaces NR1003117
Computing with algebraically closed fields
We have implemented Algorithm 1 for prime constant fields with the aim to provide examples of its effectiveness. The code is available under a GPL license as a Magma package [2] on the author's webpage at www.math.tu-berlin.de/~minzlaff.
IACR eprint:2009:376
The success of this method heavily depends on the size of the solution vector space. An implementation in Magma software actually always gave in both cases a vector space of dimension one. This revealed the secret permutation
Decomposing symmetric powers of certain modular representations of cyclic groups
arXiv:math.AC/05099044v2
We use a computer algebra system MAGMA [1] for the computation of the examples in this paper.
Efficient decomposition of dense matrices over $GF(2)$
Element-wise operations over F2 are relatively cheap compared to loads from and writes to memory. In fact, in this work we demonstrate that the two fastest implemen- tations for dense matrix decomposition over F2 (the one presented in this work and the one found in Magma [8] due to Allan Steel) perform worse for sparse matrices despite the fact that fewer field operations are performed. This indicates that counting raw field operations is not an adequate model for estimating the running time in the case of F2 .
Replaces NR1003052 "We have implemented algorithms in the computational algebra system Magma for Halphen fibrations and Geiser and Bertini involutions. Our code is available at www.kent.ac.uk/IMS/personal/gdb/ellfib.mag"
Text includes snippets of Magma code
As a final remark, we should mention that the software package Magma played an integral part in the discovery process of several results in this paper by providing data that eventually allowed us to see many general patterns.
We can compute the geometric special fiber of X at 3 and 13 by means of Cerednik-Drinfeld's theory (cf. [14,3] for a step-by-step guide on the computation of these special fibers using MAGMA.
VERIFY Came up in search but could not access to verify
arXiv:0907.4922v2 [math.QA]. We have also verified the remaining seven exchange relations, with the assistance of the computer program Magma
arXiv:0901.2920
arXiv:0910.2589. For the computations we have used a combination of the computer algebra systems MAGMA ([12]) and Maple ([13]).
Replaces NR1003123
At the end of the section we briefly discuss the implementation we made in Magma
Replaces NR1003113
Replease NR1003118 For the sake of clarity, we exhibit the following example obtained with the aid of MAGMA [1].
Another, faster, version is the new LowIndexNormalSubgroups process developed recently by Derek Holt and his student David Firth (at the University of Warwick) and available in the computational algebra system Magma [3]
arXiv:0902.1912
arXiv:0811.1463. Using MAGMA we obtain that the rank of the Jacobian of this genus 2 curve is 0, which makes it perfect for Chabauty's algorithm
Another common notation one finds in the literature is I2 = A, I4 = B, I6 = C, I10 = D, for example in the Magma help pages on February 2010, but we shall avoid using it, especially since it conflicts with Igusa notation as in [Igu4, p. 848] ... Using Magma's implementation of Mestre's algorithm, we obtain..
arXiv:0809.0369v1 [math.AG]
This algorithm was implemented in MAGMA software for symbolic calculations.
Replaces NR1003114
Hurwitz generation of the universal covering of Alt(n)
arXiv:1001.5125v1 [math.GR] Our proofs are computer independent, but the algebraic softwares Magma and GAP have been of invaluable help.
arXiv:0908.1762. Finally, I thank Steve Donnelly for helpful discussions and the Magma Group at the University of Sydney for their hospitality during a visit, in which part of this research was completed
The author would like to thank ... the Magma group at the University of Sydney for their support while writing this paper, and ...Unfortunately, at the present time the literature is much less complete in providing a suite of algorithms for computing with integral structures in such fields - particularly in the situation where one works in a relative extension of such fields despite the fact that some of these algorithms have already been implemented in Magma [3] by Hess [14].
Replaces NR1003112 This test has been implemented in Magma, and is freely available at http://www.math.univ-toulouse.fr/~cheze/.
An algorithm for computing the numbers a(^U, !) is implemented in the LiE package, [vLCL92]. This package is no longer supported but it has been incorporated into Magma, [BCP97]. The calculations in this paper used these two packages.
Involutions on surfaces with $p_g=q=1$
arXiv:0805.4513v1 [math.AG]
Finally, for the modules where these tools dont give a conclusive answer, we use MAGMA algebra software (see [BCP]) to compute the rank of the contravariant form B on a certain graded piece of Mc(^) and calculate the coefficients of the character formula from there.
GOOD PRINT
Unfortunately the author's MAGMA program to compute the general formulas (i.e., over Fp(a0, b0) with a0 and b0 algebraically independent transcendental elements) of canonical liftings modulo p3 seem to require a lot of computer power. Assuming there is no bug in the authors code (or in MAGMA), a computer with 16 gigabytes of memory cannot compute the general formula for the canonical lifting (and elliptic Teichmueller lift) modulo 173.
arXiv:0905.4798v3
The computer algebra system Magma has a built-in command DifferentialOperator for finding such operators
arXiv:math/0606182v1
Linear sets in finite projective spaces
computations
The computations were carried out with MAGMA. Programs and scripts are available from the third author's webpage.
No intext references, just the citation at the end
Low dimensional strongly perfect lattices III: Dual strongly perfect lattices of dimension 14
arXiv:0809.0593v1
The alternative approach for determining types of k-orbit maps would be simply to use LowIndexSubgroups algorithm in Magma.
arXiv:0908.1741. All our algorithms (for n = 2, 3, 4 and K = Q) have been implemented in (and contributed to) MAGMA
Modular forms on noncongruence subgroups and Atkin-Swinnerton-Dyer relations
arXiv:0805.2144v1
arXiv:0911.5024. Our test is implemented in Magma and available at: http://www.math.univ-toulouse.fr/~cheze/
Finally, in a good implementation, the worst case precision bound for the lifting is hardly never attained. These heuristics and others have been implemented by Steel in Magma [29] on the top of the algorithms designed in [1,31,27]. Our new algorithms are not intended to compete in general with Steel's implementation. Instead they sensibly improve the performances in very particular cases. Such cases are very difficult to build. One example is provided by [1, Remark 5.5].
Replaces NR1003111 Non-commutative algebra, Lower central series, Tensor field modules Combining our bounds in Theorem 1.2 with MAGMA computations, we are also able to give the complete Jordan-Holder series of Bm(An) for many new m and n. Using the computational algebra system MAGMA we were able to produce the bigraded Hilbert series of Bm(A2) up to degree 12, and the tri-graded Hilbert series for Bm(A3) up to degree 8.
For this aim, we have implemented the method developed at Section 4 in Magma [3] using W.A. Stein's Modular packages. We have obtained a total of 44 such curves that appear at Table 1.
arXiv:0904.3561v2 [math.AC] PRINT We have also compared our implementation with the normalization procedures in Macaulay2 (they use the algorithms Decker et al. (1999) and Singh and Swanson (2008)) and in Magma (they say that they use Decker et al. (1999) for the general case; however it seems to work only in characteristic 0 and the code is not accessible). Our new algorithm is always faster and succeeds where the other implementations do not finish. We do not know implementations in other computer algebra systems.
Special data structures employed in PolyBoRi are particularly useful for normal form reductions that we need for obtaining key-variables-only equations. It seems that general purpose computer algebra systems like Magma and Singular are not well suited for the purpose of our approach.
We use either of these packages (PARI or Magma) to solve the Thue equations that arise.
arXiv:0709.0715v1 Using MAGMA we checked all these calculations and obtained the more precise result that all exceptional irreducible reflection groups without polynomial ring of invariants have in fact a linear subspace whose point stabilizer is an abelian p-group with an invariant ring that is not a polynomial ring, and so the direct summand property does not hold. In fact in most cases the point stabilizer is not even generated by pseudo-reflections.
Replaces arXiv:0809.3622
Replaces NR1003110
On equations of double planes with $p_g=q=1$
arXiv:0804.2227v1 [math.AG]
The magma program used to compute them is available at http://myria.math.aegean.gr/~kontogar/sk/
For simplifying the proof we sometimes cite an easily repeatable computation with Magma
The author thanks Jeremy Rouse for his help on the computer algebra, MAGMA.
We identified using William Stein's Magma package the following Hecke eigenform
Throughout the paper we use the notation of Magma for presenting the places and the divisor of algebraic function fields.
This is shown by an standard 2-descent argument, either using Magma, Sage or PARI. ... Data: All the Magma sources are available from the first author webpage.
arXiv:0810.4788
This article grew out of work done by the second author during his visit to the Magma Group in Sydney in 2009. A partial version of the algorithm described here, in which f,p is computed up to a quadratic twist, is implemented in the computational algebra system Magma
MAJOR CODE PRINT This paper contains two algorithms, implemented in Magma, to compute singular plane algebraic curves
For the proposed parameter value N = 300, experimental results in the Magma language have led the authors of [14] to a success rate of 88% within a few minutes with moderate resources. Hence the above authentication scheme does not provide strong cryptographic security guarantees.
arXiv:0809.2315
Special thanks go to Martin Kohls for Example 4.1 and various useful MAGMA routines
arXiv:1001.3573v1. Problems of this type are amenable to the elliptic Chabauty method as implemented in a number of routines in Magma [4]. But we should stress that the application of Magma is in general not a matter of button pushing, and is sometimes far from automatic; we note later some of the problems that can arise. PRINT
Replaces NR1003108
arXiv:1004.3735v1
arXiv:1002.0492
Replaces NR1003119 For the cases not already covered, we use the computer algebra systems MAGMA and GAP together with the package GRAPE to build all possible H up to conjugacy, and then check simple connectedness in each case.
http://eprint.iacr.org/2010/177.pdf In this section we detail the results of an implementation of our Static DHP algorithm using the computational algebra system MAGMA
Extensive computer experiments using Magma
We also connected our SAGE implementation to Mathematica, Macaulay 2, MAGMA and PolyBoRi and used its Groebner algorithms. We also used SAGE to pass the Groebner basis computation to MAGMA. However, due to license issues MAGMA could not run on the same system on which all other experiments were made. We did one separate experiment (Table 3) that compares MAGMA and the best of the other algorithms (std), also running on the second server
Perfect, strongly eutactic lattices are periodic extreme
arXiv:0808.2013v1. [MAG] Computational Algebra Group, University of Sydney, ver.2.13
During the preparation of the paper the computations were performed with computer algebra system Magma
Prime order derangements in primitive permutation groups
This can be checked in the Magma software package, where the group G is SmallGroups(972)[777]. Replaces NR1003049
Thanks also go to Daniel Sutantyo for his help with Magma programs
arXiv:0912.4397v1 The complete list of mutable quantum cluster variables is then obtained by repeated mutation, to give the list in Table 1. This was obtained with assistance from the computer program Magma
Using this symmetric presentation of 0 and detailed knowledge of the coset enumeration needed to verify it Curtis and the author have been able to produce a program in Magma [13], available from the author's website (which at the time of writing may be found at http://matematicas.uniandes.edu.co/~benfairbairn/Homepage.htm),
MAGMA refuses to give any finite simple homomorphic image with a ne 1, b ne 1 for almost any choice of u and v.
Replaces NR1003120
Here, we concentrate mainly on two attacks, namely the direct attack and the Rainbow-Band-Separation attack. To study the complexity of these two attacks, we carried out a large number of own experiments, for which we used MAGMA [BC06], which contains an efficient implementation of Faugeres F4 algorithm for computing Groebner bases. We use the results of these experiments ...
Was NR1003054
Spaces of constant rank matrices over $GF(2)$
www.math.technion.ac.il/iic/ela/ela-articles/articles/vol20_pp01-05.pdf
Strongly regular graphs associated with ternary bent functions
for verification
In a series of papers the following construction was explored systematically by the authors with the help of the computer algebra program MAGMA
Replaces NR1003109 In this article we shall restrict ourselves to a computer verification using the double coset enumerator of Bray and Curtis [2], which was written in the Magma accompanied by a sketch of the manual approach
arXiv:0910.5784v2 [quant-ph] 20 pages + 189 pages of raw data (also accessible in the source in plain text files); further algebraic solutions for d=11 and d=14 added
The corresponding dimensions of the irreducible representations can then be efficiently computed using computer algebras systems such as LiE [42] and MAGMA [43] via Weyl's dimension formula.
The cohomology ring of the real locus of the moduli space of stable curves of genus 0 with marked points
arXiv:math.AT/0507514. Acknowlege significant use in calculations.
The complete generating function for Gessel walks is algebraic
arXiv:0909.1965. The proof of A. Bostan and M. Kauers ...involves, among other tools, computer calculations using a powerful computer algebra system Magma, it required immense computational effort.
We record here that we have used the Magma[6] implementation of the small group database [5, 4] to calculate the connectedness and diameters of the commuting graphs for all groups of order at most 2000, except for the orders of the form k26 for k 6= 9, 4 composite.
unable to view
"MAGMA is used to calculate the $$-invariant measuring the discrepancy between the motivic and automorphic $p$-adic $L$-functions."
arXiv:1001.3438v1 [math.NT]. The values of sp and Pk^U0 L0(2k, ^_d)/L(2k, ^_d), can be calculated with MAGMA with high precision.
arXiv:0906.1934v2 [math.NT] We have implemented this procedure in MAGMA and used it on a large number of genus 2 curves with Jacobian of Mordell-Weil rank 1.
The primitive permutation groups of degree less than 4096
arXiv:0903.4137
Note that when m = 337, we were unable to find the generator and rank using MAGMA. This was found instead using SAGE
The vertices of a class of Specht modules and simple modules for symmetric groups in characteristic 2
https://www.minet.uni-jena.de/algebra/preprints/Danz/twopartchar2_final.pdf
Using Magma one can compute the zeta function of a variety. It is important to note that V is a singular variety in our case, and Magma actually computes the zeta function of the nonsingular modelof V
These theorems were found using the embedding algorithm of Glynn, implemented using a short program in MAGMA
Traces of the group law on the Kummer surface of a curve of genus $2$ in characteristic $2$
Available in Maple or Magma format on my web site http://perso.univ-rennes1.fr/sylvain.duquesne/articles/kummer2.
arXiv:0912.3405v2 [math.RA]. We also thank Emmanuel Kowalski who introduced us to Magma [2] with much patience
Unitary reflection groups for quantum fault tolerance
arXiv:0807.3650v2 [quant-ph]
Replaces NR1003069
Carls, R., and D. Lubicz. Magma implementation of the genus 1 point counting algorithm. (2007) preprint http://www.mathematik.uni-ulm.de/ReineMath/mitarbeiter/carls/.
A 3-local characterization of $M12$ and $SL3(3)$
arXiv:0810.2384
Both the Magma computer algebra system (version 2.14-15) and Victor Shoup's NTL library (version 5.4.2) use the Sch<C6>nhage Strassen algorithm for multiplication of dense polynomials in ZTxU when (roughly speaking) the coefficient size of the input polynomials (in bits) is larger than their degree
A classification of cubic $s$-regular graphs of order $14p$
Conder and Dobcsanyi classified the cubic s-regular graphs up to order 2048 with the help of the ``Low index normal subgroups'' routine in MAGMA system
A classification of cubic $s$-regular graphs of order $16p$
A classification of transitive ovoids, spreads, and $m$-systems of polar spaces
A complete classification of cubic symmetric graphs of girth 6
No mention of Magma in the article, however Marusic says in email it is used
A complete classification of ternary self-dual codes of length 24
arXiv:0804.0637v1
A computational approach to the 2-torsion structure of abelian threefolds
Used online calculator for calculations
The Magma Computational Algebra System for Algebra, Number Theory and Geometry, Version 2.12, University of Sydney, 2005.
A construction of the sporadic Suzuki graph from $U_3(4)$
verifying calculations
Using Magma the author has calculated the first few (+) reduced Hochschild homology groups of TL.(Z; 0)
replaces NR1003018
A deformation problem for Galois representations over imaginary quadratic fields
Replaces NR1001369
Replaces arXiv:0804.3447v1
arXiv:0803.0700v1
arXiv:0810.1176
A list of 4-valent 2-arc-transitive graphs and finite faithful amalgams of index $(4,2)$
Isomorphisms between the graphs (and their further properties, such as the girth, diameter etc.) were determined by use of Magma
Replaces NR1003064
Replaces NR1001454
replaces NR1001003
A note on commuting graphs for symmetric groups
Ref:An Introduction to Algebraic programming with Magma (draft) Springer-Verlag (1997)
I omit the details, which were verified using the Computational Algebra System Magma.
In fact Table 1 lists all possible triples for which (C2) holds. These were found using the Magma computational algebra system
Replaces NR1001445
We gratefully acknowledge the assistance of the Magma system in the investigations published here. Replaces NR1003 033
A refined classification of symmetric cubic graphs
PDF from Google Scholar. Cannon/Holt issue
We also used Magma [BCP97] to check some group theoretic claims and Maple to approximate integrals
A SAGBI basis for $ F[V 2V 2V 3]C p$
A Simple Scheme for Hierarchical Threshold Access Structures
No reference in text but cite in reference list
A study of pairing computation for curves with embedding degree $15$
Used for verification
A weighted module view of integral closures of affine domains of type I
Absolutely simple Prymians of trigonal curves
arXiv:0809.4887
"we will solve the system of polynomials for the key bits using the computer algebra software Magma" "The key bits, which are the solution of the system of polynomial equations, were obtained using the variety command of the powerful F4 Groubner Basis algorithm of the computer algebra software Magma"
eprint:2008:177. For instance, by switching from Singular to PolyBoRi for Attack-B, we were able to make the consistency check up to 60 times faster. We did not see any further speed improvement by using e.g. Magma 2.14
Algorithmic Algebraic Combinatorics and Gröbner Bases
Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory,designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGMA.
We found Magma very reliable: Replaces NR1003040
An algebraic model for chains on $ BG^_p$
An algorithm for Lang's Theorem
arXiv:math.GR/0506068
An infinite family of biquasiprimitive 2-arc transitive cubic graphs
An upper bound for the minimum weight of the dual codes of Desarguesian planes
Analyse numerique et reduction de reseaux
Analysis of the efficiency of the Chor--Rivest cryptosystem implementation in a safe-parameter range
A new set of parameters q and h, which prevent this cryptosystem against Vaudenay's attack is presented, and the computational aspects of its implementation in the Magma computational algebra system are analysed. We have presented a Magma implementation of this cryptosystem suitable for the set of these new paramaters in an efficient way
Conder and Dobcsny classified the cubic s-regular graphs up to order 2048 with the help of the ``Low index normal subgroups'' routine in MAGMA system. Replaces NR1003066
Arithmetic $E_8$ lattices with maximal Galois action
arXiv:0803.3063
arXiv:0707.0593
Automorphisms of cubic Cayley graphs of order $2pq$
Many calculations are performed by using the abstract algebra software Magma
Replaces NR1001426
Replaces NR1003045
Boneh-Boyen signatures and the Strong Diffie-Hellman problem
For comparison purposes, we also conducted trials of Pollard's lambda and Pollard's rho algorithms for discrete logarithms. Our implementation of Pollard's lambda algorithm was obtained by modifying the sdh-kangaroo program, and for Pollard's rho algorithm we used the optimized implementation included in the MAGMA Computer Algebra System based on Teske's work
Bounded distance decoding of linear error-correcting codes with Gröbner bases
Brauer pairs of Camina $p$-groups of nilpotence class 2
arXiv:0809.4695
Calabi-Yau Frobenius algebras
arXiv:math.RA/0710.3391v2
Certain classical groups are not well-defined
It was previously known that these groups are not well-defined, but this knowledge was not widespread. For example, Magma contains functions to produce certain of these groups.
CI-property of elementary abelian 3-groups
The coordinate matrices of these maps were later processed by the software Magma to obtain information on the autotopism group. Replaces NR1003046
Classification of ternary extremal self-dual codes of length 28
MINOR We begin by calculating the maximal orders RE using Kohel's [16] algorithm built into MAGMA
Codes from zero-divisors and units in group rings
arXiv:0710.5893v1
Replaces NR1003020
The paper is very well written (including an extensive bibliography) and the algorithm (implemented in Magma) can be requested from the author.
Commutator maps, measure preservation, and $T$-systems
In case q = 4, due to the J2-maximal subgroup, we used computer calculations. We calculated in MAGMA, using the 6-dimensional representation of G over GF(4), that G has connected conjugacy classes of elements of order 3 with the given centralizer structure.
Computation of $p$-units in ray class fields of real quadratic number fields
Our code was written in Magma. Some of the results of this paper can be found in a somewhat different form in the author's Ph.D thesis
Replaces NR1001415
We describe briefly how this fits into a large project to implement the results of Iskovskikh's programme in Magma.
Computational construction of irreducible $W$-graphs for types $E6$ and $E7$
Magma used for all calculations
Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves
"We did most of our computations of E(Q) using Sage via mwrank, but used Magma in a few cases, since it is currently the only software in existence that implements 3-descents and 4-descents (thanks to Michael Stoll, Tom Womack, Mark Watkins, Geoff Bailey and others"
Replaces NR1003102
Computer algebra in systems biology
arXiv:0712.4248 Symbolic Computation (cs.SC); Molecular Networks (q-bio.MN); Quantitative Methods (q-bio.QM)
Replaces NR1003032
The underlying algorithm is based on a method for extending a faithful representation of a Lie algebra g to a faithful representation of a semidirect product h g. It has been implemented in the library parts of the computer algebra systems GAP4 and Magma. arXiv:0807.2345v1 [math.RT], Replaces NR1003023
Replaces arXiv:math.NT/0802.0196v1]
Computing pairings using $x$-coordinates only
cryptoeprint:2008:019
arXiv.org:math/0610372. Replaces NR1000699
Computing the $l$-power torsion of an elliptic curve over a finite field
Computing the nonabelian tensor squares of polycyclic groups
Computing with root subgroups of twisted reductive groups
Submitted to J Alg
Congruences between modular forms and lowering the level mod $l^n$
arXiv:0801.0104v1
Constructing algebraic groups from their Lie algebras
arXiv:math/0612557
arXiv:0806.4916v1 [math.GR]. Replaces NR1003028
Construction Methods for Asymmetric Multiblock Space-Time Codes
http://magma.maths.usyd.edu.au/magma/htmlhelp/text835.htm#8121
MAJOR, The computer algebra system MAGMA is described in Cannon-Playoust [1].
we report on our implementation of the algorithm, publicly available in Magma. Replaces NR1003036
Convolutional codes from units in matrix and group rings
arXiv:cs.IT/0711.3629v1
Correction to MR2468473 above
Counting powers of words in monoids
Cox rings of degree one del Pezzo surfaces
arXiv:0803.0353
Cryptanalysis of an authentication scheme using truncated polynomials
Cryptanalysis of Stream Cipher Grain Family
I think they use results of others using Magma to state their case: "Furthermore, M. Afzal and A. Masood generated algebraic equations of Grain v1 and Grain-128 in Maple 10, and solved the nonlinear equations with Magma V 2.13-5."
Cryptanalysis of the Birational Permutation Signature Scheme over a Non-commutative Ring
We use the software Magma for our implementation, and the procedure of computing a Groebner basis in Magma is F4 algorithm proposed by Faugere et al
So instead of an enumeration of all 212 possible states of of H0, . . . , H7, S0, . . . , S3 for each x-configuration of f functions, this can be done more efficiently by using tools like MAGMA
All the steps of the attack have been implemented in the Magma computer algebra system and allowed to experimentally assess the results presented in this paper.
Cubes in products of terms in arithmetic progression
unable to access
Includes Magma Code in appendix
Even though this implementation is quite easy, it is not as fast as Magma. Hence, we present and compare two methods coded in Cython, to compute codes over finite rings of the form Zm (or in particularly the prime field Zp), in much less time. Both methods use space and time tradeoffs...... With these two methods presented, we can generate codes over finite rings, Zm, almost as efficient as Magma
Used to implement algorithms
Decomposing homogeneous modules of finite groups in characteristic zero
The norm equation algorithm in Magma yields such a solution within a second.
The author has implemented the algorithm in the programming language Magma, and executed it for degenerations of curves, surfaces and threefolds of various different degrees
Replaces NR1003047
Diamonds of Finite Type in Thin Lie Algebras
arXiv:math.RA/0511256. Refers to Havas et al (ANU p-quotient programme).
Replaces IACR eprint:2008:040
Efficient Arithmetic on Low-genus Curves
used Magma for verification
Elementary roots and admissible subsets of Coxeter groups
unable to access
We did the computations by using the package Automorphism group and isometry testing of MAGMA and the computation can be done at the web page MAGMA-Calculator.
arXiv:0802.0165v2. Replaces NR1001366
Elliptic points of the Picard modular group
arXiv:math/0703603,
Replaces NR1001446
Enhancing Undergraduate Mathematics Curriculum Via Coding Theory and Cryptography
Another aspect of the course was the use of the computer algebra system MAGMA.....There were several homework assignments where students needed to use the software....
arXiv:0901.1587v1 [math.NT]
We have implemented the Algorithm 5.4 in the computer algebra programming language Magma
*
Explicit n-descent on elliptic curves, II: Geometry
arXiv:math.NT/0611606
Factoring polynomials over global fields
arXiv:0909.5406
Fast arithmetic for triangular sets: from theory to practice
Comparison: "To evaluate the quality of our implementation of modular multiplication, we compared it with Magma v. 2-11"
Faster polynomial multiplication via multipoint Kronecker substitution
arXiv:0712.4046 "We describe an implementation of multiplication in (Z/nZ)[x] for a word-sized modulus n based on these methods, and compare its performance to that of NTL and Magma."
Fields of definition of building blocks
arXiv:0801.3434 The author and P. A. Brooksbank recently revisited the essential algorithms for *-rings introduced in Sections 4 and 5 [6, 7]. The resulting algorithms make greater use of fast module theory methods, improve the complexity of those sections, and are implemented for use in MAGMA
Reference in text; In these experiments, we made use of the computer package ``MAGMA'' (http://magma.maths.usyd.edu.au/magma) Replaces NR1003068
A short program in Magma confirms that Algorithm 4.4 yields only root systems
Finiteness of stationary configurations of the four-vortex problem
21. Computational Algebra Group, MAGMA, version 2.11.11, University of Sydney.
An alternative way of proving this result is to use the build-in MAGMA function Chabauty
Floating-Point LLL: Theoretical and Practical Aspects
arXiv:0801.2282v1
An algebraic computer language like Magma [4] can do this in an efficient way.
Frobenius-Schur indicators for subgroups and the Drinfeld double of Weyl groups
arXiv:math/0703681
Full-dimensional ab initio potential energy surface and vibrational configuration interaction calculations for vinyl
The polynomial [of k(k-1)/2 variables for the case of a k-body term] is restricted to be invariant under permutation of like nuclei and this property is built into the basis using procedures of computational invariant theory and with help from the Magma computer algebra system
Full-dimensional, ab initio potential energy and dipole moment surfaces for water
The polynomial p(y) is a function of k(k-1)/2 variables for the k-atom terms and is expanded on a basis of permutationally invariant polynomials following procedures of computational invariant theory and the MAGMA computer algebra system
Submitted to Combinatoria
Further improvements on the designed minimum distance of algebraic geometry codes
The groups in Theorems 1, 2, 4 and Example 4.4 were found using Magma [12]. Bosma, W., Cannon, J. (1994). MAGMA. University of Sydney.
Galois sections for abelianized fundamental groups
arXiv:0808.2556v1
Generic one-parameter versal unfoldings of symmetric Hamiltonian systems in $1:1$ resonance
Genus 2 curves that admit a degree 5 map to an elliptic curve
Remark 8. The reader who is interested in such equations can use any computational algebra package such as Maple, Magma etc and eliminate u, v via resultants.We used Maple 9 and computations sometimes took several days.
Genus two curves with quaternionic multiplication and modular Jacobian
By the algebra software Magma, we can easily get the set of all 6-cliques.
Graphs, designs and codes related to the $n$-cube
The source code of our routines and detailed output from many calculations are posted on the second author's webpage at http://www.math.uga.edu/~davids/gs/gs.html.
Not intended for publication. Dates from 1999
Replaces NR1003060
arXiv:math/0702182. Replaces NR1001396
Hamiltonian cycles in cubic Cayley graphs: The <2, 4k, 3> case
No mention of magma in article
Handbook of Floating-point Arithmetic
Hexavalent half-arc-transitive graphs of order $4p$
In section 5 we present some numerical explorations with times of execution of the algorithm in comparison with the standard procedures to get a p-integral basis of PARI, MAGMA and SAGE.
Homogeneous factorisations of complete graphs with edge-transitive factors
Implementing cryptographic pairings: A Magma tutorial
In this paper we show an efficient implementation of the Tate, ate and R-ate pairings in magma. This will be demonstrated by using the KSS curves with embedding degree k = 18.
Improving the lower bounds on inequivalent Hadamard matrices through orthogonal designs and meta-programming techniques
We implemented a Maple package containing the necessary constructions for the generation of Hadamard matrices from sequences with zero autocorrelation in Maple, in order to achieve the best possible exibility in terms of portability with other Computational Algebra Systems, such as Magma. We finally used Magma to automatically perform the searches for inequivalent Hadamard matrices.
Isogenies and the discrete logarithm problem in Jacobians of genus $3$ hyperelliptic curves
arXiv:0905.1318v1 [math.GT]
Letterplace ideals and non-commutative Gröbner bases
we compare an experimental implementation in the computer algebra system Singular with four of the best implementations of non-commutative Groebner bases, namely the ones of Bergman, GAP, Magma and Opal
Linearizing torsion classes in the Picard group of algebraic curves over finite fields
arXiv:math.NT/0706.0272v1
To classify locally 2-arc-transitive graphs for a given group G requires knowledge of the conjugacy classes of its subgroups. The classification can be most accurately performed by machine. We have developed software in Magma for this task. Replaces NR1003037
Maximal integral point sets in affine planes over finite fields
computations
replaces NR1003034
Minimum words of codes from affine planes
The computer systems Magma and Sage include packages programmed by William Stein that are able to perform many explicit computations with those objects.... From the computational point of view, Magma includes some functions providing information about the decomposition over number fields (see [14]) but there is still a lot of work to be done, including the need of new theoretical results, compared with what is known and implemented for varieties over Q.
We have experimentally confirmed the correctness and efficiency of our attacks and algorithms with the computer algebra system Magma
arXiv:0802.2651v1. Replaces NR1001382
Multiplicity-free representations of symmetric groups
The predicted list of subgroups has been checked using the computer algebra package Magma
New developments in the theory of Gröbner bases and applications to formal verification
compared SINGULAR to Magma for computing Groebner bases
Replaces NR1003062 Comparison of the implementations of Noether normalization algorithms accessible to the author at the time of writing. Singular, Macauley, Maple
Non-associative Gröbner bases, finitely-presented Lie rings and the Engel condition: II
Also uses the monoid def of magma
Non-hyperelliptic modular Jacobians of dimension 3
arXiv:0907.2060. We perform an exhaustive computation in Magma
Nonisomorphic Verdier octahedra on the same base
arXiv:0708.0151v2
All computations done using Magma. They would also like to thank the Magma group at the University of Sydney for their continued hospitality and especially Steve Donnelly for his assistance.
Nontrivial elements of Sha explained through $K3$ surfaces
**
Normalizers of $p$-subgroups in finite groups
Ref:An Introduction to Algebraic programming with Magma (draft) Springer-Verlag (1997)
Computations using Magma code
On $m$-regular systems on $H(5,q2)$
Our search for examples was substantially assisted by computer calculations using Magma.
On a $_4,K_2,2,2$-ultrahomogeneous graph.
arXiv:0704.1493v3: version v1 cited Magma; v3 doesnt
On a certain algebra of higher modular forms
On a class of Diophantine equations related to the numbers of cells in hyperplane arrangements
One can solve the corresponding diophantine equations by subroutine IntegralPoints and IntegralQuartic Points of the program package MAGMA
Replaces NR1001006
We give some details of the computation, since it is outside the scope of the functionality that is currently provided by MAGMA (or any other software package).
On apartments in incidence geometry
Can't access content. Submitted for publication
On circulant self-dual codes over small fields
On circulant self-dual codes over small fields
Separate section in references for Software [MAGMA] MAGMA high performance software for Algebra, Number Theory, and Geometry, ver. 2.13., http://magma.maths.usyd.edu.au/.
The proof uses commutator computations guided by, but not depending on, details of p-quotient computations which were done with Magma: Replaces NR1003039
On complementary-dual quasi-cyclic codes
Replaces NR1003103
On counterexamples to the Hughes conjecture
On deciding finiteness of matrix groups
The authors are grateful to Professor Eamonn O'Brien, who recently implemented IsFiniteMat- GroupFuncNF in Magma,
On equal sums of ninth powers
All computations were performed with Magma
LOOK at hard factorisation done by pari rather than magma. The proof of the above lemmas is a straightforward computation, that has been done by using Magma and Sage. All the sources are available from the second author web page.
On generalized Paley graphs and their automorphism groups
arXiv:math/0605252
On Kostant's theorem for Lie algebra cohomology
The following low rank examples were calculated using our computer package developed in Magma.
On modular symbols and the cohomology of Hecke triangle surfaces
arXiv:math.NT/0511113
On symmetries of Cayley graphs and the graphs underlying regular maps
In this section, we give some examples of Hilbert-Siegel eigensystems for F = Q(p2). (We obtained them with a preliminary version of our algorithm, which we implemented in Magma [2].)
On the densest MIMO lattices from cyclic division algebras
arXiv:cs/0703052
On the depth of invariant rings of infinite groups
arXiv:0711.4740v1
Replaces NR1001417
The authors make extensive use of the relevant MAGMA routines. These routines, however, are based on quite a sophisticated theoretical background and some readers of the paper might probably wonder where to find the relevant theory. Unfortunately, in contrast with most other cases, MAGMA's handbook does not give any bibliographical reference concerning these specific routines and, quite unhappily, this lack of reference is present in this paper (and in many other recent papers, as well).
LatCde: Replaces NR1001459
On the groups of some fibered spaces
unable to access
On the index of congruence subgroups of $Aut(Fn)$
arXiv:0804.2578v1
On the multiplication of some semifields of order $q^6$
In fact, a quick calculation with the software MAGMA reveals that the ranks of E1785, E5865 and E161 are equal to 2.
arXiv:0805.1909v1. Replaces NR1001372
On vertices of completely spittable modules for symmetric groups and simple modules labelled by two part partitions
Our computations in Section 5 were carried out using the computer algebra system Magma
One-matching bi-Cayley graphs over abelian groups
computation and ? secondary reference "Using Magma [2], a direct check over all possible graphs"
We conclude this section by two remarks. First we note that our simple heuristic algorithm works so well is very probably due to the fact that the systems of fundamental units provided e.g. by Magma are already LLL-reduced, hence the initial system is "closely" optimal.
Parametrizing Del Pezzo surfaces of degree 8 using Lie algebras
arXiv:math.AG/05012477
Partial permutation decoding of some binary codes from graphs on triples
Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications
These experiments were performed using Magma with its implementation of the Gr?=obner basis algorithm F4 for solving the reduced polynomial systems
All computations in this paper were performed using the computer packages Magma: Replaces NR1003031
LOOK. Replaces NR1003074
Photochemical reactions of the low-lying excited states of formaldehyde: $ T1/S0 $ intersystem crossings, characteristics of the S1 and T1 potential energy surfaces, and a global T1 potential energy surface
The permutation invariant basis functions were constructed for a whole family of molecular systems (now almost all systems of at most nine atoms and any partition into identical ones) using the procedures developed by Kemper and co-workers and incorporated in the MAGMA computer algebra system
PolyBoRi: A framework for Gröbner-basis computations with Boolean polynomials
We compared the following system releases with the development version of PolyBoRi's symmgbGF2 Maple 11.01, June 2007 Gr<C6>bner package, default options FGb 1.34, Oct. 2006 via Maple 11.01, command: fgb_gbasis Magma 2.13-10, Feb. 2007 command: GroebnerBasis, default options Singular 3-0-3, May 2007 std, option(redTail) Currently PolyBoRi's implementation is less advanced than the corresponding Magma procedures.
arXiv:0912.3387v1 [math.AG]
PDF from Google Scholar search
Primitive divisors on twists of Fermat's cubic
arXiv:math/0703553
PRINT. The computer algebra package Magma [BCP97] is used in an essential way throughout. We have written MAGMA code (available at http://www.math.berkeley.edu/~brownda/) which takes as input an elliptic curve E and a prime p and returns, for each residue class Ri, a factorization
Replaces NR1003015. "Experimentation with MAGMA and Maple was also vital to this work."
Proposal of PPS Multivariate Public Key Cryptosystems
We perform the experiments using the computational algebra system Magma.
Quasi-quadratic elliptic curve point counting using rigid cohomology
arXiv:math/0701850
Reduction of the Hall-Paige conjecture to sporadic simple groups
Subsequently, Derek Holt suggested an alternative method for finding normal subgroups of finite index in a finitely-presented group, based on construction of a composition series for the quotient. This suggestion was taken up by his PhD student, David Firth, and reported in his PhD thesis [7] and has been implemented as a new procedure (called LowIndexNormalSubgroups) in the computational algebra system Magma [2]. This new method works for index up to 100,000, and much faster than the one used for [4], In August 2006 the author of this paper used the new procedure in Magma to determine all regular and orientably-regular maps of Euler characteristic to inclusive,
A thesis presented in partial fulfillment of criteria for Honors in Mathematics: In the first section of this senior thesis the author provides some new efficient algorithms for calculating with finite permutation groups.
Representing sets with sums of triangular numbers
Unable to view article
Replaces NR1001292
Sequences of words characterizing finite solvable groups
Shimura curves of genus at most two
Magma was used. Author gives Magma Group as affiliation but forgot to cite Magma as such. See letter in Voight mail folder. "The author wishes to thank ... the Magma group at the University of Sydney for their hospitality"
Simple modules for groups with abelian Sylow 2-subgroups are algebraic
arXiv:0801.2665v1
Solvability of generalized monomial groups
unable to access
In each case the characters, and if possible the maximal overgroups of the chosen elements, were taken from [4] and checked with the computer programs GAP and/or MAGMA.
Replaces NR1001381
The results are mostly computational, using Magma
Sparse Boolean equations and circuit lattices
Magma is mentioned in a discussion, but I dont think they used Magma: "It was found in [15] that a linear algebra variant(called MRHS) of the Agreeing-Gluing signicantly overcomes(on AES type Boolean equations in around 50 variables) F4 method, a Grobner Basis Algorithm implemented in Magma
**
Strongly regular tri-Cayley graphs
Acknowledgement. ... All computations made in the preparation of this manuscript were accomplished using Magma.
For example, it takes only a few seconds of computer time using the software Magma and its SmallGroups database to determine
Symmetric representation of the elements of the Conway group $0$
implemented algorithm
Ten new primitive binary trinomials
The authors thank Allan Steel, who independently verified (with Magma) the ten new primitive trinomials, and the authors of the Magma and NTL software tools that were used to check reducibility of the other trinomials
[3] J. Cannon, A. Steel, G. White, Linear codes over finite fields, in: J. Cannon, W. Bosma (Eds.), Handbook of Magma Functions, pp. 3951-4023. Replaces NR1001276
arXiv:0906.2848v2 [math.NT] The present authors use a combination of Schiemann's software, scripts in a language called Magma, and C++ code written by the second author
Replaces NR1003059
Tetravalent one-regular graphs of order $2pq$
The origin of this paper lies in computational work done to test integer factorization routines for the computer algebra system Magma
The Application of Polynomials over the Field of Two Elements to a problem in Intellectual Property
For computations."Also, the F4s Algorithm of Jean-Charles Faugere implemented in MAGMA is a common tool for this task."
"one could easily write a computer program - in some suitable computer algebra language, like Magma (Bosma et al., 1997"...) and "It is a straightforward exercise to translate all this analysis into a Magma language set of instructions.."
Conjecture 6. If $G_n(m,k)$ is perfect then either $m 2k n$ and $(n / (n,m,k), 6) = 1$ or $k0$ or $m n$. Conjecture 6 was verified using MAGMA for $n 200$.
Times are compared with the implementation of Leon's algorithm in the computer algebra system Magma
The Certicom Challenges ECC2-X
could not access
arXiv:0811.3544. Replaces NR1003077
The distance between superspecial abelian varieties with real multiplication
We prove this proposition by computation. The basic idea is as follows: we type in the 35 simple binomial relations and the relations into the computer algebra system Magma (see [BCP]). We then take the ideal these relations generate, compute the quotient ring, and verify that it is a free Z-module of the correct rank in degrees two, three, and four.
The FGLM Problem and Möller's Algorithm on Zero-dimensional Ideals
Replaces arXiv:math.AG/0512597
The Gauss higher relative class number problem
arXiv:0806.0306v1 [math.NT]
The Markov chain Monte Carlo revolution
Using Magma, we counted the number of solutions to F(x,y) = 1 for a set of forms F
The nonexistence of certain representations of the absolute Galois group of quadratic fields
He is a PhD student of Nigel Boston
The rank of the endomorphism monoid of a uniform partition
arXiv:0807.1214v1
The strongly distance-balanced property of the generalized Petersen graphs
No mention of magma in article
The trivial intersection problem for characters of principal indecomposable modules
Using the computer algebra system MAGMA, E. O Brien proved that M contains the trivial module 7 times as a composition factor.
The vanishing-off subgroup
arXiv:0806.2135v2; "Many of the examples we present were found using the small groups library in MAGMA"; Magma used for computations
The varieties for some Specht modules
uses other calculations "the software MAGMA was used by Jon Carlson to determine the rank variety"
The vertices and sources of the basic spin module for the symmetric group in characteristic 2
Towards an efficient Meat-axe algorithm using $f$-cyclic matrices: The density of uncyclic matrices in M$(n,q)$
For computation and verification
Uniform bounds on pre-images under quadratic dynamical systems
arXiv:0805.0441v1 [math.NT]
Unimodular lattices in dimensions 14 and 15 over the Eisenstein integers
Vector Bundles Near Negative Curves: Moduli and Local Euler Characteristic
A passing reference: "Now, one can use any computer algebra package (e.g., Macaulay 2 , Maple, Magma, to compute.." Does not specify they used Magma as such, and doesn't cite
Most of our results are due to calculations with the computer algebra system Magma: Replaces NR1003043
arXiv:0807.2079. Replaces NR1003017
$Li(p)$-service? An algorithm for computing $p$-adic polyalgorithms
$Q$-rational cycles for degree-2 rational maps having an automorphism
A $3$-local identification of the alternating group of degree 8, the McLaughlin simple group and their automorphism groups
A classification of subgroups of the Monster isomorphic to $S4$ and an application
A commutator description of the solvable radical of a finite group
***, arXiv:math/0610983
A complete span of $ H(4,4)$ admitting $PSL2(11)$ and related structures
A concise proof of the Kronecker polynomial system solver from scratch
A generalization of Voronoi's reduction theory and its application
arXiv:math.MG/06001084
Magma Computational Algebra System v2.13
A Gilbert-Varshamov type bound for Euclidean packings
[5] J. Cannon et al., The Magma Computational Algebra System for Algebra, Number Theory and Geometry, published electronically at http://magma.maths.usyd.edu.au/magma/.
A lower regulator bound for number fields
A method for efficiently computing the number of codewords of fixed weights in linear codes
[11] Computational Algebra Group at the University of Sydney, The Magma Computational Algebra System
Replaces NR1000038
A Multi-level Blocking Distinct Degree Factorization Algorithm
This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007
A New Construction of Multivariate Public Key Encryption Scheme through Internally Perturbed Plus
A new Petrie-like construction for abstract polytopes
? Sent by Leemans. Could not view to get details.
A one-time signature using run-length encoding
Such a database is available in the MAGMA Computational Algebra System and its Small Groups Library ([8]), and therefore Theorem F could be verified using this system alone.
A volume maximizing canonical surface in 3-space
Abelian varieties with prescribed embedding degree
arXiv:0802.1886v1 [math.NT]
Replaces NR1001400
AG Codes from Polyhedral Divisors
Algebraic attack on HFE revisited
Algebraic Attacks on the Courtois Toy Cipher
To perform these experiments, most of the algorithms presented in this article had to be implemented first. Even though for example MAGMA provides a very fast implementation of F4 (See Section 4.1) and for example Toon Segers has implemented F4 in MAGMA and provides the source code of his implementation, no true general purpose and fully functional open-source implementation exists (see section 4.1 for details). "True open source" in this context means an implementation which does not rely on proprietary software like MAGMA to perform any part of the algorithm....... The only fully functional and fast open-source implementation of F4 I am aware of is called "hotaru" or IPA-SMW and is provided under a BSD-style license by Mitsunari Shigeo. It is limited to the quotient ring,??? and seems to be hardly recognized outside Japan. But the author claims that it is faster than MAGMA in this ring and it was used to break Toyocrypt.
Algebraic Cryptanalysis of Curry and Flurry using Correlated Messages
The practical results obtained in [10] using FGLM. The authors have used the version available in Magma (version 2.11-8).
Algebraic Cryptanalysis of MQQ Public Key Cryptosystem by MutantXL
Algorithms for computations in local symmetric spaces
Algorithms for computing with nilpotent matrix groups over infinite domains
An Algebraic Approach for Proving Data Correctness in Arithmetic Data Paths
An explicit integral polynomial whose splitting field has Galois group $W(E_8)$
An extremal doubly even self-dual code of length 112
An introduction to computing modular forms using modular symbols
In the last two sections, the author presents some results and conclusions concerning the practical implementation of his algorithm. In this way, his implementation in the computer algebra system Magma works efficiently for the first few levels of the tower, but as he goes on further the running time gets very long and the computed functions become highly complex (meaning that they have thousands of terms).
An unusual decomposition of a complete 7-partite graph of order 28
An upper bound for the lower central series quotients of a free associative algebra
Representation Theory (math.RT)
Analyzing the Galbraith-Lin-Scott point multiplication method for elliptic curves over binary fields
The Magma package,running on a 1 GHz Sun V440, can compute the order of a randomly selected elliptic curve over F2254 is about 0.42 seconds. Thus, performing the explicit check would require about 1305 days of CPU time, a feasible task since it can be easily parallelized.
Another existence and uniqueness proof of the Tits group
Can't access content
IACR eprint::2007:256
Attacking Bivium Using SAT Solvers
Automata presenting structures: a survey of the finite string case
Can't access content
Replaces NR1001443
Automorphisms with finite Reidemeister number in residually finite groups
Base sizes for sporadic simple groups
Behind and beyond a theorem on groups related to trivalent graphs
Binary self-dual codes with automorphisms of order 23
Bundles, presemifields and nonlinear functions
Character values and decomposition matrices of symmetric groups
arXiv:math.RT/0610414
Class Field Theoretic Methods in the Design of Lattice Signal Constellations
Criticised memory considerations for maximal order calculations
Classic and Quantum Error Correcting Codes
Combinatorial and computational group-theoretic methods in the study of graphs, maps and polytopes with maximal symmetry
Combinatorial Diophantine equations---the genus 1 case
The equations are reduced to genus 1 equations or Mordell-type equations and solved with the so-called El-log method of Stroeker and Tzanakis and with the Magma computational algebra system.Could not read paper to check NREFS, only viewed abstract and ref list
Combinatorial method in the coset enumeration of symmetrically generated groups
"We present the input and output as they appear in Magma 2" ... "We have tried to introduce the coset enumeration in a way such that the interested reader can perform simple enumerations manually. The computer implementation, however, contains a more detailed description, which is omitted here for the sake of brevity. It, although written in Magma 2, can be readily written in any high-level language such as C++, so that the performance in terms of times can be improved"
Combinatorics of Maass-Shimura operators
Commutative presemifields and semifields
Computation in Coxeter groups. II. Constructing minimal roots
Critical of time to calculate minimal root reflection table.
Computation of 2-groups of positive classes of exceptional number fields
Calc used. They misspelt Cannon Canon
Computing a chief series and the soluble radical of a matrix group over a finite field
Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields
Computing Arakelov class groups
arXiv:0801.3835v1 [math.NT]
Computing endomorphism rings of Jacobians of genus 2 curves over finite fields
***, arXiv:math/0701305
Computing Equiangular Lines in Complex Space
Computing generators of free modules over orders in group algebras
Replaces NR1001329
Computing L-Series of Hyperelliptic Curves
ZZZ 14 pages, to appear in the Proceedings of ANTS VIII (2008)
Computing minimal polynomials of matrices
Computing the height of volcanoes of $l$-isogenies of elliptic curves over finite fields
Misspelt Cannon Canon
Computing Zeta Functions in Families of $C_a, b$ Curves Using Deformation
Connectivity of the product replacement graph of simple groups of bounded Lie rank
*Minor*
Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
[10] MAGMA Group: MAGMA Computational Algebra System, http://magma.maths.usyd.edu.au
Constructing the group preserving a system of forms
Construction of global function fields from linear codes and vice versa
Construction of hyperelliptic function fields of high three-rank
Construction of self-dual codes over finite rings $Zpm$
Constructions for chiral polytopes
submitted for publication
Constructions of small complete arcs with prescribed symmetry
Constructive and Destructive Use of Compilers in Elliptic Curve Cryptography
Constructive membership in black-box groups
Cryptanalysis of an Authentication Scheme Using Truncated Polynomials
An attack on a recently proposed authentication scheme of Shpilrain and Ushakov is presented. The public information allows the derivation of a system of polynomial equations for the secret key bits. Our attack uses simple elimination techniques to distill linear equations. For the proposed parameter choice, the attack often finds secret keys or alternative secret keys within minutes with moderate resources
Cryptanalysis of MinRank
Cryptanalysis of the TRMS Signature Scheme of PKC'05
Homepage listed as footnote
Curve parametrization over optimal field extensions exploiting the Newton polygon
Can't access content.
Cycles of covers
Cyclic polygons with rational sides and area
Cyclic quasi-symmetric designs and self-orthogonal codes of length 63
Cannon, J.J., 1997. An Introduction to Algebraic Programming with Magma. Springer, Be rlin.
Deciding existence of rational points on curves: an experiment
arXiv:math.NT/0604524
arXiv:cs.SC/0601133. "A Steel has reported on similar efforts [towards effective reduction] within his implementation of some Magma routines."
Derived arithmetic Fuchsian groups of genus two
arXiv:0803.1519v1
Descent via isogeny on elliptic curves with large rational torsion subgroups
Designs from subcode supports of linear codes
Dickson Polynomial Permutations
Dihedral side extensions and class groups
Distinguishing contragredient Galois representations in characteristic two
ZZZ
ECM using Edwards curves
According to Magm this curve has exactly the eight points ...
IACR eprint:2008:250
Efficiently Computable Distortion Maps for Supersingular Curves
Examples of 3-dimensional 1-cohomology for absolutely irreducible modules of finite simple groups
[6] J. J. Cannon et al . The Magma programming language, Version 2.11. School of Mathematics and Statistics, University of Sydney (2004).
Examples of rank 3 product action transitive decompositions
Explicit $n$-descent on elliptic curves. I. Algebra
Explicit calculations of automorphic forms for definite unitary groups
Replaces NR1001316
Extractors for binary elliptic curves
Fast addition on non-hyperelliptic genus 3 curves
Magma used in calculations.
Fast constructive recognition of black box symplectic groups
Fast separable factorization and applications
Filtrations in semisimple Lie algebras. II
Finding rational points on elliptic curves using 6-descent and 12-descent
ZZZ
Finite field experiments
Finite Field Experiments (with an Appendix by Stefan Wiedmann)
Most of the computations are carried out using the computer algebra systems GAP and MAGMA.
Frobenius polynomials for Calabi-Yau equations
arXiv:0802.3994v2
Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface
As in our earlier work, we relied on invariant theory and the MAGMA computer algebra system to construct a basis for the space of invariant polynomials.
Further properties of a function of Ogg and Ligozat
Fusions of character tables and Schur rings of abelian groups
Bosma and Cannon, MAGMA, 1994
Group theory for quantum gates and quantum coherence
arXiv:0803.1911v2
Gröbner bases and Diophantine analysis
Hamiltonicity of vertex-transitive graphs of order $4p$
arXiv:math.CO/0606585
Hauteur asymptotique des points de Heegner
High-Performance Symbolic Computation in a Hybrid Compiled-Interpreted Programming Environment
We investigate the integration of C implementation of fast arithmetic operations into MAPLE, focusing on triangular decomposition algorithms. We show substantial improvements over existing MAPLE implementations; our code also outperforms MAGMA on many examples
Higher-dimensional 3-adic CM construction
arXiv:math/0607583
Homogeneous factorisations of Johnson graphs
arXiv:math.AT/0709.3489v2
Improved Results on Algebraic Cryptanalysis of A5/2
Can't access content
Incompleteness of the Giulietti-Ughi arc for large primes
Index calculus in class groups of non-hyperelliptic curves of genus three
Infinite classes of dihedral snarks
Integral points on hyperelliptic curves
arXiv:math.NT/0801.4459v1
Involution graphs where the product of two adjacent vertices has order three
Irregular and Singular Loci of Commuting Varieties
arXiv:0801.3074v1
Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
IACR eprint:2007:428
Joint moments of derivatives of characteristic polynomials
K3 Surfaces of Picard Rank One and Degree Two
Kernel Dimension for Some Families of Quaternary Reed-Muller Codes
4. Pernas, J., Pujol, J., Villanueva, M.: Codes over Z4. A Magma package. Universitat Aut`onoma de Barcelona (2008), http://www.ccg.uab.cat
Key Recovery on Hidden Monomial Multivariate Schemes
Kipnis-Shamir Attack on HFE Revisited
Kloosterman sums, elliptic curves, and irreducible polynomials with prescribed trace and norm
arXiv:0706.2112
Local torsion on elliptic curves and the deformation theory of Galois representations
arXiv:math/0701882
Maximal Orders in Space-Time Coding: Construction and Decoding
LatCde
USYD Thus as before finding a minimal permutation representation reduces to simply searching through the subgroup lattice for core-free subgroups and selecting the one of minimal index. The LowIndexSubgroups command in magma returns that the smallest such index is 120, thus proving xx = 120.
Minimum Lee weights of type II codes over $F 2 r$
Mod $4$ Galois representations and elliptic curves
Modular forms
The final chapter discusses the computational aspects of modular forms. Most of the first half of the chapter is spent on three software packages: MAGMA, SAGE, and PARI. Each discussion is illustrated with examples of how the software is called and what results look like. Also, the pros and cons of each software package are discussed. The second half of the chapter talks about computation in general as it relates to modular forms.
Montgomery Ladder for All Genus 2 Curves in Characteristic 2
MULTIMODE quantum calculations of intramolecular vibrational energies of the water dimer and trimer using ab initio-based potential energy surfaces
We use the permutation symmetry group of degree 6!3! to define the space of invariant polynomials, and the MAGMA computer algebra system was employed to help generate the basis.
MXL2: Solving polynomial equations over GF$(2)$ using an improved mutant strategy
Magma
New $[47,15,16]$ linear binary block code
New Differential-Algebraic Attacks and Reparametrization of Rainbow
New families of quadratic almost perfect nonlinear trinomials and multinomials
Nilpotent Groups: Explicit Examples
Non-Euclidean Pythagorean triples, a problem of Euler, and rational points on $K3$ surfaces
arXiv:math.NT/0606700
Nonlinear piece-in-hand matrix method for enhancing security of multivariate public key cryptosystems
Normal Forms, K3 Surface Moduli, and Modular Parametrizations
Note on the paper: ``An extension of a theorem of Euler'' by N. Hirata-Kohno, S. Laishram, T. N. Shorey and R. Tijdeman
Bruin's routines related to the elliptic Chabauty method are contained in Magma
Obtaining and solving systems of equations in key variables only for the small variants of AES
We could not perform necessary reductions with F4 implementation in Magma. We tried NormalForm, Reduce, ReduceGroebnerBasis both with and without field equations. The reduction was done with respect to lex ordering.PolyBoRi- and Magma-examples together with the running scripts can be downloaded from http://www.mathematik.uni-kl.de/~bulygin/en/files.html
Odd-Char Multivariate Hidden Field Equations
Switching to odd characteristics in HFE-like schemes affects how an attacker can make use of field equations. Extensive empirical tests (using magma-2.14, the best commercially available F4 implementation) suggests that our new construction is indeed secure against algebraic attacks using Groebner Basis algorithms
On 2-Fold Covers of Graphs
arXiv:math.CO/0701722
On a conjecture of Serre on abelian threefolds
On a Diophantine Equation of Stroeker
Accepted for publication
VERIFY -- not yet viewed
On Atkin and Swinnerton-Dyer congruence relations (II)
arXiv:math.NT/0512614
**
On computing the subgroup lattice of O'N
On double circulant doubly even self-dual $[72,36,12]$ codes and their neighbors
Can't access content
On Elkies subgroups of $l$-torsion points in elliptic curves defined over a finite field
arXiv:0809.2774
On Galois groups of unramified pro-$p$ extensions
On mod $p$ modular representations which are defined over $F_p$
arXiv:math/0606052
On Prime-Order Elliptic Curves with Embedding Degrees k=3,4, and 6
On projective linear groups over finite fields as Galois groups over the rational numbers
arXiv:math/0606732
Replaces NR1001404
On rational embeddings of curves in the second Garcia-Stichtenoth tower
On self-dual codes over $F5$
On skew-Hadamard matrices
When we apply the Magma software ver.2.10-17 we have found 9 more inequivalent matrices. These matrices are also given in the web page http://www.math.ntua.gr/people/ckoukouv/en_index.html
On some double circulant binary extended quadratic residue codes
On some questions about a family of cyclically presented groups
On the classification of APN functions up to dimension five
On the Classification of Solvable Lie Algebras of Finite Dimension Containing an Abelian Ideal of Codimension One
On the computation of the Cassels pairing for certain Kolyvagin classes in the Shafarevich-Tate group
On the connection between Kloosterman sums and elliptic curves
On the decomposition of rational functions
Cannon, John, Playoust, Catherine, 2007. Algebraic Programming with Magma I An Introduction to the Magma Language
On the Diophantine equation $x2+5a13b=yn$
Replaces NR1001255
On the Diophantine equation $x^2+C=2y^n$
On the equation $Y2=X5+k$
Can't access content
arXiv:math.NT/0612317
On the irreducibility of Hecke polynomials
On the lower central series of an associative algebra (with an appendix by Pavel Etingof)
"We also thank Prof. Ju-Lee Kim for many useful discussions and Jennifer Balakrishnan for much help with the software Magma."
On the moduli space of pointed algebraic curves of low genus. II. Rationality
Can't access content
On the non-existence of exceptional automorphisms on Shimura curves
arXiv:0804.4276v2
On the number of solutions of Goormaghtigh equation for given $x$ and $y$
computations
On the periodicity of Coxeter transformations and the non-negativity of their Euler forms
On the slopes of the $U5$ operator acting on overconvergent modular forms
arXiv:math/0606363
On vertices of simple modules for symmetric groups of small degrees
On: ``$(1-u)$-cyclic codes over $ Fpk+u Fpk$''
Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
Order-Theoretic Methods for Space-Time Coding: Symmetric and Asymmetric Designs
Pairings on hyperelliptic curves with a real model
Pairings on Hyperelliptic Curves with a Real Model
Partial permutation decoding for codes from affine geometry designs
PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of $PG(5,2)$
Permutation decoding for binary codes from lattice graphs
Point counting in families of hyperelliptic curves
arXiv:math.NT/0601438
Polarization of separating invariants
"We also note that the computer algbera system Magma stores relation as written: it does not introduce new relations unless asked."
Primitive decompositions of Johnson graphs
arXiv:0804.2181
Ranks of elliptic curves over function fields
Rational 6-cycles under iteration of quadratic polynomials
arXiv:0803.2836v1
Rational tetrahedra with edges in geometric progression
Recognition of small dimensional representations of general linear groups
Regular hypermaps over projective linear groups
REMART
Remarks on the Attack of Fouque et al. against the lIC Scheme
Residually weakly primitive and locally two-transitive geometries for sporadic groups
Acad. roy. Belgique, Mem. Cl. Sci., Coll. 4, Ser. 3, Tome XI(2008), 173pp
Root numbers of elliptic curves in residue characteristic 2
Search techniques for root-unitary polynomials
arXiv:math/0608104
Secret sharing schemes based on self-dual codes
Self-orthogonal designs and codes from the symplectic groups $S4(3)$ and $S4(4)$
Shimura Curve Computations Via K3 Surfaces of Neron-Severi Rank at Least 19
arXiv:0802.1301v1 [math.NT]
Short two-variable identities for finite groups
Used for computations
arXiv:math.AG/0608015
Skew codes of prescribed distance or rank
Skew constacyclic codes over Galois rings
Skew Hadamard Designs and Their Codes
Software Integrity Checking Expressions (ICEs) for Robust Tamper Detection
Solutions of the Diophantine equation $xy+yz+zx=n!$
Solving multiple right hand sides linear equations
eprint:2007:285
Some heuristics about elliptic curves
arXiv:math.NT/0608766
He also describes a method for computing small representatives of Selmer group elements from large ones. The method is based on an analysis of the groups $K(S,n)$ and the LLL algorithm. Finally, he gives a test for equivalence of $4$-coverings that generalizes the known tests for $2$-coverings and $3$-coverings. The test is implemented in the case $K=Q$ using Magma.
Some inequalities for the order of the Schur multiplier of a pair of groups
Example: "Then using Magma, Algebraic Programming Language, the Schur multiplier M(G, N) turns out to be an elementary abelian 3-group of order 27"
Some irreducible codes invariant under the Janko group, J1 or J2
Speeding-up lattice reduction with random projections (extended abstract)
Squares in products in arithmetic progression with at most one term omitted and common difference a prime power
To exclude certain cases for $k=7$ the problem is reduced to the computation of integral points on some quartic equations, as well as on some elliptic curves where the elliptic Chabauty method is used; subsequently both cases are handled with the help of the computer algebra system MAGMA. The remaining arguments are elementary and tedious.
Replaces NR1001423
We present a black box algorithm...The algorithms have been implemented in the computer algebra system Magma.
Supersingular genus-2 curves over fields of characteristic 3
arXiv:math.NT/0604413
Replaces NR1001401
The Alperin weight conjecture and Dade's conjecture for the simple group $Fi24'$
Procedures implemented as routine in Magma. Routines and transcripts available from http://www.cecm.sfu.ca/$$nbruin/eq239
The Brauer-Manin obstruction on del Pezzo surfaces of degree 2 branched along a plane section of a Kummer surface
[22] J. CANNON ET AL. MAGMA software. http://magma.maths.usyd.edu.au.
The classification of $p$-compact groups for $p$ odd
The classification of surfaces with $pg=q=0$ isogenous to a product of curves
arXiv:math/0610267
The cohomology of real De Concini-Procesi models of Coxeter type
The elementary obstruction and homogeneous spaces
*
The groups of symmetric genus $8$
The software package MAGMA was employed to help with the calculations, and the MAGMA library of small groups was essential to the classification.
The Hall-Janko graph and the Witt system $W10$
The hardness of computing an eigenform
arXiv:0708.1192v2
The hidden root problem
"To compare version 1 and version 2 of the algorithm described in Section 4 we ran several tests using Magma for some interesting cases of k"
The invariants of a genus one curve
arXiv:math.NT/0610318
The invariants of modular indecomposable representations of $Zp2$
The large sieve, monodromy, and zeta functions of algebraic curves. II. Independence of the zeros
arXiv:0807.2118v1
The McKay conjecture for exceptional groups and odd primes
The Ore Conjecture
The polynomial degrees of Grassmann and Segre varieties over $GF(2)$
The ramification sequence for a fixed point of an automorphism of a curve and the Weierstrass gap sequence
arXiv:0804.1509v1 [math.AG]
The Steinberg symbol and special values of $L$-functions
McCallum, W., Sharifi, R.: Magma routines for computing the table of pairings for p < 1000, http://abel.math.harvard.edu/~sharifi/computations.html,http://math.arizona
The symmetric genus of groups of odd order
Can't access content
The transitive and co-transitive blocking sets in $P2(Fq)$
The transitive permutation groups of degree 32
The uniform primality conjecture for elliptic curves
0712.2696v1 [math.NT]
Torelli actions and smooth structures on four manifolds
Total Break of the l-IC Signature Scheme
Homepage mentioned in footnote
Towards the Siegel ring in genus four
In French
Transitive decompositions of graph products: Rank 3 grid type
Twisted ate pairing on hyperelliptic curves and applications
computation and verification
Vertices of low-dimensional simple modules for symmetric groups
for calculations
Vertices of simple modules for the symmetric groups in blocks of small weights
could not view article
Weak approximation on del Pezzo surfaces of degree 1
Weights in Serre's conjecture for Hilbert modular forms: the ramified case
arXiv:math.NT/0610488: "We have used Magma to find (elliptic) modular newforms f with integer coefficients."
arXiv:0803.0862v1
$F$-actions and parallel-product decomposition of reflexible maps
$K3$ surfaces with Picard number one and infinitely many rational points
math.AG/0506416v2. Mentions that efficient algorithms are available in Magma.
$K3$ surfaces with Picard number three and canonical vector heights
$S$-extremal strongly modular lattices
***DONE***
3-local Identifications of some Finite Simple Groups
A bound for certain $s$-extremal lattices and codes
LatCde
A computational verification of Alperin's weight conjecture for groups of small order and their prime fields
Has not been reviewed by MR
A database of polarized $K3$ surfaces
ZZZ Can't access content
A disk-based parallel implementation for direct condensation of large permutation modules
A geometric construction of finite semifields
A GMP-based implementation of Schönhage-Strassen's large integer multiplication algorithm
A multivariate signature scheme with an almost cyclic public key
We carried out some experiments with MAGMA, which contains an implementation of Faugeres F4 algorithm. As you can see from the Table, MAGMA works slightly faster on our scheme than on a random system. However, the speed up factor is so small that it isn't a major drawback of our scheme...***** could not view entire paper
A note on the group of projectivities of finite projective planes
Algorithm implemented in GAP and Magma
A polynomial time attack on RSA with private CRT-exponents smaller than $N0.073$
A polynomial with Galois group $SL2( F16)$
arXiv:math/0701442
A search algorithm for linear codes: Progressive dimension growth
Addendum to: ``An elementary introduction to coset table methods in computational group theory''
Algebraic and Slide Attacks on KeeLoq
Algebraic Cryptanalysis of the Data Encryption Standard
Algebraic side-channel collision attacks on AES
Algèbres tensorielles, algèbres extérieures, algèbres symétriques
Can't access content. Also matches in Structures algebriques which is another chapter in the same book
Alternating forms and self-adjoint operators
An action of subgroups of mapping class groups on polynomial algebras
Magma used extensively in calculations.
An algebraic analysis of Trivium ciphers based on the boolean satisfiability problem
An algorithmic approach to resolutions
Refers to package written by Jon Carlson
An Efficient LLL Gram Using Buffered Transformations
21. Stehlé, D.: The New LLL Routine in the Magma Computational Algebra Syste m. Magma 2006 Conference (2006), http://magma.maths.usyd.edu.au/Magma2006/
An elliptic $K3$ surface associated to Heron triangles
for computations
arXiv:math.AG/0403182
An explicit treatment of biquadratic function fields
An extremal singly even self-dual code of length 88
An ultradiscrete matrix version of the fourth Painlevé equation
arXiv:nlin.SI/0610041
For computations: For example, for extension degree d = 163, a simple Magma script determined all 713 (special) type I SSRF pentanomials of degree 163 in less than one minute
Artin presentations from an algebraic viewpoint
Attacks on the ESA-PSS-04-151 MAC Scheme
Binary codes from rectangular lattice graphs and permutation decoding
Black box groups
Bounds on the minimum homogeneous distance of the $p$-ary image of linear block codes over the Galois ring $GR(pr,m)$
Branching rules for Specht modules
arXiv:math.RT/0408088
Breaking the symmetry: A way to resist the new differential attack
Certification of the $QR$ factor $R$ and of lattice basis reducedness
arXiv:cs.SC/0701183
Certified Computer Algebra on Top of an Interactive Theorem Prover
Classes of codes from quadratic surfaces of $PG(3,q)$
Classification of 6-dimensional nilpotent Lie algebras over fields of characteristic not 2
Implemented recognition procedure in Magma; used in calculations.
Classification of eight-dimensional perfect forms
Codes from the line graphs of complete multipartite graphs and PD-sets
Cohomology for quantum groups via the geometry of the Nullcone
PDF from Google Scholar search
Commuting involution graphs for sporadic simple groups
Compactness of the space of left orders
Comparing Implementation Efficiency of Ordinary and Squared Pairings
Our programs are written in MAGMA and ran on an AMD Opteron, 2GHZ dual core machine with 4GB of memory. Below are the tables for the average timings of the algorithms in seconds.
Compiler Assisted Elliptic Curve Cryptography
"However, interpreted languages which support the types and operations required, such as Magma [9], are unlikely to yield efficient results on a mobile computing device."
Complete arcs in $PG(2,25)$: the spectrum of the sizes and the classification of the smallest complete arcs
Complex group algebras of finite groups: Brauer's problem 1
*Read* Misspelt Cannon Canon
Computations of elliptic units for real quadratic fields
Magma used for computations
***
Computing decompositions of modules over finite-dimensional algebras
Computing the fine structure of real reductive symmetric spaces
Computing with 4-Engel groups
Conjugacy in Garside groups. III. Periodic braids
Constructing even radius tightly attached half-arc-transitive graphs of valency four
Constructing pairing-friendly elliptic curves using Gröbner basis reduction
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Construction of elliptic curves with large Iwasawa $$-invariants and large Tate-Shafarevich groups
Magma's homepage is written as a footnote
Construction of MDS self-dual codes over Galois rings
Constructive Sylow theorems for the classical groups
Convolution congruences for the partition function
"The author thanks Ken Ono for his advising, Jeremy Rouse for assistance with the computer system MAGMA, and the referee for splendid and insightful comments."
Convolutional and tail-biting quantum error-correcting codes
Counting characters of upper triangular groups
Cryptanalysis of a Hash Function Proposed at ICISC 2006
Cryptanalysis of Rational Multivariate Public Key Cryptosystems
Curves of fixed points of trace maps
[BC] W. Bosma and J. Cannon. MAGMA (University of Sydney), 1994.
Cyclic codes and reducible additive equations
Decoding the Mathieu group $M12$
[5] J. J. Cannon et al., The Magma programming language, Version 2.11, School of Mathematics and Statistics, University of Sydney (2004).
Decomposed Attack for the Jacobian of a Hyperelliptic Curve over an Extension Field
for computations
Differential equations for algebraic functions
arXiv:cs/0703121
Double circulant and quasi-twisted self-dual codes over $F5$ and $F7$
Double circulant codes from two class association schemes
Not seen
Ducci-sequences and cyclotomic polynomials
Efficient Methods for Conversion and Solution of Sparse Systems of Low-Degree Multivariate Polynomials over $GF(2)$ via SAT-Solvers
Elliptic curves associated with simplest quartic fields
Content not yet available
Enumerating Motzkin-Rabin geometries
Enumeration-based Algorithms in Coding Theory
Error-correcting codes on low rank surfaces
Evaluating convolution sums of the divisor function with quasimodular forms
arXiv:math.NT/0510429
Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics
Possibly a reference
Exceptional regions and associated exceptional hyperbolic 3-manifolds
Can't access content
Extra special defect groups of order $p3$ and exponent $p$
Extremal self-dual codes of length 64 through neighbors and covering radii
Extremal ternary self-dual codes constructed from negacirculant matrices
[5] Brown, G., Suzuki, K.: Lists of examples and Magma code available for download at www.kent.ac.uk/ims/grdb
Fast arithmetic for triangular sets: from theory to practice
Fast computation of power series solutions of systems of differential equations
arXiv:cs.SC/0604101
Fast Jacobian group operations for $C3,4$ curves over a large finite field
Faster Addition and Doubling on Elliptic Curves
EFD currently consists of 123 scripts for the Magma computer-algebra system checking the correctness of algorithms for elliptic curves in the following forms
Faster inversion and other black box matrix computations using efficient block projections
arXiv:cs.SC/0701188
Finding all elliptic curves with good reduction outside a given set of primes
Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras
Finding the characteristic of a group of Lie type
Fingerprinting Codes for Live Pay-Television Broadcast Via Internet
Flippable pairs and subset comparisons in comparative probability orderings
Galois 2-extensions unramified outside 2
Galois groups of tamely ramified $p$-extensions
Can't access content yet
General error locator polynomials for binary cyclic codes with $t2$ and $n<63$
Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces
Authors wrote code for Magma.
Generalizing a theorem of Huppert and Manz
Can't access content
Generalizing the generalized Petersen graphs
Not seen
Generating functions, Fibonacci numbers and rational knots
Generating spaces of modular forms with $$-quotients
arXiv:math.NT/0701487v1
Generation of groups of square-free order
Geometric automorphism groups of graphs
Groups of even real genus
Can't access content
Gröbner basis techniques to compute weight distributions of shortened cyclic codes
Can't access content
Hadamard Matrices and their Applications
arXiv:quant-ph/0010082. Google Scholar says BoCaPl is cited.
Higher genus icosahedral Painlevé curves
arXiv:math.AG/0506407
Homogeneous factorisations of complete multipartite graphs
Implementing Cryptographic Pairings over Curves of Embedding Degrees 8 and 10
Improved analysis of Kannan's shortest lattice vector algorithm (extended abstract)
Improved bounds for the spread of sporadic groups
Managed to access content through www.lms.ac.uk
Inequivalent Hadamard matrices of order $2n$ constructed from Hadamard matrices of order $n$
Can't access content
Inner reflectors and non-orientable regular maps
??classes of a linear group
Intersection-number operators and Chebyshev polynomials. IV. Non-planar cases
Invariants de classes: exemples de non-annulation en dimension supérieure
In French
Isogeny cordillera algorithm to obtain cryptographically good elliptic curves
Iwasawa theory and the Eisenstein ideal
Jacobian Nullwerte, periods and symmetric equations for hyperelliptic curves
*
Kedlaya's algorithm in larger characteristic
Kummer surfaces for the self-product of the cuspidal rational curve
math.AG/0504023
VERIFY
Lie algebras of small dimension
Acknowledge Magma's success in classifying groups.
Lifting and recombination techniques for absolute factorization
Algorithms implemented in Magma.
Local-global properties of torsion points on three-dimensional abelian varieties
Combinatorics (math.CO); Computer Vision and Pattern Recognition (cs.CV)
Maximal elementary abelian subgroups of rank 2
Maximal unramified 3-extensions of imaginary quadratic fields and $SL2(Z3)$
arXiv:math.NT/0602364
Modular Forms: A Computational Approach
Electronic book under the GNU Free Documentation License: "have spent several years trying to find the best ways to compute with classical modular forms...have implemented most of these algoritms...then in Magma..."
MPFR: a multiple-precision binary floating-point library with correct rounding
Includes homepage as foot note
arXiv:quant-ph/0610161
New cyclic and quasi-cyclic quaternary linear codes
Can't access content
New extremal self-dual codes of length 66
Can't access content
New integer representations as the sum of three cubes
New two-variable full orthogonal designs and related experiments with linear regression models
Nonbinary quantum Goppa codes exceeding the quantum Gilbert-Varshamov bound
Noncommutative complete intersections and matrix integrals
arXiv:math.AG/0603272
Number Theory: Volume I: Tools and Diophantine Equations
O'Nan group uniquely determined by the centralizer of a 2-central involution
Can't access content
On $[A,A]/[A,[A,A]]$ and on a $W_n$-action on the consecutive commutators of free associative algebra
arXiv:math.QA/0610410
On 4-Engel groups
On a very particular class of Ramanujan-Nagell type equations
Can't access content
On approximate triangular decompositions in dimension zero
On Binary and Ternary Kloosterman Sums
On central extensions of preprojective algebras
*
On commutators in groups
Could not access content
*
On proofs in finitely presented groups
On selection of nonmultiplicative prolongations in computation of Janet bases
Using a standard database of benchmarks designed for testing programs computing Groebner bases, we compare these algorithmic modifications (in terms of their efficiency)with Faugere's F4 algorithm, which is built in the Magma computer algebra system.
On strongly regular bicirculants
On surfaces with $pg=q=1$ and non-ruled bicanonial involution
arXiv:math.AG/0510302
On the $(2,3)$-generation of matrix groups over the ring of integers
Can't access content
On the computation of integral closures of cyclic extensions of function fields
On the efficiency of the simple groups of order less than a million and their covers
On the faithfulness of parabolic cohomology as a Hecke module over a finite field
Unsure if real reference in here, can't access article and can't search arxiv version at arXiv:math/0511115
On the Galois groups of the 2-class towers of some imaginary quadratic fields
"To study properties of the above groups and compute Hilbert 2-class fields, we used the software package MAGMA version 2.11 [3]."
On the parameters of $r$-dimensional toric codes
Refers to Joyner's work on toric codes using Magma.
To provide these data we refer to [9,21] and some subroutines of MAGMA
On the resolution of equations $Axn-Byn=C$ in integers $x,y$ and $n3$. I
Could not access content
On the Security of the LILI Family of Stream Ciphers Against Algebraic Attacks
On the Virtues of Generic Programming for Symbolic Computation
"The MAGMA [2,1] computer algebra system, developed at the University of Sydney since the 1990's, has succeeded in providing both generic types and high- performance. As opposed to many previous systems, a strong emphasis was put on performance: asymptotically fast state-of-the art algorithms are implemented in MAGMA, which has become a De facto reference regarding performance."
On toric codes and multivariate Vandermonde matrices
8. Joyner, D.: Toric codes over finite fields. Appl. Algebra Eng. Commun. Comput. 15, 63-79 (2004)
On vertices of exterior powers of the natural simple module for the symmetric group in odd characteristic
One-cusped congruence subgroups of Bianchi groups
3. Cannon, J.: Magma. University of Sydney, Sydney (2000)
Optimal double circulant self-dual codes over $F4$. II
Can't access content
Replaces NR1001033: Fortunately, all of the latest improvements have been collected into the Bernstein/Lange "Explicit-Formulas Database" (EFD) [3], with Magma scripts verifying the correctness of the formulas.
Orders on multisets and discrete cones
Ordinary abelian varieties having small embedding degree
Magma used in calculations.
Parallel algorithms for Gröbner-basis construction
Permutation groups and binary self-orthogonal codes
**
Planar polynomials for commutative semifields with specified nuclei
Plane quartic twists of $X(5,3)$
Polyadic codes of prime power length
PRESENT: An Ultra-Lightweight Block Cipher
31. MAGMA v2.12. Computational Algebra Group, School of Mathematics and Statis- tics, University of Sydney (2005), http://magma.maths.usyd.edu.au
Principles of Mathematics in Operations Research
Unable to access content
Products of foldable triangulations
arXiv:math.CO/0508180 [6] John Cannon, et al., Magma, version 2.11, http://magma.maths.usyd.edu.au/, 2004.
http://eprint.iacr.org/2006/051.pdf
Quadratic forms that represent almost the same primes
arXiv:math.NT/0410266v2
Quasiclassical trajectory calculations of the $OH+NO_2$ association reaction on a global potential energy surface
In order to develop the basis of permutationally invariant polynomials in a compact, computationally efficient form we rely on powerful mathematical results on the invariants of finite groups and on the implementation of constructive invariant theory in the Magma computer algebra system. Finally, one of us (B.J.B.) thanks Professor Gregor Kemper and Allan Steel for advice about invariant computations and Magma.
Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms
"The similarities of the quaternionic M-symbols with the usual M-symbols over Q suggests that one could implement them in a package similar to the Magma package of Stein [16, 9] for a wide range of number fields, especially real quadratic fields. "
Marston Conder checked result of thereom 6 and corrected it
Regular Cayley maps for finite abelian groups
Relative rigid cohomology and deformation of hypersurfaces
Results on binary cyclic codes
Rigid analytic uniformization of curves and the study of isogenies
Saito-Kurokawa lifts and applications to the Bloch-Kato conjecture
Scaling Security of Elliptic Curves with Fast Pairing Using Efficient Endomorphisms
Secure PRNGs from Specialized Polynomial Maps over Any F$_q$
Self-points on an elliptic curve of conductor 14
Semisymmetric cubic graphs of twice odd order
Magma used in calculations
Semisymmetric elementary abelian covers of the Möbius-Kantor graph
arXiv:math.CO/0510383
To rule out a zero of H^i on the set H = 0 we began by computing two Groebner bases (using Magma) of the following systems.
Simplified pairing computation and security implications
Skew Hadamard difference sets from the Ree-Tits slice symplectic spreads in $PG(3,32h+1)$
arXiv:math/0609586
Smallest irreducible of the form $x^2-dy^2$
Accepted for publication
Some designs and codes invariant under the simple group $Co2$
Magma version 2.12 of July 2005 was used.
Some self-dual codes invariant under the Hall-Janko group
Sparse representation for cyclotomic fields
Strategies for selecting non-multiplicative prolongations in computing Janet bases
translation in Program. Comput. Software 33 (2007), no. 3, 147--153
Subgroups of pure braid groups generated by powers of Dehn twists
Replaces NR1000532
Support varieties for Weyl modules over bad primes
Support varieties for Weyl modules over bad primes
Symmetric and alternating groups as monodromy groups of Riemann surfaces. I. Generic covers and covers with many branch points
Can't access content
Symmetric cubic graphs of small girth
Symmetric generation of groups
Can't access content
Symmetric presentation of the Janko group $J4$
Tate-Shafarevich groups and K3 surfaces
Testing sign conditions on a multivariate polynomial and applications
[31] G. Lecerf. Kronecker magma package for solving polynomial systems. Available at http://www.math.uvsq.fr/~lecerf/software/
The Brauer-Manin obstruction and Sh[2]
A. Logan, 'Magma programs for computing the Brauer-Manin obstruction on a del Pezzo surface of degree 4', http://www.math.uwaterloo.ca/~a5logan/math/index.html. 361
The Brauer-Manin obstruction on del Pezzo surfaces of degree 2
The character table of a maximal subgroup of the Monster
Managed to access content through www.lms.ac.uk
The Chow rings of $G2$ and Spin(7)
Used to ceertify results.
The computation of invariant fields and a constructive version of a theorem by Rosenlicht
The Diophantine equation $(xk-1)(yk-1)=(zk-1)t$
"We note that computation of the newforms in question may be carried out via Magma or one may consult William Stein's Modular Forms Database.
The fine Tate-Shafarevich group
The group $GL(6, Z)$ is $(2,3)$-generated
The isomorphism problem for cyclic algebras and an application
arXiv:math/0702681
The Kodaira dimension of the moduli of $K3$ surfaces
The linear programming bound for codes over finite Frobenius rings
Could not view to verify
The module structure of a group action on a polynomial ring: a finiteness theorem
The order bound for general algebraic geometric codes
The quadratic extension extractor for (hyper)elliptic curves in odd characteristic
The real genus of 2-groups
Can't access content
The unstable integral homology of the mapping class groups of a surface with boundary
Always referred to as lower case
Toward a rigorous variation of Coppersmith's algorithm on three variables
Toward Non-parallelizable Client Puzzles
Link to homepage given twice after mention of Magma program
Tree-based construction of LDPC codes having good pseudocodeword weights
Triangles with two integral sides
**
Trivializing a central simple algebra of degree 4 over the rational numbers
Twists of $X(7)$ and primitive solutions to $x2+y3=z7$
Used for computations.
Units in some parametric families of quartic fields
Universal torsors of del Pezzo surfaces and homogeneous spaces
Using the Malcev correspondence for collection in polycyclic groups
Visibility of the Shafarevich-Tate group at higher level
"The statements in this section all make the hypothesis that certain Magma commands have correct output when we used them"
When e-th Roots Become Easier Than Factoring
Which point configurations are determined by the distribution of their pairwise distances?
Replaces NR1000669
Üeber die Tiefe von Invariantenringen unendlicher Gruppen
In German
$CM$-values of Hilbert modular functions
Used in computations.
20 years of ECM
Magma used for computation.
A census of semisymmetric cubic graphs on up to 768 vertices
Sent by Conder
A computer-assisted analysis of some matrix groups
MRC
Replaces NR1000661
A database of local fields
passing reference:"e.g., they are used in the computer systems magma and gap"
A family of skew Hadamard difference sets
computations
A generalized floor bound for the minimum distance of geometric Goppa codes
A Lie algebra method for rational parametrization of Severi-Brauer surfaces
Implemented in Magma
A low-memory algorithm for point counting on Picard curves
we used the function field arithmetic by Florian Hess implemented in Magma.
A New Minimum Weight Algorithm for Additive Codes
A New Tool: Constructing STBCs from Maximal Orders in Central Simple Algebras
STBC = space-time block code
A New Type of Fast Endomorphisms on Jacobians of Hyperelliptic Curves and Their Cryptographic Application
A note on integral points on elliptic curves
Replaces NR1000361
A recursive method for computing zeta functions of varieties
"We have implemented the fibration algorithm for these surfaces over prime fields using the Magma programming language"
A unified approach to computations with permutation and matrix groups
ZZZ Can't access content. Review mentions Magma.
A Weil Descent Attack against Elliptic Curve Cryptosystems over Quartic Extension Fields
http://eprint.iacr.org/2004/240.pdf
Algebraic Aspects of the Advanced Encryption Standard
In chapter: Analysis of AES Equation Systems
Algorithms for Computing Restricted Root Systems and Weyl Groups
Couldn't acess content
Algorithms for Crystallographic Groups
Includes home page
Algorithms for twisted involutions in Weyl groups
An atlas of abstract regular polytopes for small groups
An elliptic curve trapdoor system
Magma used in computations.
An explicit class of codes with good parameters and their duals
An index calculus algorithm for plane curves of small degree
Author implemented algorithms in Magma.
Application of point-group symmetries in chemistry and physics: A computer-algebraic approach
" In molecular physics and crystallography, of course, it is the calculus of the point-group symmetries that provides the mathematical basis and that is needed to explain the observed spectra. This ubiquitous need for point-group symetries has also motivated the design of Magma, Gap, and others.....often less suitable for applications as required in chemistry and physics. An alternative view is taken by the Bethe program, which has been built on Maple.."
Applications of computer algebra to finite geometry
ZZZ Can't access content. Review mentions Magma is used.
Applications of the class field theory of global fields
Arc-transitive homogeneous factorizations and affine planes
Arithmetic progressions consisting of unlike powers
"Greatly indebted to.."; Used in computations.
Automorphic forms and rational homology 3-spheres
arXiv:math.GT/0508271
Automorphism groups of some AG codes
Automorphisms and equivalence of bent functions and of difference sets in elementary abelian 2-groups
MAGMA in particular, has powerful procedures which determine automorphisms and isomorphisms of designs and can therefore be applied to D(B).
Block ciphers sensitive to Gröbner basis attacks
Magma used for computations.
Implemented algorithm in Magma.
Brauer groups of diagonal quartic surfaces
Magma used for computation and verification
Cancellation in totally definite quaternion algebras
Used in calculations.
Central extensions of preprojective algebras, the quantum Heisenberg algebra, and 2-dimensional complex reflection groups
arXiv:math.RT/0503393
Central values of Rankin $L$-series over real quadratic fields
Certain Roman and flock generalized quadrangles have nonisomorphic elation groups
"Our proof is theoretical, but it was inspired by the insight gained from detailed group computations for the smallest of these groups conducted using the computer algebra systems GAP [3] and Magma [1]."
Classical and modular approaches to exponential Diophantine equations I: Fibonacci and Lucas perfect powers
Classical and modular approaches to exponential Diophantine equations II: The Lebesgue-Nagell equation
Classification of extremal double circulant self-dual codes of lengths 74--88
Classification of genus 3 curves in special strata of the moduli space
Used in calculations.
Classification of linear codes exploiting an invariant
Codes auf Hyperelliptischen und Trigonalen Kurven
Codes und Automorphismen optimaler Artin-Schreier-Turme
Cohomology and group extensions in Magma
Coincident root loci and Jack and Macdonald polynomials for special values of the parameters
See arXiv:math.QA/0404079
Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one
Complex surfaces of general type: Some recent progress
In French
Computation of $p$-adic heights and log convergence
Used in calculations.
Includes description of why Magma was chosen
Computational approaches to lattice packing and covering problems
Computational experiences on norm form equations with solutions forming arithmetic progressions
Computer aided discovery of a fast algorithm for testing conjugacy in braid groups
Computing conjugacy class representatives in permutation groups
Implementation of algorithm
Computing Gröbner bases for vanishing ideals of finite sets of points
Implemented algorithms in Magma.
This was given at Clay Instititute Summer School, August 2006
Computing in algebraic geometry
In chapter: Introductory Remarks on Computer Algebra
Computing restrictions of ideals in finitely generated $k$-algebras by means of Buchberger's algorithm
Computing the character table of a finite group
Computing the primitive permutation groups of degree less than 1000
Computing the soluble radical of a permutation group
Computing with elation groups
ZZZ Can't access content. Review mentions Magma is used.
Computing with the analytic Jacobian of a genus 2 curve
Conjugacy search in braid groups: From a braid-based cryptography point of view
Constructing class fields over local fields
Constructing endotrivial modules
Constructing Matrix Representations of Finite Groups in Characteristic Zero
Can't access content
Constructing the split octonions
Constructions for Hadamard matrices of Williamson type
ZZZ Magma used in search for H-matrices
Constructive recognition of $PSL(2,q)$
Report on the performance of an implementation in Magma
Can't access contact
"A Steel has reported on similar efforts [towards effective reduction] within his implementation of some Magma routines."
Dependency of units in number fields
Implemented algorithms.
J. Cannon, A Draft Description of the Group Theory Language Cayley, In SYMSAC 76: Proceedings of the third ACM symposium on Symbolic and algebraic computation, pages 66 84, New York, NY, USA, 1976. ACM Press.
Distance $k$ colorings of Hamming graphs
Distance-balanced graphs: Symmetry conditions
Efficient calculation of Stark-Heegner points via overconvergent modular symbols
Describes a Magma package for Stark-Heegner points.
Efficient decoupling schemes with bounded controls based on Eulerian orthogonal arrays
Efficient Hyperelliptic Curve Cryptosystems Using Theta Divisors
The Institute of Electronics, Information and Communication Engineers
Efficient polynomial time algorithms computing industrial-strength primitive roots
Efficient presentations for the Mathieu simple group $M_22$ and its cover
Sent by Conder
Embedding 2-groups in groups generated by involutions
Reviewer says: "The author notes that he was led to conjecture this result by calculations performed in MAGMA."
Endomorphism algebras of hyperelliptic Jacobians and finite projective lines
Used to verify calculations.
Endotrivial modules for finite groups of Lie type
Entropy quotients and correct digits in number-theoretic expansions
Entwurf von Algorithmen zur Konstruktion von Differentialgleichungen mit vorgegebener endlicher Galoisgruppe
A lot of references, includes magma code
Explicit representations of maximal subgroups of the Monster
Magma used extensively in calculations.
Factorisations of sporadic simple groups
Magma used extensively in calculations.
Fast constructive recognition of black box orthogonal groups
FPGA Vendor Agnostic True Random Number Generator
Includes link to homepage as footnote
Fundamental units in a parametric family of not totally real quintic number fields
Galois $p$-groups unramified at $p$---a survey
Generators and relations for matrix algebras
Special thanks are due to John Cannon and Allan Steel of the MAGMA project for their help with the implementation.
Geometries, the principle of duality, and algebraic groups
Graded rings and special $K3$ surfaces
Groups $G_2(p)$ as quotients of $(2,3,7;2p)$
MRC
Gröbner bases and generalized Padé approximation
Used in computations.
Gröbner bases and generation of difference schemes for partial differential equations
"However, the fastest implementation of these algorithms for commutative polynomial algebra is done in the specialpurpose systems Singular [19] and Magma [20]."
Hadamard ideals and Hadamard matrices with circulant core
Hadamard ideals and Hadamard matrices with two circulant cores
Implemented algorithm in Magma to compute Shimura-Heegner points on specified elliptic curves
Height difference bounds for elliptic curves over number fields
Heron triangles via elliptic curves
Magma used in computations
Hidden pairings and trapdoor DDH groups
Cites "The Magma computer algebra system. University of Sydney" in the reference list, but there is no mention in the body of the text.
Highly transitive imprimitivities
Sent by Conder
Hyperelliptic Jacobians with real multiplication
[21] W. Stein, PARI & MAGMA Calculator
Identities for finite solvable groups and equations in finite simple groups
"Not only proofs but even precise statements of our results would hardly be possible without extensive computer experiments".
Implementation of Fast Polynomial Arithmentic in Aldor
Can't access all of postscript document
Indigenous bundles with nilpotent $p$-curvature
Information sets and partial permutation decoding for codes from finite geometries
Integer Factorization and Computing Discrete Logarithms in Maple
Integer points on the curve $Y^2=X^3p^kX$
Integral points on a class of elliptic curve
ZZZ Can't access content. Review mentions Magma.
Invariant subspaces, duality, and covers of the Petersen graph
Invariants of the diagonal $C_p$-action on $V_3$
Authors used Magma in their investigations
Irreducible $(2,3,7)$-subgroups of $PGL_n(F)$, $n7$
Irreducible constituents of monomial representations
Not seen
Is the group $SL(6,Z)$ $(2,3)$-generated?
There is a chapter called Groups Acting on Lattices within Martin Lorenz's book Multiplicative Invariant theory MR2131760. See http://www.springerlink.com/content/nw35826278671337/
Key substitution attacks revisited: Taking into account malicious signers
Kneser-Hecke-operators in coding theory
LDPC codes generated by conics in the classical projective plane
Legendrian subvarieties of projective space
Used in computations. See also AG/0503528 v1
Lie-theoretischer Zugang zur Erzeugung unitärer Transformationen auf Quantenrechnern
Local characteristic $p$ completions of weak $BN$-pairs
[B] G. Brown. Finding special K3 surfaces with Magma. Preprint
Maximal symmetry groups of hyperbolic 3-manifolds
Sent by Conder
References home page as foot note
Minimal degree liftings in characteristic 2
Modelling inheritance as coercion in the Kenzo system
Multivariate Public Key Cryptosystems
New computations in the Monster
HPage
New linear codes derived from binary cyclic codes of length 151
Nielsen periodic point theory for periodic maps on orientable surfaces
"We relied extensively on the computational power of Magma [1] to obtain these formulas, which in theory (but perhaps not in practice) could be reproduced from Wang s methods with any even g."
Non-elliptic Shimura curves of genus one
*
Non-simple localizations of finite simple groups
Magma used to verify calculations.
Normal subgroups of the modular group and other Hecke groups
Numerical cubature using error-correcting codes
math.NA/0402047
On certain combinatorial Diophantine equations and their connection to Pythagorean numbers
On computing all harmonic frames of $n$ vectors in $C^d$
"Here we give details of the implementation of our algorithm in the computer algebra system Magma (cf. [1]), which is ideally suited to computing with groups."
On Computing Janet Bases for Degree Compatible Orderings
On Euclidean tight 4-designs
[9] Magma. The magma computational algebra system for algebra, number theory and geometry. Version V2.11.
On Some Necessary Conditions of Boolean Functions to Resist Algebraic Attacks
On the classification of all self-dual additive codes over $GF(4)$ of length up to 12
On the coinvariants of modular representations of cyclic groups of prime order
See arXiv:math.AC/04409107
On the computation of the coefficients of a modular form
On the number of conjugates defining the solvable radical of a finite group
For all groups except the Monster M, our main tool was MAGMA.
On the orders of automorphism groups of finite groups. II
Magma used for calculations.
[4] The Computational Algebra Group: MAGMA-V2.10 | The Magma Computational Algebra System, School of Mathematics and Statistics, University of Sydney, 2003.
On the security of stepwise triangular systems
On the structure of certain Galois cohomology groups
We would also like to thank Mike Harrison for discussions about his implementation of Kedlaya's algorithm in Magma,
On the trace map between absolutely abelian number fields of equal conductor
Magma used to verify computations
LatCde
Orthogonal designs and MDS self-dual codes
Can't access content
Orthogonal designs via computational algebra
[1] G. Bailey, Hadamard matrices, Chapter 112, in Handbook of Magma functions, J. Cannon and W. Bosma (Editors), Version 2.11, Sydney, 2004, pp. 3456 3462.
Parameterized norm form equations with arithmetic progressions
Perfect forms and the moduli space of abelian varieties
Polly Two: A new algebraic polynomial-based public-key scheme
Potential energy surfaces and MULTIMODE vibrational analysis of $C_2H_3+$
Powers from products of consecutive terms in arithmetic progression
Practical solution of the Diophantine equation $y^2=x(x+2^ap^b)(x-2^ap^b)$
Primitive polynomials with a prescribed coefficient
"The calculations here (and wherever composite ground fields are involved) were performed using Magma"
Qualitative Theory of Planar Differential Systems
In chapter: Centers and Lyapunov Constants
Quantum convolutional codes: Encoders and structural properties
PDF from Google Scholar
Quartic $K3$ surfaces without nontrivial automorphisms
arXiv:math.AG/0511542 v1
Rational and Heron tetrahedra
for computation
Rational parametrisation for degree 6 Del Pezzo surfaces using Lie algebras
Implemented in Magma
Rationality and the Tangent Function
Submitted, Calcut links to Magma on his homepage
Recent developments in permutation decoding
Recognising the Suzuki groups in their natural representations
Implemented in Magma
Relation between the XL Algorithm and Groebner Basis Algorithms
Refers to A. Steel's work
Representations and rigidity of $Aut(F_3)$
Used in calculations
Representations of $G_k$-groups and twists of the genus two curve $y^2=x^5-x$
The explicit computations with this group can be performed using a system for computational algebra such as GAP or Magma
Representations, commutative algebra, and Hurwitz groups
Self-dual Codes and Invariant Theory
Couldn't access content but chapter containing reference is Weight Enumerators and Important Types, pages 29--81
Self-orthogonal 3-$(56, 12, 65)$ designs and extremal doubly-even self-dual codes of length 56
Used to verify calculations.
Short presentations for alternating and symmetric groups
Shult sets and translation ovoids of the Hermitian surface
Couldn't access through journal but you can find it at http://www.math.udel.edu/~ebert/papers/transovs.pdf
Simple Lie algebras of low dimension over $GF(2)$
Small derived quotients in finite $p$-groups
See arXiv:math.GR/0510223
Solving conics over function fields
Some computational experiments in number theory
Some ternary Diophantine equations of signature $(n,n,2)$
String rewriting for double coset systems
arXiv:math.CO/0508391
Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma
Computations done in Magma.
Support varieties for modules
Symmetric generation and existence of $J_3:2$, the automorphism group of the third Janko group
Whilst these calculations, if one had the requisite patience, could be done by hand, we use the computer package Magma
Symmetric groups and completions of the Goldschmidt amalgams of type $G_1$
Symmetric powers of elliptic curve $L$-functions
Supported during parts of this research by ... and the MAGMA Computer Algebra Group at the University of Sydney.
Ten problems in experimental mathematics
Mainly discusses Maple and Mathematica but passing reference to Magma, "these computations can also be recreated very quickly in Magma"
Testing equivalence of ternary cubics
The 2-adic CM method for genus 2 curves with application to cryptography
arXiv:math.NT/0503148, Implements algorithm for CM, using Magma (local rings)
The automorphism group of a binary self-dual doubly even $[72,36,16]$ code is solvable
The class-breadth conjecture revisited
Used extensively in investigations.
The elliptic curve database for conductors to 130000
Homepage included in text
The Geometry of Additive Quantum Codes
Submitted for publication
The group of Weierstrass points of a plane quartic with at least eight hyperflexes
Used in calculations.
The Manin constant
Computations done in Magma.
The moduli space of surfaces with $K^2=6$ and $p_g=4$
The Noether numbers for cyclic groups of prime order
The number of extensions of a number field with fixed degree and bounded discriminant
Magma used in calculation.
The polynomial degree of the Grassmannian $G_1,n,2$
Theory of Finite Simple Groups
There may be more references not all of book was available
Thompson's sporadic group uniquely determined by the centralizer of a 2-central involution
Not seen
Toric surface codes and Minkowski sums
Used in computations.
Towards effective algorithms for linear groups
Tree polynomials and non-associative Gröbner bases
Uno's conjecture for the Chevalley simple groups $G2(3)$ and $G2(4)$
ZZZ Can't access content. Review mentions that article uses Magma, able to access citations
Using systems like MAGMA, finding minimum words in such codes takes only a fraction of a second.
When is projectivity detected on subalgebras?
Wild monodromy and automorphisms of curves
Writing projective representations over subfields
Implementation of algorithm
Zagier duality for the exponents of Borcherds products for Hilbert modular forms
4-Engel groups are locally nilpotent
A characterization of finite soluble groups by laws in two variables
A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type
? Sent by Leemans. Could not view to get details.
A concrete matrix field description of some Galois fields
A Diophantine equation associated to $X_0(5)$
A Fast Cryptanalysis of the Isomorphism of Polynomials with One Secret Problem
A generalization of a construction due to Van Nypelseer
A new algorithm for the computation of logarithmic $l$-class groups of number fields
? Could not view text.Citation verified.
A new approach to the conjugacy problem in Garside groups
A New Method of Building More Non-supersingular Elliptic Curves
Used in computations and verification. Thanks authors of Magma in text.
A self-orthogonal doubly even code invariant under $McL:2$
A study of the security of unbalanced oil and vinegar signature schemes
A systematic evaluation of compact hardware implementations for the Rijndael S-box
Used Magma for systematic evaluation.
A twisted Laurent series ring that is a noncrossed product
Ab initio potential energy and dipole moment surfaces for $H_5O_2$+
For our implementation we relied on the exposition of computational invariant theory by Derksen and Kemper and on the procedures for invariant computation in the Magma computer algebra system B.J.B. thanks Professor Gregor Kemper and Allan Steel for advice about invariant computations and Magma
Abelian surfaces of $GL_2$-type as Jacobians of curves
Used for computations.
Algorithms for the non-monic case of the sparse modular GCD algorithm
Can't search text
All geometries for the smallest sporadic groups
(joint work with Dimitri Leemans)
All in the XL Family: Theory and Practice
Magma mentioned in algorithm discussion.
Almost perfect powers in products of consecutive integers
An Introduction to Algebraic Coding Theory
Analysis of the Bit-Search Generator and Sequence Compression Techniques
Another existence and uniqueness proof for the Higman-Sims simple group
? Unable to verify.
Application of Gröbner bases Techniques for searching new sequences with good periodic correlation properties
Applications and adaptations of the low index subgroups procedure
Computes automorphism groups of graphs obtained by enumerating certain subgroups of a finitely presented group
Arakelov class groups and ideal lattices
Arithmetic of singular moduli and class polynomials
Aspects of the linear groups $GL(n,2)$, $n<7$
Atlas de polytopes réguliers issus de groupes presque simples
? sent by Leemans. could not view to add details
Beauville surfaces without real structures
Binary fingerprinting codes
Building curves with arbitrary small MOV degree over finite prime fields
Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS
Passing reference; "Magma reputed to be the best.."
Capability of nilpotent products of cyclic groups
arXiv:math/0403188
Chirality of toroidal molecular graphs
Circle geometry and three-dimensional subregular translation planes
Magma used to show existence of Sherk surfaces for q-4,5
Classification of solvable Lie algebras
MRC
Cohomology, computations, and commutative algebra
HBook
Combinatorics of trees
Can't access content
Compact hyperbolic 4-manifolds of small volume
Complexity estimates for the $F_4$ attack on the perturbed Matsumoto-Imai cryptosystem
Magma used in calculations.
Computation of Maximal Orders of Cyclic Extensions of Function Fields
Magma used for computations. Algorithms implemented.
Computation of Poincaré-Betti series for monomial rings
Computation of sets of rational points of genus-3 curves via the Demjanenko-Manin method
Used in computations.
Computer search in projective planes for the sizes of complete arcs
Algorithm implemented using Magma.
Computing modular polynomials
Computing residue class rings and Picard groups of orders
Implemented algorithms.
Computing subgroups of bounded index in a finite group
Implementation of algorithm
Computing the Betti numbers of arrangements in practice
HPage cited as footnote
Computing the minimal distance of cyclic codes
Computing the Uniformity of Power Mappings: A Systematic Approach with the Multi-Variate Method over Finite Fields of Odd Characteristic
Magma used in calculations and verification.
Computing weight 2 modular forms of level $p^2$
HPage
Computing zeta functions of surfaces
Congruence classes of presentations for the complex reflection groups G(m, 1, n) and G(m, m, n)
Conquering inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic
Consta-abelian polyadic codes
Constructing invariants for finite groups
Constructing maximal subgroups of classical groups
Constructing transitive permutation groups
Construction of CM Picard curves
Used for computations.
Constructive recognition of normalizers of small extra-special matrix groups
Correction to the paper: ``Almost perfect powers in products of consecutive integers''
This thesis is by someone from France
Coset enumeration of groups generated by symmetric sets of involutions
Counting generating systems of a finite group from given conjugacy classes
I couldn't access the content but there must be a reference
Cryptanalysis of HFEv and internal perturbation of HFE
Cryptanalysis of the tractable rational map cryptosystem
Authors built random public key with Magma.
Deconstructing the Zeilberger algorithm
Design and Analysis of LDPC Convolutional Codes
Used in calculations.
Design and Properties of a New Pseudorandom Generator Based on a Filtered FCSR Automaton
Division-ample sets and the Diophantine problem for rings of integers
Double-coset enumeration algorithm for symmetrically generated groups
Effective Methods for Diophantine Equations
Tengely, S., 2005. Doctoral thesis, Leiden University
Efficient computation of the characteristic polynomial
arXiv:cs.SC/0501074
Efficient Cryptanalysis of RSE(2) PKC and RSSE(2) PKC
Efficient doubling on genus two curves over binary fields
Magma used to create good random curve equations.
Elementary divisors of Specht modules
Elements of prescribed order, prescribed traces and systems of rational functions over finite fields
Elliptic curves suitable for pairing based cryptography
Magma used in calculations.
Entwurf von Algorithmen zur Konstruktion von Differentialgleichungen mit vorgegebener endlicher Galoisgruppe
Algorithms are implemented in an extensive Magma package.
Experimental mathematics: Examples, methods and implications
Explicit 8-Descent on Elliptic Curves
Explicit computations of Hilbert modular forms on $Q(5)$
Explicit computations supporting a generalization of Serre's conjecture
Used in computations.
Book is not yet published
Extracting bits from coordinates of a point of an elliptic curve
It is well known how to construct such a curve using the SEA algorithm (for instance, this is implemented in Magma
Fast algorithms for polynomial solutions of linear differential equations
Fast genus 2 arithmetic based on Theta functions
Magma used in calculations; Magma source file provided.
Masters Thesis, includes references to Allan Steel
Finite field elements with specified order and traces
Finite-dimensionality and growth of algebras defined by polylinearly connected generators
Finiteness results for modular curves of genus at least 2
Floating-point LLL revisited
Formulae for arithmetic on genus 2 hyperelliptic curves
Generalised sifting in black-box groups
Mention Magma as useful for checking results.
Generalized normal forms and polynomial system solving
Handbook of Computational Group Theory
MRC
In chapter: Algebraic Techniques for Calculating the Nielsen Number on Hyperbolic Surfaces
Hecke actions on certain strongly modular genera of lattices
Magma used for calculations.
Hemisystems on the Hermitian surface
Magma used to search for a metacyclic group.
How to Embed Short Cycles into Large Nonlinear Feedback-Shift Registers
Magma used in computations.
Hyperelliptic curves with compact parameters
Used in calculations.
Implementing Minimized Multivariate Public-Key Cryptosystems on low-resource embedded systems
Implicitizing rational hypersurfaces using approximation complexes
Index Calculus in Class Groups of Plane Curves of Small Degree
Implemented algorithm in Magma.
Infinite families of pairs of curves over $Q$ with isomorphic Jacobians
***, "We relied heavily on the computer algebra system Magma"
Interactive conjecturing with VEGA
Acknowledge the need for VEGA to interface with Magma
Invariant rings of orthogonal groups over $F_2$
"14. A. Steel, Calculation of the factors of Omega6(X) using Magma, Private communication, June 2002, http://www.maths.gla.ac.uk/~phk/Steel.htm."
Invarianten zusammenhaengender Gruppen und die Cohen-Macaulay Eigenschaft
In German
Involutions and characters of upper triangular matrix groups
MRC
Knot theory and the Casson invariant in the Artin presentation theory
Kummer theory for norm algebraic tori
for verification
Author thanks authors of Magma (and other programs), 3. Kasper K. S. Andersen, Magma code for the De Concini-Salvetti algorithm, Private Communication (2002), http://www.math.purdue.edu/~ wilker/labnotes.
Linear groups of small degree over finite fields
List decoding of generalized Reed-Solomon codes over commutative rings
To access it, download the source files for the paper math.MG/0405441
Low-dimensional strongly perfect lattices I: The 12-dimensional case
[11] The Magma Computational Algebra System for Algebra, Num- ber Theory and Geometry. available via the magma home page http://www.maths.usyd.edu.au:8000/u/magma/
Matrix Groups: Theory, Algorithms and Applications
Modular equations for hyperelliptic curves
Used in computations.
Modular Forms and Elliptic Curves over Imaginary Quartic Fields
Implemented algorithms in Magma
Modular Forms for the Orthogonal Group $O(2,5)$
Modular Forms of Weight One over Finite Fields
Magma used in computations
Modular representations on some Riemann-Roch spaces of modular curves X(N)
See arvix:math.AG/0502586 for preprint
Multivariate Quadratic Polynomials in Public Key Cryptography
PhD thesis
Near-extremal formally self-dual even codes of lengths 24 and 32
New codes from chains of quasi-cyclic codes
New Families of Hyperelliptic Curves with efficient Gallant-Lambert-Vanstone Method
Normal subgroup growth in free class-2-nilpotent groups
***
On a (flawed) proposal to build more pairing-friendly curves
On coefficient valuations of Eisenstein polynomials
Magma used in calculations.
On Fibonacci numbers with few prime divisors
On minimal logarithmic signatures of finite groups
On modularity of rigid and nonrigid Calabi-Yau varieties associated to the root lattice $A_4$
On perfect powers in Lucas sequences
Magma used for computations.
On power bases in number fields
Magma used in calculations.
On reconstructing configurations of points in $P^2$ from a joint distribution of invariants
On Representations of Affine Hecke Algebras of Type $B$
Magma used in calculations. MRC
On some self-dual codes and unimodular lattices in dimension 48
LatCde
On standardized models of isogenous elliptic curves
On Stern's attack against secret truncated linear congruential generators
On the behavior of the algebraic transfer
On the Brauer class of modular endomorphism algebras
Prepared tables using Magma
On the discrete logarithm problem on algebraic tori
Magma used in calculations.
On the Galois group of generalized Laguerre polynomials
Magma mentioned in software discussion.
On the group of automorphisms of cyclic covers of the Riemann sphere
On the self-dual $F_5$-codes constructed from Hadamard matrices of order 24
On the strongly regular graphs obtained from quasi-symmetric 2-$(31, 7, 7)$ designs
?Proof of theorem given as Magma programme.
On the thin regular geometries of rank four for the Janko group $J1$
Can't access content
On the variation of Tate-Shafarevich groups of elliptic curves over hyperelliptic curves
On the weight enumerators of duadic and quadratic residue codes
On two doubly even self-dual binary codes of length 160 and minimum weight 24
One-point codes using places of higher degree
Orbifold Riemann-Roch for threefolds with an application to Calabi-Yau geometry
Parallel integer factorization using quadratic forms
U.S.N.A. Trident Scholar project report; no. xxx (2005)
Partial permutation decoding for codes from finite planes
Partitions and permutations
Mentions lists of groups in GAP and Magma
Point counting on Picard curves in large characteristic
Pointless curves of genus three and four
***, arXiv:math.NT/0403178
Quadratic Forms and Quaternion Algebras: Algorithms and Arithmetic
Quantum Block and Convolutional Codes from self-orthogonal product codes
arXiv:quant-ph/0703181
Reducing the Fontaine-Mazur conjecture to group theory
Reduction of Smith normal form transformation matrices
Root numbers and ranks in positive characteristic
The actions were found for us by N. Boston using MAGMA
SAGE: System for Algebra and Geometry Experimentation
"The design of SAGE is heavily influenced by the carefully thought out and mature class structure of the closed source computer algebra program Magma."
Sets of transvections generating subgroups isomorphic to special linear groups
Small scale variants of the AES
Solving Algebraic Computational Problems in Geodesy and Geoinformatics
In chapter: Computer Algebra Systems
Some additive Galois cohomology rings
used V2.10
Some binary codes from symplectic geometry of odd characteristic
Some Calculations Related To The Monster Group
Some computational tools for estimating the parameters of algebraic geometry codes
Some Improved Algorithms for Hyperelliptic Curve Cryptosystems Using Degenerate Divisors
Magma used to generate random curves.
Some results on orthogonal designs and Hadamard matrices
Speeding up Scalar Multiplication in Genus 2 Hyperelliptic Curves with Efficient Endomorphisms
Magma used in calculations.
Study and computation of a Hurwitz space and totally real $PSL_2(F_8)$-extensions of $Q$
For calculations
Symmetric $(4,4)$-nets and generalized Hadamard matrices over groups of order 4
Symmetric functions and the phase problem in crystallography
Tame pro-$p$ Galois groups: A survey of recent work
Magma used for calculations.
The 2-adic eigencurve at the boundary of weight space
The Alperin and Uno conjectures for the Fischer simple group $Fi_22$
The bad behavior of representation groups
Couldn't access content
The classification of torsion endo-trivial modules
The edge-transitive but not vertex-transitive cubic graph on 112 vertices
The graded ring of quaternionic modular forms of degree 2
Magma used for calculations; modular forms, invariant rings.
The groups with order $p^7$ for odd prime $p$
MRC
The minimal degrees of faithful representations of the sporadic simple groups and their covering groups
The Performance of $LDPC$ codes with Large Girth
The primitive permutation groups of degree less than 2500
The primitive solutions to $x^3+y^9=z^2$
Extensive use. "We have made available a complete electronic transcript of the computations in Magma"
The residually weakly primitive geometries of HS
? sent by Leemans. Could not view to add details.
The structure of irreducible matrix groups with submultiplicative spectrum
Tomography of quantum states in small dimensions
Torsion in boundary coinvariants and $K$-theory for affine buildings
Towers of 2-covers of hyperelliptic curves
"A 2-descent ... implemented by Michael Stoll in Magma gives ..."
Two rank six geometries for the Higman-Sims sporadic group
Unimodular Hermitian lattices
This was part of a 6 day workshop
Unitriangular actions on quadratic forms and character degrees
Magma used to verify results; codes implemented.
Using Algebraic Geometry
In chapter: Polyhedral Regions and Polynomials
Varieties of nilpotent elements for simple Lie algebras. II. Bad primes
Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
Weak keys in $MST_1$
Weights in codes and genus 2 curves
Weil descent attacks
? unable to view to verify
Über Torsionspunkte elliptischer und hyperelliptischer Kurven nebst Anwendungen
3-manifolds from Platonic solids
? Cannon etal cite; Used in computations.
A binary recursive GCD algorithm
Software comparison.
A chosen IV attack against Turing
Magma used in computations.
A counterexample to Fishburn's conjecture on finite linear qualitative probability
A counterexample to the Gouvêa-Mazur conjecture
A low-memory parallel version of Matsuo, Chao, and Tsujii's algorithm
Author used high level implementation in Magma.
A new quasi-symmetric 2-$(56, 16, 6)$ design obtained from codes
A note on the Ramanujan-Nagell equation
A note on the Tate pairing of curves over finite fields
A Polly Cracker system based on satisfiability
Algebraic Attacks from a Gröbner Basis Perspective
Author implements algorithm in Magma.
An addition algorithm on the Jacobian varieties of curves
Used to verify calculations.
An algorithm for computing isomorphisms of algebraic function fields
An algorithmic analysis of the intersection property
An efficient algorithm for the computation of Galois automorphisms
Magma used for computations
An elliptic curve trapdoor system (extended abstract)
Magma used to construct elliptic curve cryptosystems.
Applied abstract algebra
Can't access content
Approximation of eigenforms of infinite slope by eigenforms of finite slope
Magma mentioned in abstract, use this address for all papers
Bruen chains over fields of small order
"We use the built in classical permutation group PGO (4; q) (acting on the points of the elliptic quadric), but note that Magma Version 2.8-2 (which we are using), erroneously gives a subgroup of index 2 of this group."
Circulant based extremal additive self-dual codes over $GF(4)$
Classical covariants and modular invariants
Used in calculations; written script implemented.
Classification of Highly Nonlinear Boolean Power Functions with a Randomised Algorithm for Checking Normality
As we did not expect to find a closed formula for the time complexity of the combine-procedure, we used [MAG] to compute it numerically. As all computations are done with rational numbers there are no rounding errors in MAGMA. 3rd International Conference on Theoretical Computer Science, 2004
Classification of the $(n,3)$-arcs in $PG(2,7)$
Commuting involution graphs in special linear groups
Ref:An Introduction to Algebraic programming with Magma (draft) Springer-Verlag (1997)
Comparison between XL and Gröbner basis algorithms
Complementation in the group of units of matrix rings
Find minimal double coset representatives with MAGMA
Complex Multiplication Tests for Elliptic Curves
All calculations were done using Magma
Computation of the decomposition group of a triangular ideal
Computational and Algebraic Aspects of the Advanced Encryption Standard
Magma used in calculations.
Computing Generators and Relations for Matrix Algebras
Computing in groups of Lie type
Computing maximal subgroups of finite groups
Computing the level of a modular rigid Calabi-Yau threefold
Used in calculations
Computing with graphs and groups
In book MR2125091
Computing zeta functions via $p$-adic cohomology
Harrison has implemented...Magma.
Congruence subgroups of groups commensurable with $PSL(2, Z)$ of genus 0 and 1
Conjectures about discriminants of Hecke algebras of prime level
Conjugacy of subgroups of the general linear group
Construction of BLT-sets over small fields
Magma used to search for BLT-sets.
Construction of good LDPC codes using dilation matrices
Construction of new extremal unimodular lattices
Construction of new skew Hadamard matrices and their use in screening experiments
Construction of secure random curves of genus 2 over prime fields
Algorithm implemented in Magma
Constructions of rank five geometries for the Mathieu group $M_22$
Counting nilpotent Galois extensions
Passing reference to Magma.
Counting solutions to equations in many variables over finite fields
Deciding the nilpotency of the Galois group by computing elements in the centre
Magma used in calculations.
Derived subgroups of products of an abelian and a cyclic subgroup
Designs and self-dual codes with long shadows
Magma used in computations.
Designs, Geometry, and a Golfer's Dilemma
Downloaded as image, can't search content
For the class of pc presented finite supersolvable groups, we propose a new DFT-basedword normalization strategy, which principally differs from classical collection strategies used in computer algebra system such as GAP orMAGMA.
Dickson polynomials that are permutations
Magma used in calculations.
Dihedral Galois representations and Katz modular forms
?cites articles she wrote "computing Hecke algebras...in Magma"
Double coset enumeration of symmetrically generated groups
Efficient scalar multiplication in hyperelliptic curves using a new Frobenius expansion
Magma used for calculations.
Elementary abelian covers of graphs
Elliptic curves of large rank and small conductor
Elliptic curves with nonsplit mod 11 representations
Erasure thresholds for efficient linear optics quantum computation
? Needs verification
Euclidean and Hermitian self-dual MDS codes over large finite fields
Used Magma to construct examples of self-dual codes.
Evidence that XTR is more secure than supersingular elliptic curve cryptosystems
Magma used in calculations.
Exact computation of the bifurcation point $B_4$ of the logistic map and the Bailey-Broadhurst conjectures
Explicit construction of families of LDPC codes with no 4-cycles
Computations may be done in ... Magma
Explicit matrices for irreducible representations of Weyl groups
Magma mentioned in passing, MRC
Factoring polynomials via polytopes
Used Magma to develop and implement algorithm.
Fast software-based attacks on SecurID
FFPACK: finite field linear algebra package
Finite analogues of non-Euclidean spaces and Ramanujan graphs
Magma website is referenced
Finite Hurwitz braid group actions for Artin groups
Bosma and Cannon, MAGMA, 1994
Fixity and free group actions on products of spheres
arXiv:math/0304078v1
Further results on strongbox secured secret sharing schemes
Galois Theory and Modular Forms
Could not view to verify
Generation of Random Picard Curves for Cryptography
Author used function field arithmetic implemented in Magma.
Genus one curves defined by Pfaffians
"Step 1 may be accomplished using standard Gröbner basis algorithms, as implemented in Magma for example"
Geometric realisation of the graphs of McKay-Miller-Sirán
Globally maximal arithmetic groups
Magma used for calculations.
Groups and nilpotent Lie rings whose order is the sixth power of a prime
MRC
Handbook of Number Theory II
Couldn't access content, contained somewhere in "The many facets of euler's totient"
Hermitian function fields, classical unitals, and representations of 3-dimensional unitary groups
Higher composition laws I: A new view on Gauss composition, and quadratic generalizations
How to do a $p$-descent on an elliptic curve
Hurwitz groups of intermediate rank
Implementation of a new algorithm of computation of the Poincaré-Liapunov constants
Implementing the arithmetic of $C_3,4$ curves
Magma code written and made available on the web.
Index calculus for abelian varieties and the elliptic curve discrete logarithm problem
Used in calculations.
Involutions in Conway's largest simple group
Magma used in calculations.
Irreducible monomial linear groups of degree four over finite fields
LDPC block and convolutional codes based on circulant matrices
LDPC codes from triangle-free line sets
Linear recurrences with polynomial coefficients and computation of the Cartier-Manin operator on hyperelliptic curves
Local densities and explicit bounds for representability by a quadratric form
"Using Magma on a Celeron 386 JONATHAN HANKE (Coppermine) 1GHz, it takes approximately 17 hours to compute the first 106 Fourier coefficients of 2Q(z), which makes a direct computation up to 2 � 10^11 infeasible."
Local densities of 2-adic quadratic forms
Lucas sequences whose 12th or 9th term is a square
Refers to software performance generally.
"The latest release of Magma now contains Bruin's routines for much of the calculations of this paper."
Mathematics by Experiment
?unable to verify citation: Magma mentioned.
Mathematics on the (Semantic) NET
Maximal quotient rational reconstruction: An almost optimal algorithm for rational reconstruction
Comparison of software performance.
MDS codes over $F_9$ related to the ternary Golay code
Minimal degree liftings of hyperelliptic curves
Minimizing representations over number fields
MuPAD-Combinat, an open-source package for research in algebraic combinatorics
Magma has impressive efficiency but closed development model in C will not scale in the long run
New algorithms for generating Conway polynomials over finite fields
Authors present two new algorithms for generating Conway polynomials that avoid brute force search. One is implemented in Magma
New bounds for $n_4(k,d)$ and classification of some optimal codes over $GF(4)$
New good linear codes by special puncturings
Nice efficient presentations for all small simple groups and their covers
Note on Marsaglia's Xorshift Random Number Generators
Note on the Biweight Enumerators of Self-Dual Codes over $Z_k$
Note on: ``The Diophantine equation $x^n=Dy^2+1$'' by J. H. E. Cohn
On arithmetically equivalent fields with distinct $p$-class numbers
On cubic graphs admitting an edge-transitive solvable group
On minimal factorisations of sporadic groups
On negative orbits of finite Coxeter groups
MRC
On optimal quantum codes
On primitive permutation groups with small suborbits and their orbital graphs
Magma used for calculations.
On quantum MDS codes
On reconstructing $n$-point configurations from the distribution of distances or areas
On the arithmetic of del Pezzo surfaces of degree 2
On the computation of square roots in finite fields
Authors compare their method with Mathematica, Maple and Magma.
On the covering radius of ternary extremal self-dual codes
LatCde
On the cutting edge: Simplified $O(n)$ planarity by edge addition
Refers to work by Lieby in Magma.
On the Diophantine equation $1^k+2^k++x^k=y^n$
Only viewed references. Could not read document
On the Diophantine equation $x^2+a^2=2y^p$
Magma used to find all integral solutions of polynomial equations and for verification.
On the efficiency of some finite groups
MRC
On the graphs of Hoffman-Singleton and Higman-Sims
Magma used for exploration of graphs.
On the structure of nonstabilizer Clifford codes
Packing triangles in a graph and its complement
Permutation decoding for the binary codes from triangular graphs
Point counting on genus 3 non hyperelliptic curves
Polyadic codes revisited
Discuss method to solve the word problem implemented in Magma.
Polynomial factorization algorithms over number fields
Passing reference to software.
Post-Quantum Signatures
Mentions calculation by Allan in Magma.
Properness defects of projections and computation of at least one point in each connected component of a real algebraic set
Our implementation of the algorithm of Roulier, Roy and El Din is based on the Magma Kronecker package by Lecerf which implements the algorithm of Giusti, Lecerf and Slavy. On this basis, we implemented the algorithm of Schost to solve polynomial systems with infinitesimal coefficients.
Quantum and classical studies of vibrational motion of $CH_5$+ on a global potential energy surface obtained from a novel ab initio direct dynamics approach
Quantum Goppa Codes over Hypereliptic Curves
? citation needs verification: Magma used in calculations.
Quasimultiples of geometric designs
Magma used throughout paper for computations and verification.
Quotients of a universal locally projective polytope of type $5,3,5$
Rational torsion of $J_0(N)$ for hyperelliptic modular curves and families of Jacobians of genus 2 and genus 3 curves with a rational point of order 5, 7 or 10
"Made extensive use of...for computations".
Remarks on Clifford codes
Shafarevich-Tate groups of nonsquare order
Used for big calculations,include Magma code for readers.
Slopes of 2-adic overconvergent modular forms with small level
Solving solvable sextics using polynomial decomposition
Some Hadamard matrices of order 32 and their binary codes
Some remarks on flocks
Special polycyclic generating sequences for finite soluble groups
Straight-line programs in polynomial equation solving
Remarks on availability of algorithms discussed in Magma package.
Strong bias of group generators: An obstacle to the ``product replacement algorithm''
Strongly modular lattices with long shadow
Magma used for calculations.
Sur les nombres de Fibonacci de la forme $q^ky^p$
Symmetric informationally complete quantum measurements
Passing reference made to Magma.
Symmetry groups, semidefinite programs, and sums of squares
States that Magma supports invariant theory computations
The Alperin and Dade conjectures for the Conway simple group $Co_1$
The Alperin weight conjecture and Uno's conjecture for the Baby Monster $B$, $p$ odd
Magma used in calculations.
The classification of endo-trivial modules
? Could only view references.
The computational complexity of the Chow form
[45] G. Lecerf, Kronecker, a Magma package for polynomial system solving, available at http://kronecker.medicis.polytechnique.fr/.
The discrete logarithm in logarithmic $l$-class groups and its applications in $K$-theory
Implemented algorithms.
The equivalence between the DHP and DLP for elliptic curves used in practical applications
Author implemented algorithm in Magma.
The graded ring of Hermitian modular forms of degree 2 over $Q(-2)$
The Hasse principle and the Brauer-Manin obstruction for curves
The mechanization of mathematics
The Puzzle Layout Problem
Used in calculations.
The residually weakly primitive geometries of $J_3$
The residually weakly primitive geometries of $M_23$
? sent by Leemans. Could not view to add details
The residually weakly primitive geometries of $PSL(3,q)$ with $q<8$
The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series
Used in calculations. Mentions software.
Toral arrangements
Torelli Actions and Smooth Structures on 4-manifolds
Toric codes over finite fields
Toric surfaces and codes, techniques and examples
Refers to Joyner's work on Toric codes with Magma.
Treillis de codes quasi-cycliques
Unexpected connections between Burnside groups and knot theory
Uniform bounds on the number of rational points of a family of curves of genus 2
Used for computations.
Unitals in the code of the Hughes plane
Magma used for computations
Visualising $Sha[2]$ in abelian surfaces
Weight Enumerators of Duadic and Quadratic Residue Codes
[1] W. Bosma and J. Cannon, The Magma Computational Algebra System for Algebra, Number Theory and Geometry (Version 2.9). Univ. Sydney, 2002.
Weil restriction of an elliptic curve over a quadratic extension
Magma used in computations.
Yet another sieving device
$J_1(p)$ has connected fibers
Used in calculations.
$n$-covers of hyperelliptic curves
Used Magma to check calculations.
2-local amalgams for the simple groups $GL(5,2)$, $M_24$ and $He$
2-local amalgams for the simple groups $GL(5,2)$, $M_24$ and He. II
A class of complete arcs in multiply derived planes
A classical characterization of newforms with equivalent eigenforms in $S_k+1/2(4N,)$
"We are currently developing algorithms to compute the dimensions of the missing subspaces for any speci ed level. (These algorithms use MAGMA and are based on trace formulas of Ross [21], Yamauchi [33], and Saito Yamauchi [22].)"
A cup product in the Galois cohomology of number fields
C. Fieker, R. Sharifi, and W. Stein, Magma code for verifying nontriviality of the pairing for $p = 37$, available from http://abel.math.harvard.edu/$$sharifi/computations.html and http://www.math.arizona.edu/$$wmc Cites Fieker et al. Magma used in calculations.
A GAP package for braid orbit computation and applications
A new class of designs which protect against quantum jumps
A new class of ternary cocyclic Hadamard codes
A new computer construction of the Monster using 2-local subgroups
Magma used in calculations.
A redundant representation of $GF(q^n)$ for designing arithmetic circuits
A short comment on the affine parts of SFLASHv3
A strategy for human-computer study of equations and identities in finite groups
Used in computations.
A systematic construction of self-dual codes
A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer
Algebraic cryptanalysis of hidden field equation (HFE) cryptosystems using Gröbner bases
Compared implementation in several systems including Magma.
Algorithms of Representation Theory
"The most comprehensive systems for computational group and representation theory are GAP and Magma"
An algorithm for computing invariants of linear actions of algebraic groups up to a given degree
An attack on the isomorphisms of polynomials problem with one secret
Another existence and uniqueness proof for McLaughlin's simple group
Application of Gröbner bases to the analysis of certain two or three level factorial designs
Can't access content
Arithmetic of characters of generalized symmetric groups
We have used MAPLE and MAGMA to obtain some of the examples in this paper
(French) [Arithmetic of elliptic curves with supersingular reduction at $p$]
Attacks on Asymmetric Cryptosystems: An Analysis of Goubin's Refined Power Analysis Attack
Used Magma to compute data table.
Automorphism group computation and isomorphism testing in finite groups
Blocking semiovals in $PG(2,7)$ and beyond
Bounds for the number of automorphisms of a compact non-orientable surface
Broué's conjecture for the Hall-Janko group and its double cover
Centralizers of Strongly Real Elements in Finite Groups
Magma used in calculations
Certifying solutions to permutation group problems
Classification of flocks of the quadratic cone over fields of order at most 29
Used in calculations and for verification.
Cohomology Rings of Finite Groups
Magma Computer Algebra. Sydney. 2002.
Combinatorial properties of free algebras of Schreier varieties
Can't access content
Commuting involution graphs for finite Coxeter groups
MRC
Commuting involution graphs for symmetric groups
Magma used in calculations. MRC
Complete spans on Hermitian varieties
Magma used for extensive search for complete spans.
Complexity results for triangular sets
Implemented algorithms.
Computation of Galois groups associated to the 2-class towers of some quadratic fields
Computation of the fundamental units and the regulator of a cyclic cubic function field
Implementation written in Magma.
Computational aspects of hyperelliptic curves
"implemented in Magma by P.van Wamelen"
Computer Algebra System Maple: A New Software Library
Computing homomorphism spaces between modules over finite dimensional algebras
Computing invariants of reductive groups in positive characteristic
Computing minimal generating sets of invariant rings of permutation groups with SAGBI-Gröbner Basis
We ran systematic computations of minimal generating sets of invariant rings of permutation groups with both PerMuVAR and Magma. PerMuVAR and Magma appears to be complementary; depending on the group, both can in turn be up to several orders of magnitude faster than the other. Some further comments are still in order, since their practical behavior are completely different.
Computing parametric geometric resolutions
"40. Lecerf, G.: Kronecker, a package for Magma for polynomial system solving. UMS MEDICIS, Laboratoire GAGE, http:// kronecker.medicis. polytechnique. fr/, 1999"
Computing relations in divisor class groups of algebraic curves over finite fields
Computing the $M=UU^t$ integer matrix decomposition
[Sto01] Michael Stoll. Hyperelliptic curves magma package. http://www.math. uni-duesseldorf.de/~stoll/magma/ or as part of Magma, Version 2.9-23, http://magma.maths.usyd.edu.au/magma/, March 2001.
Computing the equidimensional decomposition of an algebraic closed set by means of lifting fibers
?cites 4 sources. Need to verify them
Computing the multiplicative group of residue class rings
Magma used in calculations.
Computing with matrix groups
"We will make a few comments concerning the expected uses in GAP and Magma of the results presented here."
Congruence subgroups of $PSL(2,Z)$ of genus less than or equal to 24
Conjectures on the character degrees of the Harada-Norton simple group HN
Used Magma in calculations.
Constructing elements in Shafarevich-Tate groups of modular motives
Constructing Elliptic Curves with Prescribed Embedding Degrees
Magma used in calculations.
Constructing pairs of compatible characters
? not verified.
Construction of new extremal self-dual codes
Construction of some extremal self-dual codes
"Two numerical packages for computational group theory are widely used: GAP (Groups, Algorithms, and Programming), which free software, and Magma, costing about $US 1000 for a single license at the time of this writing."
Counting points on an abelian variety over a finite field
Author implemented algorithm.
Cryptanalysis of a Cryptosystem based on Drinfeld modules
Magma used in calculations.
Cubic self-dual binary codes
Used for calculations
We remark that Allan Steel has implemented an SGB algorithm in Version 2.8 of Magma [3] using [15, Corollary 5.13] generalising Fauge` re's algorithm [7] to Galois rings.
Cyclic relative difference sets and their $p$-ranks
Used in calculations.
Datagraphs in algebraic geometry and $K3$ surfaces
Designs in additive codes over $GF(4)$
Determining the automorphism group of a hyperelliptic curve
Magma used for computations.
Efficient solution of rational conics
Even lattices with covering radius $<2$
Magma used for calculation and verification.
Experimental constructions of self-dual codes
By using the software package MAGMA [2], we checked that there are no linear subspaces attaining such a bound for small values of q, n and r.
Extremal self-dual [50, 25, 10] codes with automorphisms of order 3 and quasi-symmetric 2-$(49, 9, 6)$ designs
Extremal self-dual codes over $F_2F_2$
Familles de polynômes liées aux courbes modulaires $X_(l)$ unicursales et points rationnels non-triviaux de courbes elliptiques quotient
Fast algorithms for zero-dimensional polynomial systems using duality
Finite Hurwitz braid group actions on sequences of Euclidean reflections
Magma used to calculate and verify.
Flocks, generalised quadrangles and translation planes from BLT-sets
Used Magma to seach for BLT-sets.
Formally self-dual codes related to Type II codes
Fourth order linear differential equations with imprimitive group
Fundamental domains for Shimura curves
Fundamentals of Error-correcting Codes
?unable to verify
Generalizations of a lemma of Freudenburg
Used to calculate an example to illustrate the main theorem
Generic SBDD Using Computational Group Theory
Authors indicate they could have used Magma for calculations.
Geometric codes over fields of odd prime power order
Geometric Reed-Solomon codes of length 64 and 65 over $F_8$
Geometries for the group $PSL(3,4)$
Graded rings of Hermitian modular forms of degree 2
Magma used to compute the invariant polynomials ."We thank W. Plesken and O. Heidbuchel for their help in the calculations using Magma."
Graph Algebras and Automata
[193] Magma Computational Algebra System, MRC
Group actions on graphs, maps and surfaces with maximum symmetry
Acknowledge Magma and use in computations.
Group extensions and automorphism group rings
Groups of prime-power order with a small second derived quotient
Gröbner Bases and the Computation of Group Cohomology
Site wouldn't load
Harada group uniquely determined by centralizer of a 2-central involution
? Unable to verify
Heegner zeros of theta functions
Used in computations.
High-rate LDPC codes from unital designs
Higher Weierstrass points on $X_0(p)$
Higher weights and graded rings for binary self-dual codes
"Fortunately, there is a wonderful computer algebra package known as Magma [5] that can be used to evaluate seemingly complex probabilities."
Improved upper bounds for the number of points on curves over finite fields
Liouvillian solutions of third order differential equations
Minimal 1-saturating sets in $PG(2,q), q16$
Minimal discriminants for fields with small Frobenius groups as Galois groups
Monomial modular representations and symmetric generation of the Harada-Norton group
Magma used in calculations.
Multidimensional companding quantization of the Gaussian source
Natural existence proof for Lyons simple group
? Unable to verify.
Nested symmetric representation of elements of the Suzuki chain groups
*CFR*
New extremal binary $[44,22,8]$ codes
New extremal type I codes of lengths 40, 42, and 44
Wrote and executed algorithms in Magma; used to verify results.
Nonlinear $p$-ary sequences
Magma used in computations.
Odd order flag-transitive affine planes of dimension three over their kernel
On 2-arc-transitivity of Cayley graphs
On a rank four geometry for the Hall-Janko sporadic group
On a theorem of Artin
Magma used in calculations.
On a theorem of supersoluble automorphism groups
On asymmetric coverings and covering numbers
On binary linear $[160,80,24]$ codes
On extendability of group actions on compact Riemann surfaces
On minimal length factorizations of finite groups
On some designs and codes from primitive representations of some finite simple groups
On the $p$-adic $L$-function of a modular form at a supersingular prime
On the closed image of a rational map and the implicitization problem
On the Gröbner bases of some symmetric systems and their application to coding theory
On the linear complexity of the Sidelnikov-Lempel-Cohn-Eastman sequences
Magma used in calculations.
On the product of two primitive elements of maximal subfields of a finite field
Magma "inspired the method"; used in calculations.
On the sum of two primitive elements of maximal subfields of a finite field
Magma "inspired the method"; used in calculations.
Parallel Algorithms for Computing the Smith Normal Form of Large Matrices
Points rationnels et méthode de Chabauty elliptique
In French
Polynomial equivalence problems and applications to multivariate cryptosystems
Magma used in computations
Projections of binary linear codes onto larger fields
Realizations of Real Low-Dimensional Lie Algebras
arXiv:math-ph/0301029
Regular low-density parity-check codes from oval designs
Used to compute minimum weights.
Residually weakly primitive geometries of small sporadic and almost simple groups: a synthesis
? Use Cayley andd mention Magma.
RWPRI and $(2T)_1$ flag-transitive linear spaces
Self-orthogonal codes from symmetric designs with fixed-point-free automorphisms
Used in calculations and for verification.
Short balanced presentations of perfect groups
Some extremal self-dual codes with an automorphism of order 7
Symmetric presentations for the Fischer groups. I. The classical groups $Sp6(2), Sp8(2)$, and $3O7(3)$
results have been obtained but with (single) coset enumeration carried out by computer, and indeed, we admit that the presentations considered in this paper have all been checked in this way by MAGMA
Symmetries of BLT-sets
No mention in body of text; Presume use in calculations.
The 2-power degree subfields of the splitting fields of polynomials with Frobenius Galois groups
? Could not view text.
The affine primitive permutation groups of degree less than 1000
The AGM-$X_0(N)$ Heegner point lifting algorithm and elliptic curve point counting
Used in computations.
The Alperin weight conjecture and Dade's conjecture for the simple group $J_4$
The Andrews-Curtis conjecture and black box groups
The Arithmetic of Hyperbolic 3-manifolds
Reference in Ch11
The connective $K$-theory of finite groups
MINOR The group G has order 217 and this has been confirmed using MAGMA by M. F. Newman, to whom we are most grateful. MAGMA also showed that G has class 4.
The Fischer-Clifford matrices of a maximal subgroup of $Fi'_24$
No mention in body of text. Presume Magma used in computations.
The GHS attack in odd characteristic
The maximum number of points on a curve of genus 4 over $F_8$ is 25
The residually weakly primitive geometries of $M_22$
The virtual Haken conjecture: experiments and examples
Used in calculations.
Two-variable identities for finite solvable groups
"Not only proofs but even precise statements of our results would hardly be possible without extensive computer experiments".
Ultraconnected and Critical Graphs
Lists Magma source codes.
Unitary error bases: Constructions, equivalence, and applications
Upper bounds on the dual distance of $BCH(255,k)$
Weight distributions of cyclic self-dual codes
Weil descent of Jacobians
2-generator Arithmetic Kleinian groups. III
2-modular lattices from ternary codes
LatCde
A fast algorithm for polynomial factorization over $Q_p$
A fresh approach to the exceptional automorphism and covers of the symmetric groups
Unable to verify.
A group-theoretic method for drawing graphs symmetrically
Algorithm implemented in Magma
A millennium project: Constructing small groups
MRC
A mod five approach to modularity of icosahedral Galois representations
A new scheme for computing with algebraically closed fields
A quasi-symmetric 2-$(49, 9, 6)$ design
Includes link to home page
Algorithms and proofs inheritance in the Foc language
"Even in Axiom [16], Aldor, or Magma, where the user language is a central part of the system, computer algebra issues take precedence over the language design and specification."
Algorithms for function fields
"I would like to thank John Cannon and the Magma group. I implemented most of the above algorithms during a two month stay in Sydney"
An algorithm for computing Weierstrass points
An extension of Kedlaya's algorithm to Artin-Schreier curves in characteristic 2
Used to generate curves suitable for cryptography.
An improved baby step giant step algorithm for point counting of hyperelliptic curves over finite fields
An infinite series of regular edge- but not vertex-transitive graphs
Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree
Authors used sevral systems....including Magma.
Artin presentations. I. Gauge theory, $3+1$ TQFT's and the braid groups
A prominent theme of the paper is that Artin presentations lend themselves to systematic use of computer algebra systems. Many examples are obtained using the system MAGMA.
Attacking a polynomial-based cryptosystem: Polly Cracker
Used extensively in calculations.
Automorphismes des courbes modulaires $X(n)$ en caractéristique $p$
In French. Magma used in computations
The second column gives the number of the group in the Neubueser catalog used in MAGMA and GAP
Bridging semisymmetric and half-arc-transitive actions on graphs
Information processed with Magma
Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture
Used in computations and for verification.
Centralisers of involutions in black box groups
Magma mentioned in relation to software.
Classification of Some Homogenous and Ultrahomogenous Structures
Magma used extensively throughout paper.
Classifying subspaces of Hamming spaces
Codes, designs and graphs from the Janko groups $J_1$ and $J_2$
Comment on: ``A new representation of elements of finite fields $GF(2^m)$ yielding small complexity arithmetic circuits'' by G. Drolet
Computations on modular Jacobian surfaces
Used in calculations.
Computing Generators for Rings of Multiplicative Invariants
Author wrote code and implemented algorithms in Magma.
Computing modular invariants of $p$-groups
Computing Riemann-Roch spaces in algebraic function fields and related topics
Constructing automorphism groups of $p$-groups
Constructing coset geometries with MAGMA: An application to the sporadic groups $M_12$ and $J_1$
Constructive and destructive facets of Weil descent on elliptic curves
Used in calculation: Plan to write code to include in Magma.
Cryptanalysis of a knapsack-like cryptosystem
? unable to view and verify
Degree bounds and lifting techniques for triangular sets
Degree- and time-constrained broadcast networks
Degrees of the elliptic Teichmüller lift
Die Nenner des Kontsevich-Integrals und ein spezieller Drinfeld-Assoziator
In German
Double coverings of Klein surfaces by a given Riemann surface
Used in calculations.
Dual codes of translation planes
Efficient collection in infinite polycyclic groups
Elliptic curves from Mordell to Diophantus and back
Embeddings of $SL(2,27)$ in complex exceptional algebraic groups
Equality in computer algebra and beyond
Explicit computation of Galois $p$-groups unramified at $p$
Explicit Construction of Families of LDPC Codes with Girth at Least Six
Magma used in calculations.
Extending the GHS Weil descent attack
Factoring polynomials and the knapsack problem
Fano 3-folds, $K3$ surfaces and graded rings
Galois representations with conjectural connections to arithmetic cohomology
Generators and relations for the Lyons sporadic simple group
Calculations play a major role in the proof of the main theorem.
Genus 2 curves with $(3,3)$-split Jacobian and large automorphism group
Groebner bases and distance of cyclic codes
Groups acting on products of trees, tiling systems and analytic $K$-theory
Heuristics on lattice basis reduction in practice
Magma mentioned in software discussion.
Homogeneous bent functions, invariants, and designs
Implicitizing without tag variables
Inductive theorem proving and computer algebra in the MathWeb Software Bus
Integral points on punctured abelian surfaces
Acknowledge use of Maagma in body of text.
Invariants and differential Galois groups in degree four
Irreducible decomposition of curves
Jacobi polynomials for singly even self-dual codes and the covering radius problems
LatCde
Matrices, graphs and equivalence relations
Minimal and maximal length involutions in finite Coxeter groups
? Cite 97 Springer; Used Magma in calculations, MRC
Models for a finite universe
NMDS codes of maximal length over $F_q$, $8q11$
Extension process and classification of examples done using Magma.
Noether numbers for subrepresentations of cyclic groups of prime order
Obstacles in two public key cryptosystems based on group factorizations
On 2-Local Amalgams Proving Existence and Uniqueness of $McL$ and $3.McL$
Magma used in calculations.
On arithmetically equivalent number fields of small degree
On pointwise conjugacy of distinguished coset representatives in Coxeter groups
Could not view to add details
On the combinatorial structure of the approval-voting polytope
On the computation of elementary divisors of integer matrices
The L-function calculations below were done using a short program written on Magma.
On the existence of absolutely simple abelian varieties of a given dimension over an arbitrary field
On the height constant for curves of genus two. II
On the homotopy type of the classifying space of the exceptional Lie group $F_4$
MRC
On Weight Distribution of Cyclic Self-Dual Codes
Text of pdf is not searchable
Quadratic double circulant codes over fields
Quadratic Newton iteration for systems with multiplicity
Quantum hidden subgroup algorithms: A mathematical perspective
Quasi-optimal algorithms for multiplication in the extensions of $F_16$ of degree 13, 14 and 15
Random matrix theory over finite fields
Mentioned in discussion computer of systems.
Rational points on hyperelliptic curves and an explicit Weierstrass preparation theorem
Used in calculations.
Representing the quotient groups of a finite permutation group
Magma used for verification.
Revealing the Affine Parts of SFLASHv1, SFLASHv2, and FLASH
Some computations with Hecke rings and deformation rings
Some new results for optimal ternary linear codes
Some non-Gorenstein Hecke algebras attached to spaces of modular forms
Subcodes of the projective generalized Reed-Muller codes spanned by minimum-weight vectors
Symbolic dynamic systems and their invariants
Magma used in calculations.
Ten consecutive primes in arithmetic progression
Ternary code construction of unimodular lattices and self-dual codes over $Z_6$
Magma used for verification
Testing equality in differential ring extensions defined by PDE's and limit conditions
"Except in strongly typed system such as Axiom or Magma, the choice of possible fields is in general very limited."
The 2-generator restricted Burnside group of exponent 7
MRC
The Alperin and Dade conjectures for the O'Nan and Rudivalis simple groups
The calculation of radical ideals in positive characteristic
The character values of the irreducible constituents of a transitive permutation representation
Magma used in calculations.
The compositional inverse of a class of permutation polynomials over a finite field
The lattice of $N$-run orthogonal arrays
The Nonexistence of a Bijective Almost Perfect Nonlinear Function of order 16
The residually weakly primitive geometries of $J_2$
The residually weakly primitive geometries of $M_24$
? Sent by Leemans. Could not view to get details.
The residually weakly primitive geometries of $S_52$
There are genus one curves over $Q$ of every odd index
Used in calculations.
Three-dimensional Galois representations with conjectural connections to arithmetic cohomology
"Wish to thank authors of Magma..", Used to compute and verify.
Toric varieties, Hirzebruch surfaces and error-correcting codes
Refers to extensive calculations by Joyner using Magma.
Transitive permutation groups without semiregular subgroups
Magma used in calculations.
Transportable modular symbols and the intersection pairing
Trinomials $ax^7+bx+c$ and $ax^8+bx+c$ with Galois groups of order 168 and $8168$
Trivalent symmetric graphs on up to 768 vertices
Uniform and natural existence proofs for Janko's sporadic groups $J_2$ and $J_3$
Magma used for computation and verification.
Universal simulation of Hamiltonians using a finite set of control operations
Variants of product replacement
Vertex partitioning of a class of digraphs
Magma used in calculations.
Visibility of Shafarevich-Tate groups of abelian varieties
VLSI Aspects on Inversion in Finite Fields
Magma used to find irreducible polynomials
Weighted Grassmannians
Mentions Magma's database.
$(p,q,r)$-generations of the Conway group $Co1$ for odd $p$
Can't access content
$S$-integral points on elliptic curves. Notes on a paper of B. M. M. de Weger
A geometric construction of an optimal $[67,9,30]$ binary code
A Gröbner free alternative for polynomial system solving
A new computer construction of the irreducible 112-dimensional 2-modular representation of Janko's group $J_4$
Magma used for computation and verification.
A new existence proof for Ly, the sporadic simple group of R. Lyons
A note on line-Baer subspace partitions of $PG(3,4)$
Furthermore, the fact that v3 , v5 , v7 , v9 is a radical ideal (this is tested by using the algebraic package MAGMA), and the fact that its zero set coincides with the set of centers of F, we have that, for n vn rad (v3, v5, v7, v9) = v3, v5, v7, v9 and hence B(F) = 4.
A trace conjecture and flag-transitive affine planes
Uses results verified by computations done in Magma.
[MA] Bosma W., Cannon J., MAGMA (University of Sydney), 1994.
Algorithms in pure mathematics
Magma mentioned in general discussion.
An extension of Kedlaya's point-counting algorithm to superelliptic curves
Used Magma in calculations; Implemented algorithm.
Analysis of the GHS Weil descent attack on the ECDLP over characteristic two finite fields of composite degree (extended abstract)
Used several computer algebra systems,including Magma
Applications of algebraic curves to constructions of sequences
Asymptotic $K$-theory for groups acting on $A_2$ buildings
Attacking the affine parts of SFLASH
In chapter: Gyrogroups: Modeled on Einstein'S Addition
Bhaskar Rao designs and the alternating group $A_4$
Binary optimal odd formally self-dual codes
Used Magma to verify calculations.
Black box classical groups
Blocking semiovals of type $(1,M+1,N+1)$
Unable to view text. Citation verified.
Bounding minimum distances of cyclic codes using algebraic geometry
Calculating group cohomology: Tests for completion
Very supportive of Magma ,recommend.
Certain cyclically presented groups are infinite
Challenges in mathematical computing
Check character systems and anti-symmetric mappings
Refers to computations by Giesse with Magma.
Class number relations from a computational point of view
Classification of formally self-dual even codes of lengths up to 16
Clouds over a public key cryptosystem based on Lyndon words
Complex structures on nilpotent Lie algebras
Magma used to check cohomological data. MRC
Computers in algebra: New answers, new questions
Computing automorphism groups of finite groups
Computing double cosets in soluble groups
Computing the Galois group of a linear differential equation of order four
Computing the subgroups of a permutation group
Constructing critical indecomposable codes
Mentions Cayley
Construction of large permutation representations for matrix groups II
Magma used in calculations.
Constructions in finite geometry using computer algebra systems
Cuspidal modular symbols are transportable
Computations done in Magma.
Cyclic matrices and the MEATAXE
Derived Equivalences for Group Algebras
Magma used extensively in calculations; appendix of codes.
Determination of all regular maps of small genus
Used in checking and confirming calculations
Duadic codes over $F_2+uF_2$
Efficient Enumeration of Extensions of Local Fields with Bounded Discriminant
Embeddings of $DI2$ in $F4$
19 pages didn't search them all
Used in calculations, provides programming routines.
Factorizations of Cunningham numbers with bases 13 to 99: Millennium edition
Fast recognition of classical groups over large fields
Field theory and the cohomology of some Galois groups
Generating maximal subgroups of sporadic simple groups
Also cites BoCa Handbook of Cayley Functions: Used to check calculations.
Giesbrecht's algorithm, the HFE cryptosystem and Ore's $p^s$-polynomials
Gyrogroups and the decomposition of groups into twisted subgroups and subgroups
Géométries des groupes $PSL(3,q)$, $q<7$
? sent by Leemans. could not view to add details
Harmonic weight enumerators of nonbinary codes and MacWilliams identities
Hecke module structure of quaternions
Heteroclinic cycles and wreath product symmetries
Implementing 2-descent for Jacobians of hyperelliptic curves
Interrelationships between orthogonal, unitary and symplectic matrix ensembles
Results can be verified (using Magma, for instance)
Intersection-number operators for curves on discs. II
Used in calculations.
Iterative decoding of codes from oval designs
Janko's simple groups $J_2$ and $J_3$ are irreducible subgroups of $SL_85(5)$ with equal centralizers of an involution
Konkrete Charaktertafeln und kompatible Charaktere
Can't access content
Linear groups over $GF(2^k)$ generated by a conjugacy class of a fixed point free element of order 3
Magma used for calculations.
Loopholes in two public key cryptosystems using the modular group
Matrix generators for exceptional groups of Lie type
Megamaps: Construction and examples
Used in computation.
Modular forms, lattices and spherical designs
New binary codes from a chain of cyclic codes
New extremal self-dual codes of lengths 36, 38, and 58
New Good Hermitian Self-Dual Codes over $GF(4)$
Note on the $g$-fold joint weight enumerators of self-dual codes over $Z_k$
On a family of cyclically-presented fundamental groups
On a rank five geometry of Meixner for the Mathieu group $M_12$
On a result of Cameron and Praeger on block-transitive point-imprimitive $t$-designs
"Using DISCRETA, GAP or MAGMA..."
On additive $GF(4)$ codes
On extremal additive $F_4$ codes of length 10 to 18
On homogeneous bent functions
On Liouvillian solutions of linear differential equations of order 4 and 5
On narrow hexagonal graphs with a 3-homogeneous suborbit
On the classification of extremal even formally self-dual codes of lengths 20 and 22
Magma used extensively in computations.
On the existence and uniqueness of the sporadic simple groups $J_2$ and $J_3$ of Z. Janko
On the invariants of the quotients of the Jacobian of a curve of genus 2
On the number of inductively minimal geometries
On the Petrials of thin rank 3 geometries
"We submitted the question to programs written in Magma.".
On the relation between upper central quotients and lower central series of a group
On type II codes over $F_4$
Optimal double circulant $Z_4$-codes
Orthogonal frames in the Leech lattice and a type II code over $Z_22$
Magma used to verify calculations.
Parallel GAP: Mature interactive parallel computing
Permutations amongst the Dembowski-Ostrom polynomials
Regular hyperbolic fibrations
Magma used in computation and for verification..
Representing subgroups of finitely presented groups by quotient subgroups
RWPRI geometries for the alternating group $A_8$
Magma used in calculations.
Solvability by radicals from an algorithmic point of view
Finding polycyclic generating sequences...is routine..Magma.
Solving the Birkhoff Interpolation Problem via the Critical Point Method: An Experimental Study
Some applications of Magma in designs and codes: Oval designs, Hermitian unitals and generalized Reed-Muller codes
Some geometry of the isomorphism $Sp(4,q)O(5,q)$, $q$ even
Magma used in calculations.
Some introductory remarks on computer algebra
Some rank five geometries related to the Mathieu group $M_23$
Sporadic simple groups which are completions of the Goldschmidt $G_3$-amalgam
Extensive use of Magma in calculations.
Strong Gröbner bases for polynomials over a principal ideal ring
In French
The form of these mappings was found with extensive searching and experimentation using the software package MAGMA
Supersingular curves in cryptography
Magma used in calculations.
Symmetric powers of modular representations for groups with a Sylow subgroup of prime order
Ternary dual codes of the planes of order nine
The cohomology of the Sylow 2-subgroup of the Higman-Sims group
Used in calculations.
The computational matrix group project
Quote in intro: "However, I must first and fore- most acknowledge the importance of the group theory packages GAP [GAP] and MAGMA [BCP] (alphabetical order) without which we could not move"
The groups of order at most 2000
The non-compact arithmetic generalised triangle groups
Used in calculations.
The product replacement algorithm and Kazhdan's property (T)
The zero-divisor graph of a commutative ring: II
Toric morphisms between $p$-compact groups
Used to compute admissible homomorphisms.
Triangular Surface Tiling Groups for Low Genus
Used extensively for calculations.
Unitals in finite Desarguesian planes
Magma search to verify calculations.
What do we know about the product replacement algorithm?
Mentioned on page 302
$$-covers of graphs
Magma used in calculations.
2-groups with few conjugacy classes
3-colored 5-designs and $Z_4$-codes
"The author would like to thank...A. Steel for his help regarding Magma computations"
A Hensel lifting to replace factorization in list-decoding of algebraic-geometric and Reed-Solomon codes
A Note on Timing Attacks Based on the Evaluation of Polynomials
A systematic approach to symmetric presentations II: Generators of order 3
Abstract data types in computer algebra
However, Axiom and Magma cannot be said to be "pure" Abstract Data Type systems. Building them has thrown up many research issues, of which we have highlighted the following 1. The problem of coercion (see section 4). 2. (closely related to the above) the meaning of "isomorphic" (see section 6.1). 3. The interplay between mathematical equality and data-structure equality (see section 5). 4. The proper handling of operators such as factor, whose action depends on the type of the arguments, as well as the value, and therefore is contrary to order-sorted algebra (see section 6.3)
Advanced Topics in Computational Number Theory
Content is locked
Advances in Cryptology---Eurocrypt 2000
Algebraic curves over finite fields and MAGMA
In Italian. Can't access content
Algebraic invariants of graphs; A study based on computer exploration
arXiv:0812.3082 (2008 revision)
Algorithms for polynomials in two variables
Mention of code available in Magma.
An algorithm for solving the discrete log problem on hyperelliptic curves
Algorithm implemented in Magma.
An analysis of Chen's construction of minimum-distance five codes
An enumeration of 1-perfect binary codes
An improved method for generating the centralizer of an involution
Magma used in calculations.
An infinite family of Petersen geometries with nonlinear diagram
An introduction to cocyclic generalised Hadamard matrices
Baer subgeometry partitions
Magma used in calculations
Binary quasi-cyclic Goppa codes
Used in a computation.
Caps embedded in the Klein quadric
Cited, but no references and no actual use of citation, which is very strange
Cayley type graphs and cubic graphs of large girth
Magma used in calculations.
Chazy classes IX--XI of third-order differential equations
Classical groups in dimension 3 as completions of the Goldschmidt $G_3$-amalgam
Cohomology of the double cover of the Mathieu group $M_12$
Magma used in calculations.
Component groups of quotients of $J_0(N)$
Computer algebra methods for equivariant dynamical systems
Reference contained in chapter 1 Grobner bases and chapter 2 Algorithms for the computation of invariants and equivariants
Computing 2-cocycles for central extensions and relative difference sets
Computing the Galois group of a polynomial using linear differential equations
Constructing a short defining set of relations for a finite group
Constructing endomorphism rings via duals
Constructing hyperbolic manifolds
Used in calculations.
Constructions for octonion and exceptional Jordan algebras
Counting crystallographic groups in low dimensions
Counting points on hyperelliptic curves over finite fields
Decomposing a matrix into circulant and diagonal factors
Each invertible sharply $d$-transitive finite permutation set with $d4$ is a group
Elementary 2-group character codes
Explicit Approaches to Modular Abelian Varieties
"I wish to thank....the Magma group for their computational support.". Algorithms implemented in Magma.
Explicit Galois realization of transitive groups of degree up to 15
Magma used for calculations.
Factoring polynomials over $p$-adic fields
Freeness, linear disjointness, and implicitization---a classical approach
Galois group computation for rational polynomials
1X For Steps 1 and 2 we use the algorithms implemented in Magma (Kemper and Steel, 1999). Step 2 is the most expensive one of our algorithm.
Goppa and related codes invariant under a prescribed permutation
Graded Lie algebras of maximal class. II
HNO97 G. Havas, M. F. Newman, and E. A. O Brien, ANU p-quotient program version . 1.4 , written in C, available as a share library with GAP and as part of Magma, or from http:rrwwwmaths.anu.edu.aurservicesrftp.html, School of Mathematical Sciences, Australian National University, Canberra, 1997.
Graded rings and birational geometry
Used to verify calculations.
Groups, transversals, and loops
Used magma in computations
Gröbner bases applied to finitely generated field extensions
Heteroclinic cycles and wreath product symmetries
This seems identical to the one above.
Hyperbolic trigonometry in the Einstein relativistic velocity model of hyperbolic geometry
Multiplication table of a nongyrocommutative gyrogroup of order 16 is generated using Magma
Integration of Deduction and Computation
Designed and implemented interfaces between...DTP and Magma.
Involutory decomposition of groups into twisted subgroups and subgroups
unable to access to verify
Isodual codes over $Z_2k$ and isodual lattices
LatCde
Lie Algebras: Theory and Algorithms
References group and program with no website, also reference in review, MRC
Lie powers of the natural module for $GL(2)$
MRC
Linearly equivalent actions of solvable groups
Maximal 2-extensions with restricted ramification
Minimum-weight codewords as generators of generalized Reed-Muller codes
Mixed partitions of projective geometries
New geometries for finite groups and polytopes
On a sequence of cyclic codes with minimum distance six
On cocyclic weighing matrices and the regular group actions of certain Paley matrices
On Computing a Separating Transcendence Basis
On extremal additive $F4$ codes of length 10 to 18
On some maximal Galois coverings over affine and projective planes. II
Can't access content
On stably decomposing products of classifying spaces
On the data structure straight-line program and its implementation in symbolic computation
On the largest conjugacy class size in a finite group
On the Minimum Distance of some Quadratic-Residue Codes
Optimal subcodes of second order Reed-Muller codes and maximal linear spaces of bivectors of maximal rank
Ovoids of parabolic spaces
Software not named but corresponding MSc cites Magma for computations
Perfect Baer subplane partitions and three-dimensional flag-transitive planes
Magma used to verify calculations.
Projective character degree patterns of 2-groups
Proving a group trivial made easy: A case study in coset enumeration
Rank 2 geometries of the group $PSL(2,q)$
? sent by Leemans. could not view to add details
Recent progress and prospects for integer factorisation algorithms
Used Lenstra's implementation of PP-MPQS in the Magma package.
Recognizing simple subextensions of purely transcendental field extensions
Rigidity theorems for a class of affine resolvable designs
Root systems for two dimensional complex reflection groups
Magma used in computations.
Some aspects of finite linear groups: a survey
Some linear representations of braid groups
Magma used in calculations.
Some new codes from algebraic curves
Split group codes
Sporadic groups and automorphisms of linear spaces
Symmetric powers of modular representations, Hilbert series and degree bounds
Tensor products of representations of the symmetric groups and related groups
The canonical height of an algebraic point on an elliptic curve
Authors grateful to John Cannon for implementing our algorithm in Magma
The product replacement algorithm is polynomial
The regular projective solution space of the figure-eight knot complement
The residually weakly primitive geometries of the dihedral groups
The residually weakly primitive pre-geometries of the Suzuki simple groups
The strongly perfect lattices of dimension 10
Magma used for calculations.
Reference is NOT present in MR1892843 (2003d:11088)
Torsion endo-trivial modules
Magma used for performing homological algebra calculations for modules over basic algebras; author gives personal thanks.
Treating the exceptional cases of the MeatAxe
could not access but Magma mentioned in abstract
Two short presentations for Lyons' sporadic simple group
Weakness in the $SL_2(F_2^n)$ hashing scheme
$C$-extensions of the Petersen geometry for $M_22$
Magma used in calculations
A group-theoretic framework for the construction of packings in Grassmannian spaces
A new existence proof of Janko's simple group $J4$
could not access but Magma mentioned in abstract
A polynomial-time theory of black box groups. I
"Many of the algorithms referred to below have not been shown to run in polynomial time. However, implementations in GAP and Magma are available with impressive test data; they work even in dimensions over 100."
A presentation for the Lyons simple group
We refer to [1] for this fact, which was checked using the computer algebra system MAGMA.
A recognition algorithm for non-generic classical groups over finite fields
Can't access content
A survey of computational class field theory
Addenda and errata: ``Extended GCD and Hermite normal form algorithms via lattice basis reduction''
Algebraic geometry and computer vision: Polynomial systems, real and complex roots
"More modern (starting 1980) are Maple, Mathematica, Derive, Magma (which does algebra, number theory and geometry), and Axiom (the heir of the Scratchpad system)."
An algorithm to calculate optimal homogeneous systems of parameters
An atlas of regular thin geometries for small groups
An atlas of residually weakly primitive geometries for small groups
?sent by Leemans. Unable to view to add details.
Automated deduction---CADE-16
System Description: MATHWEB, an Agent-Based Communication Layer for Distributed Automated Theorem Proving "Computer Algebra Systems. There are services wrapping the systems Maple, MagMa, GAP and CAS (see [KKS98] for references). Here, the MathWeb approach is particularly interesting, since a licensee of commercial software systems like Maple and MagMa can export the corresponding services to the deduction community."
Automorphism groups of certain non-quasiprimitive almost simple graphs
Basic algorithms for rational function fields
Binary codes of odd-order nets
"The electronic computations were done with MAGMA"
Binary optimal linear rate $1/2$ codes
Brill-Noether Algorithm Construction of Geometric Goppa Codes and Absolute Factorization of Polynomials
Central configurations of the 5-body problem with equal masses in three-dimensional space
Classifying 2-groups by coclass
Prepared electronic files for use in Magma ... implemented algorithms.
Paper includes magma code, Key Laboratory of Mathematics-Mechanization (KLMM) Academy of Mathematics and Systems Sciences Academia Sinica
Thanks John Cannon for a review copy of Magma
Complete systems of lines on a Hermitian surface over a finite field
Magma used in computations.
Computation of invariants for reductive groups
Passing reference."Kemper wrote the INVAR package for the computer algebra system Maple and his algorithms have been implemented in Magma too."
Butler, G. and Cannon, J. Cayley V4
Computing immersed normal surfaces in the figure-eight knot complement
Computing second cohomology of finite groups with trivial coefficients
Computing subgroups invariant under a set of automorphisms
Computing with abelian sections of finitely presented groups
1. W. Bosma and J. Cannon, MAGMA Handbook, University of Sydney, 1993.
Construction of an extremal self-dual code of length 62
Counterexamples to a conjecture of Lemmermeyer
Cyclic codes and self-dual codes over $F_2+uF_2$
Decomposing algebraic varieties
Decomposing systems of polynomial equations
Engel-4 groups of exponent 5. II. Orders
Enumerating $p$-groups
Enumerating prime-power homotopy $k$-types
Explorations in Nielsen periodic point theory for the double torus
Factorization of the tenth Fermat number
Acknowledgment to John Cannon for access to Magma.
Gauss sums, Jacobi sums, and $p$-ranks of cyclic difference sets
Used in calculations.
Generalized cyclotomic codes of length $p_1^e_1p_t^e_t$
Geometric codes over fields of odd prime power order
Gröbner bases, invariant theory and equivariant dynamics
Géométries résiduellement faiblement primitives de pitits groupes affins
? sent by Leemans. could not view to add details
Hyperbolic fibrations of $PG(3,q)$
Magma used in examining specific examples for small values of q
Intelligent front-end for solving differential and non-linear equations systems
Intersections, ideals, and inversion
Magma mentioned in passing.
Invariant fields of finite irreducible reflection groups
Inviluppi di $k$-archi in piani proiettivi sopra campi finiti e basi di Gröbner
"Per calcolare l'inviluppo di tale arco (unico perché k > 2t) é stato implementato un algoritmo elementare in MAGMA cosí strutturato"
Jacobi polynomials, type II codes, and designs
Minimum weight and dimension formulas for some geometric codes
Used Magma in computations.
New algorithms for generating Conway polynomials over finite fields
Can't access content
New extremal self-dual codes of lengths 36 and 38
On $Z_4$- and $Z_9$-linear lifts of the Golay codes
On a geometry of Ivanov and Shpectorov for the O'Nan sporadic simple group
On cyclic groups of automorphisms of Riemann surfaces
Used to verify results.
On harmonic weight enumerators of binary codes
Used to compute auto groups.
On the automorphism groups of quasiprimitive almost simple graphs
On the classification of extremal even formally self-dual codes
On the crosscorrelation of sequences over $GF(p)$ with short periods
On the depth of the invariants of the symmetric power representations of $SL_2(F_p)$
Ovoids of Parabolic and Hyperbolic Spaces
Acknowledges help for computations done in Magma.
Packing Planes in Four Dimensions and Other Mysteries
arXiv:math.CO/0208017v1
Polynomial-time computation in matrix groups
Cites Cannon, Cayley: Mentions Gap and Magma as important tools for profound discoveries in group theory
Primitive prime divisor elements in finite classical groups
Problems in the calculation of group cohomology
Quantum BCH Codes
Reconstructing simple group actions
Mentions Magma along with other software.
Representing group codes as permutation codes
Mentions groups databases.
Simulating quantum operations with mixed environments
Magma used in calculations.
Solving some overdetermined polynomial systems
Some algorithms in invariant theory of finite groups
Some challenging group presentations
Some error-correcting codes and their applications
"Magma is a good computational tool for this type of problem"
Some results on the Derived Series of Finite $p$-groups
Used in calculation.
Some sets of type $(m,n)$ in cubic order planes
Highly computer dependent constructions using...Magma.
Speeding up the discrete log computation on curves with automorphisms
Magma used in calculations.
Sphere Packings, Lattices and Groups
? unable to verify
Symmetric generation and existence of the Janko group $J1$
System Description: MATHWEB, an Agent-Based Communication Layer for Distributed Automated Theorem Proving
The Alperin and Dade conjectures for the Fischer simple group $Fi_23$
The cohomology of the sporadic groups $J_2$ and $J_3$
The group of automorphisms of cyclic extensions of rational function fields
for calculations
The groups of order at most 1000 except 512 and 768
The minimal basis for the centre of an Iwahori-Hecke algebra
The minimum distance of the $[137,69]$ binary quadratic residue code
The minimum distance of the $[83,42]$ ternary quadratic residue code
The module structure of a group action on a polynomial ring
"Acknowledgement. We wish to thank Dikran Karagueuzian for providing the computer calculations using Magma [4] that motivated this work."
The rank 3 geometries of the simple Suzuki groups $Sz(q)$
The residually weakly primitive geometries of the Suzuki simple group $Sz(8)$
The zero-divisor graph of a commutative ring
Three-dimensional presentations for the groups of order at most 30
Used in calculations.
Triangular sets for solving polynomial systems: A comparative implementation of four methods
Type II codes over $F_2+uF_2$
Type II codes, even unimodular lattices, and invariant rings
Using Cartan subalgebras to calculate nilradicals and Levi subalgebras of Lie algebras
We have implemented the algorithms described in this paper using the library of Lie algebra functions in the package ELIAS, which is built inside the computer algebra systems GAP4 and Magma
Zeta functions of crystallographic groups and analytic continuation
A determination of the weight enumerator of the code of the projective plane of order 5
A family of optimal packings in Grassmannian manifolds
A local strategy to decide the Alperin and Dade conjectures
A note on arc-transitive circulants
A procedure to calculate torsion of elliptic curves over $Q$
Software performance ccomparison.
A recognition algorithm for classical groups over finite fields
Authors implemented algorithm.
ALL TYPES: An Algebraic Language and TYPE System
Mentioned in software discussion.
An algorithm for solving the factorization problem in permutation groups
Magma mentioned in software discussion
Application of the Bruhat--Tits tree of $SU_3(h)$ to some $A_2$ groups
Bases of minimum-weight vectors for codes from designs
Beiträge zum Entwurf schneller Spektraltransformationen
Caps embedded in Grassmannians
Magma used to combine full Singer line orbits and a unique short line orbit to produce a cap.
Classification of extremal double circulant self-dual codes of lengths 64 to 72
Classification of RWPRI Geometries for the Suzuki Simple Groups
Codes and finite geometries
Computational invariant theory
? unable to verify
Computing in groups with exponent six
Computing in the composite $GF(qm)$ of characteristic $2$ formed by means of an irreducible binomial
Can't access content
Computing local invariants of quantum-bit systems
Computing local invariants of quantum-bit systems
Conjugacy in groups of upper triangular matrices
the assertion was confirmed in two different ways using the computer algebra system Magma
Constructions for cubic graphs with large girth
Refers to work done by Conder in Magma
Crystallographic algorithms and tables
Deciding isomorphism of Lie algebras
The Magma System for Algebra, Number Theory and Geometry, Computational Algebra Group, School of Mathematics and Statistics, University of Sydney, Australia.
Del Pezzo Surfaces and the Brauer-Manin Obstruction
Used extensively in calculations.
Descriptions of groups of prime-power order
Discussion on algorithm development generally.
Design of regular nonseparable bidimensional wavelets using Gröbner basis techniques
"There is a Gröbner function in every computer algebra system (Maple, Mathematica, Axiom, ), but it must be emphasized that these implementations are very inefficient compared with recent software; even the specialized software (Magma, Singular, Macaulay, Asir) are unable to solve the most difficult systems of the paper. Two of the authors have developed efficient C/C++ software in their respective field"
Double circulant self-dual codes over $Z_2k$
Enantiomeric labelling of reaction graphs
Erratum: ``Conjugacy in groups of upper triangular matrices'' [J. Algebra 202 (1998), no. 2, 704--711; MR1617655 (99b:20011)]
erratum
Extended GCD and Hermite normal form algorithms via lattice basis reduction
Finding a finite group presentation using rewriting
Finite quaternionic matrix groups
Magma used in calculations.
Geometries of small almost simple groups based on maximal subgroups
Gröbner bases and invariant theory
Linear sections of $GL(4,2)$
Matrix generators for the orthogonal groups
Nearly linear time algorithms for permutation groups: an interplay between theory and practice
Bosma, W. and Cannon, J.: A Handbook of Cayley Functions, Computer Algebra Group, Univ. Sydney, 1991.
On flag-transitive incidence geometries of rank 6 for the Mathieu group $M_12$
On groups with a finite nilpotent upper central quotient
On isomorphisms of finite Cayley graphs
Magma used in calculations.
On the computation of certain homotopical-functors
On transitive permutation groups
Groups listed according to degree in the order in which they were published....(as used in Magma)
Partial fraction decomposition in $C(z)$ and simultaneous Newton iteration for factorization in $C[z]$
Polynomial codes and finite geometries
Primality proving using elliptic curves: An update
Problems in the Steenrod algebra
Quantum error correction via codes over $GF(4)$
Semiclassical parabolic systems related to $M_24$
Simple 8-designs with small parameters
Simple groups in computational group theory
Magma mentioned in software discussion
Some root invariants and Steenrod operations in $Ext_A(F_2,F_2)$
The construction given here was originally obtained by extensive computer experimentation using the package MAGMA
Symmetric presentations and orthogonal groups
Testing modules of groups of even order for simplicity
Magma used in calculations and as a benchmark.
The Algorithmic Resolution of Diophantine Equations
Author states that "access to Magma is desirable".
The cohomology of the Lyons group and double covers of alternating groups
Some of the calculatons in this papeer were first performed or susequently checked using Magma. We thank the Magma project for their assistance in the use of this valuable tool"
The cohomology of the regular semisimple variety
The Meataxe as a tool in computational group theory
? could not view to verify
The rank 2 geometries of the simple Suzuki groups $Sz(q)$
? sent by Leemans. could not view to add details
The residually weakly primitive geometries of the Janko group $J_1$
The shadow theory of modular and unimodular lattices
The weight enumerator of the code of the projective plane of order 5
See also MR1759017
Thin geometries for the Suzuki simple group $Sz(8)$
Trades and Defining Sets: Theoretical and Computational Results
Walks on generating sets of groups
"The Cellar et al. algorithm is...being implemented in both "Magma" and "Gap""
A new algorithm for the computation of canonical forms of matrices over fields
A use of computers to teach group theory and introduce students to research
In this case the software system was CAYLEY (which has now been developed into a broader computer algebra system Magma). One outcome was a joint publication by the class
Algorithms for Modular Elliptic Curves
Unable to view and verify, but there is at least a passing mention
An introduction to computational group theory
Software discussion. Cites: Computational Group Theory I, II from J. Symbolic Comput. 1990, 1991
Binary codes of structures dual to unitals
Buekenhout-Tits unitals
Calculating Invariants of Modular Reflection Groups with Magma
Tutorial in use of Magma to compute invariants.
Calculation of direct summands of $FG$-modules
"The main idea of this preprocessor is to reduce the difficulty of computing large modules by decomposing them roughly into direct summands and then applying Schneider's algorithm. This preprocessor is implemented as a procedure based on the algebra system MAGMA"
Classification of extremal double circulant formally self-dual even codes
Classification of some optimal ternary linear codes of small length
Classification of two genera of 32-dimensional lattices of rank 8 over the Hurwitz order
Passing acknowledgment.
Cocyclic Hadamard matrices and Hadamard groups are equivalent
Codes for the quantum erasure channel
Computational group theory in St.~Petersburg
Passing reference to Magma and other systems
Computational results for the known biplanes of order 9
Computer Algebra Software
Listed along with other software.
Computing chief series, composition series and socles in large permutation groups
From review: "The algorithm is implemented in Magma, and its performance, demonstrating significant gains over previous approaches, for a large range of examples is reported."
Computing Ext algebras for finite groups
Used in calculations; mentions Magma and Cayley
Computing Sylow subgroups in permutation groups
Computing with subfields
Discussion re algorithm implementation in Magma.
[1] BOSMA, W., CANNON, J. J., AND PLAYOUST, C. The Magma algebra system. School of Mathematics and Statistics, University of Sydney, 1996.
Constructing permutation representations for matrix groups
Cites several Cannon Technical Reports. "One strategy is to ... then to use either ... or the deterministic Brownie-Sims Verify routine ... in Magma"
Construction of classes of subgroups of small index in $p$-groups
Calculations comparing Magma with C-programme.
Double circulant codes over $Z_4$ and even unimodular lattices
LatCde
Engel-4 groups of exponent 5
Graded Lie algebras of maximal class
G. Havas, M. F. Newman, and E. A. O Brien, ANU p-quotient program ... and as part of Magma
Inscribed bundles, Veronese surfaces and caps
Magma is also quoted in the frontmatter do I reference it?
Lattices of compatibly embedded finite fields
Low Rank Representations and Graphs for Sporadic Groups
On full automorphism groups of Riemann surfaces
Used in calculations
On the computation of conjugacy classes in permutation groups
Could not view
On the nilpotent multipliers of a group
Optimal permutation codes for the Gaussian channel
Order Sorted Computer Algebra and Coercions
? Needs verification.
Partition graphs for finite symmetric groups
Polygonal graphs: New families and an approach to their analysis
Polynomial time algorithms for modules over finite dimensional algebras
Mentioned along with other software.
Recent developments in the cohomology of finite groups
Use to find low-dimensional generators for cohomology of p-group.
Relative resolvents and partition tables in Galois group computations
Replaceable nests
Sign patterns of nonnegative normal matrices
Some algorithms for nilpotent permutation groups
From review: "Implementations in GAP and Magma are practical for degrees large enough to present difficulties for general-purpose methods. "
Some transitive Steiner triple systems of Bagchi and Bagchi
Subexponential algorithms for class group and unit computations
Teaching computational abstract algebra
The 2-Compact Groups in the $A$-Family are $N$-Determined
Used in calculations.
The Alperin and Dade conjectures for the simple Held group
The Magma algebra system. I. The user language
Thue and Thue-Mahler equations over rings of integers
Trying to do group theory with undergraduates and computers
packages such as Magma, which is a revamping of Cayley, or GAP are essential for abstract algebra because they enable students to respond to questions by experimenting with meaningful examples.
Two nearly isomorphic groups
Using the Magma computer algebra system in abstract algebra courses
A systematic approach to symmetric presentations I: Involutory generators
All geometries of the Mathieu group $M_11$ based on maximal subgroups
Also used Cayley
Application of computers to questions like those of Burnside. II
Cacti, braids and complex polynomials
Acknowledged use in computations.
Central factors of deficiency zero groups
Computation of Nielsen numbers for maps of closed surfaces
Computational aspects of curves of genus at least 2
"it seems reasonable to expect that within a few years, packages will be available for doing genus-2 computations analogous to the elliptic curve computations that are currently possible in PARI, Magma, SIMATH, apecs, and the "Elliptic Curve Calculator." "
Computational aspects of Kummer theory
The basic algorithms for calculating an integral basis, the unit and the class group (of absolute extensions) are already implemented in computer algebra systems like KANT, MAGMA and PARI.
Computing matrix group decompositions with respect to a normal subgroup
Construction d'une extension régulière de $Q(T)$ de groupe de Galois $M_24$
In French
Dade's conjecture for the Tits group
Density computations for real quadratic units
Designs and codes: an update
Extendable Steiner designs from finite geometries
Extensions of irreducible representations
The new method has been implemented in the language of the Magma system
Groups of deficiency zero
However, this time it is not clear why in general larger cliques cannot exist. For q = 9 the clique number of GI is 6 (one can find a 6-arc of interior points which forms a maximum clique), but for all other odd q with 3 <q 627 it has been verified using the software package Magma that the clique number is i(q - 1). Again very little is known about the maximal cliques of G that are not maximum.
Multilinear algebra and chess endgames
On lattices over number fields
Couldn't access content
On the computation of quadratic $2$-class groups
On the list of finite primitive permutation groups of degree $50$
Reed-Muller codes and Hadamard designs from ovals
Symbolisches Lösung mathematischer Probleme durch Kooperation algorithmischer und logischer Systeme
A lot of references
Symmetric representation of the elements of the Janko group $J_1$
Testing reducibility of linear differential operators: A group-theoretic perspective
The complexity of algorithms
? Cayley citation. Discussion on software.
The state of the art in the computation of Kazhdan-Lusztig polynomials
An implementation of the elliptic curve integer factorization method
An improvement on the Erdos bound for graphs of girth 16
An introduction to MAGMA (Japanese)
only viewed the contents page
An invitation to computational group theory
Computation of cyclotomic polynomials with Magma
Computing automorphism groups of $p$-groups
Also used Cayley
Computing finite soluble quotients
Computing Schur multipliers and tensor products of finite groups
Mentions Cayley
Construction of groups and the constructive approach to group actions
Constructions for arc-transitive digraphs
Exploiting Symmetry on Parallel Architectures
Magma mentioned as being useful.
Finite groups and geometries: A view on the present state and on the future
Generating random elements of a finite group
Generators for the group of units of $Zn$
CHECK that Magma is used
Groups acting simply transitively on the vertices of a building of type $A_n$
Hyperbolic pyritohedra constructed from the Coxeter group $[4,3,5]$
Low index subgroups used to enumerate complements of the subgroup <b,c,d> in [4,3,5]
Large Cayley graphs and digraphs with small degree and diameter
Linear codes and doubly transitive symmetric designs
Minimal-energy clusters of hard spheres
Necessary conditions for Liouvillian solutions of (third order) linear differential equations
On Hadamard matrices from resolvable Steiner designs
On the computation of ordinary irreducible representations of finite groups
Projective injections of geometries and their affine extensions
? Sent by Leemans. Could not view to get details.
Selecting base points for the Schreier-Sims algorithm for matrix groups
Semi-automated theorem proving -- the impact of computers on research in pure mathematics
? sent by Conder. Could not view to add details
Standard generators for $J_3$
Magma used as case study for implementation.
Steiner triple systems with many affine hyperplanes
Symmetric generation of the Higman-Sims group
The Alperin and Dade conjectures for the simple Mathieu groups
The characterisation of modular group algebras having unit groups of nilpotency class 3
Two element generation of the finite reflection groups
Unitals embedded in finite projective planes
Magma used to study patterns.
Vanishing orbit sums in group algebras of $p$-groups
A Bruen chain for $q=19$
A database of groups of prime-power order
No MR found
A finite soluble quotient algorithm
Algorithm discussion.
A first report on the A Sharp compiler
l
Algorithmen zur symbolischen Lösung homogener linearer Differentialgleichungen
Application of computational tools for finitely presented groups
Bases for codes of designs from finite geometries
Classifying geometries with Cayley
Combining Theorem Proving and Symbolic Mathematical Computing
?could not view article
Computing a set of generators of minimal cardinality in a solvable group
Contribution á l'élaboration d'un ATLAS de géométries: Volumes I and II
Conway's group $Co_3$ and the Dickson invariants
Designs with the symmetric difference property on 64 points and their groups
Exotische meetkunden van rang twee
Finite $p$-quotients of some cyclically presented groups
Inverse planes with a given collection of common blocks
Isomorphism testing for $p$-groups
Kooperation eines Theorembeweisers und eines Computeralgebrasystems
New results for the degree/diameter problem
Projective bundles
Quotients of Coxeter complexes, fundamental groupoids and regular graphs
Regular maps with small parameters
Subgroups of 3-transposition groups generated by four 3-transpositions
Testing modules for irreducibility
? Unable to view to verify
The structure of the projective indecomposable modules of $3 M_22$ in characteristic 2
Zeta functions do not determine class numbers
Refers to verification by Bosma using Magma.
A construction of $3McL$ and some representation theory in characteristic 5
A design and a code invariant under the simple group $Co_3$
Algorithmensynthese für lineare Systeme mit Symmetrie
An application of group theory to extremal graph theory
Codes of Steiner triple and quadruple systems
Constructing integral lattices with prescribed minimum. II
Cusps, triangle groups and hyperbolic 3-folds
Explicit primality criteria for $h2^k1$
Galois groups of second and third order linear differential equations
Generating the Mathieu groups and associated Steiner systems
Groups acting simply transitively on the vertices of a building of type $A_2$. I
Groups acting simply transitively on the vertices of a building of type $A_2$. II. The cases $q=2$ and $q=3$
Isomorphisms of modular group algebras: an algorithm and its application to groups of order $2^6$
Konstruktion der Konjugiertenklassen von Untergruppen mit kleinem Index in $p$-Gruppen
Liouvillian and algebraic solutions of second and third order linear differential equations
On a third order differential equation whose differential Galois group is the simple group of 168 elements
On finite affine 2-arc transitive graphs
Recognizing badly presented $Z$-modules
Some 5-modular representation theory for the simple group $McL$
Some results about flag transitive diagram geometries using coset enumeration
Symmetric presentations. II. The Janko group $J_1$
The proportion of fixed-point-free elements of a transitive permutation group
The restricted Burnside problem
***
The structure of the projective indecomposable modules of the Suzuki group $Sz(8)$ in characteristic 2
The symmetric genus of sporadic groups: Announced results
Sent by M. Conder
The transitive groups of degree fourteen and fifteen
Wall and Vinson revisited
$t$-Designs zu vorgegebener Automorphismengruppe
A characterization of the groups $Fi_22$, $Fi_23$ and $Fi_24$
A computer-aided analysis of some finitely presented groups
Algorithms for groups
Corrigendum: ``Classification of 4- and 5-arc-transitive cubic graphs of small girth'' [J. Austral. Math. Soc. Ser. A 50 (1991), no. 1, 138--149; MR1094065 (92e:05053)]
Finite simple groups with few conjugacy classes of subgroups
Group actions on the cubic tree
Hadamard matrices and their designs: A coding-theoretic approach
Nonspherical spheres
On Buekenhout-Metz unitals of odd order
On Liouvillian solutions of linear differential equations
On nonisomorphic BIBD with identical parameters
Presentations for 3-dimensional special linear groups over integer rings
Presentations for unit groups of modular group algebras of groups of order 16
Processor interconnection networks from Cayley graphs
Rewriteability in finite groups
Symmetric presentations. I. Introduction, with particular reference to the Mathieu groups $M_12$ and $M_24$
The block-transitive, point-imprimitive 2-$(729, 8, 1)$ designs
The symmetric genus of sporadic groups
A geometric characterization of the groups $M_12$, $He$ and $Ru$
A geometric characterization of the groups $McL$ and $Co_3$
A new uniqueness proof for the Held group
A question by Graham Higman concerning quotients of the $(2,3,7)$ triangle group
An upper bound for the $p$-rank of a translation plane
Computational aspects of representation theory of finite groups
Computational problems in the theory of finite fields
Correction: ``Translation planes and derivation sets''
Coset enumeration strategies
Embeddings of symmetric graphs in surfaces
Etude de petits groupes et des geometries associees a l'aide de Cayley
Group Graphs and Computational Symmetry on Massively Parallel Architecture
Géométries, language Cayley et groupe de Hall-Janko
? sent by Leemans. could not view to add details
Insoluble groups with the rewriting property $P_8$
On algebraic solutions of linear differential equations with primitive unimodular Galois group
On flag-transitive geometries and groups
? Sent by Leemans. Could not view to get details.
On the Frobenius groups with kernel of order 64
On the Wielandt length of metabelian $p$-groups
Random walks in large finite groups
Strata for randomized experiments
The computation of normalizers in permutation groups
The symmetric genus of the Mathieu groups
A computation of Green functions for some classical groups
A geometric approach to some group presentations
A new construction of the group $Ru$
Baer subplanes, ovals and unitals
Canonical bases for cyclotomic fields
Computing with endomorphism rings of modular representations
Finite Bol quasifields are nearfields
Hurwitz groups: a brief survey
Intersection of unitals in the Desarguesian plane
Leopoldt's conjecture for imaginary Galois number fields
On the minimum number of blocks defining a design
Operation of class sums on permutation modules
Recherche de notations structurales pour les groupes d'ordre inférieur ou égal á 100 á l'aide de CAYLEY
Solution of the solubility problem for rewritable groups
Some problems in computational representation theory
Some subgroups of $SL(3,Z)$ generated by involutions
The $p$-group generation algorithm
A CAYLEY library for the groups of order dividing 128
A characterisation of some finite inversive planes
An infinite family of 4-arc-transitive cubic graphs each with girth 12
Arcs and ovals in the Hermitian and Ree unitals
Automatisierter Entwurf schneller Spektraltransformationen
Automorphism groups of symmetric graphs of valency 3
Codes from symmetry groups, and a $[32,17,8]$ code
Codes of Designs
Constructing symmetric graphs
? sent by Conder. Could not view to add details
Constructing the vertex-transitive graphs of order 24
Fast Fourier transforms for metabelian groups
Free products in mapping class groups generated by Dehn twists
Linear groups and distance-transitive graphs
Natural constructions of the Mathieu groups
On certain coverings of generalized polygons
On the Möbius function of a finite group
Partitioning sets of quintuples into designs
Recent progress on rewritability in groups
Spreads admitting regular elliptic covers
The coding theory of finite geometries and designs
The construction of Tutte's 8-cage and the Conder graph
The finite quotient groups of the plane crystallographic group $p6m$
The group of automorphisms of a transitive 2-$(91, 6, 1)$ design
The modular group algebra of a central-elementary-by-abelian $p$-group
Verbal embeddings and a geometric approach to some group presentations
A new class of translation planes
An algorithm for determining the simplicity of a modular group representation
Another look at Bruen chains
Cayley, Version 4: The User Language
Character degrees and derived length in $p$-groups
Construction of two-dimensional flag-transitive planes
Finite linear spaces with flag-transitive groups
Maximal automorphism groups of symmetric Riemann surfaces with small genus
Modified Steinberg relations for the group $J_4$
Nests of size $q-1$ and another family of translation planes
Parallel algorithms for solvable permutation groups
The characters of the centralizer of an involution in $C_1$
The construction of some trivalent symmetric graphs
The subgroup structure of the Mathieu group $M_12$
Character degrees of finite $p$-groups
Erzeugende und Relationen gewisser orthogonaler und symplektischer Gruppen über $GF(2)$
Groups of minimal genus including $C_2$ extensions of $PSL(2,q)$ for certain $q$
Modular properties of the hard hexagon model
Noncommutators and the number of projective characters of a finite group
On the $k$-closure of finite linear groups
Presentations for $(G,s)$-transitive graphs of small valency
Regular sets and geometric groups
Regular sets in Incidence Structures
Superimprimitive 2-generator finite groups
The genus of compact Riemann surfaces with maximal automorphism group
The transitive groups of degree twelve
Three-relator quotients of the modular group
A family of Hurwitz groups with nontrivial centres
A note on Cayley graphs
Charaktertafeln von Sylownormalisatoren sporadischer einfacher Gruppen
Closure properties of the special linear groups
Computing character degrees in $p$-groups
Efficient presentations for three simple groups
Hurwitz groups with arbitrarily large centres
Some group presentations and enforcing the associative law
The geometry of the finite simple groups
The Steiner system $S(5,8,24)$ constructed from dual affine planes
A characterization of the group $M_12$
MRC
Computing Galois groups over the rationals
Constructing integral lattices with prescribed minimum. I
Finite unimodular groups of prime degree and circulants
Géométries des groupes $PSL(2,q)$
On the $p$-rank of $t$-designs
Sylow's theorem in polynomial time
The symmetric genus of alternating and symmetric groups
CAS; design and use of a system for the handling of characters of finite groups
Distinguishing eleven crossing knots
On the Affine Geometries of $M_24$
Presentations for cubic graphs
Some results on quotients of triangle groups
Two groups which act on cubic graphs
Presentations for some direct products of groups
The vertices of the simple modules of $M_12$ over a field of characteristic 2
Computing double coset representatives for the generation of solvable groups
Counting with groups and rings
The maximal subgroups of the Chevalley group $G_2(4)$
Computation of Pólya polynomials of primitive permutation groups
More on generators for alternating and symmetric groups
On the group of Rubik's ``magic'' cube
The maximal subgroups of the sporadic simple group of Held
Generators for alternating and symmetric groups
On maximal finite irreducible subgroups of $GL(n,,Z)$. III. The nine-dimensional case
On maximal finite irreducible subgroups of $GL(n,,Z)$. IV. Remarks on even dimensions with applications to $n=8$
On maximal finite irreducible subgroups of $GL(n,,Z)$. V. The eight-dimensional case and a complete description of dimensions less than ten
Generators for the mapping class group
The last of the Fibonacci groups
The nonabelian simple groups $G$, $G< 10^5$---presentations
The nonabelian simple groups $G$, $G<10^6$---minimal generating pairs
The nonabelian simple groups $G$, $G< 10^6$---maximal subgroups
Von Untergruppen der Triangel-Gruppen
On maximal finite irreducible subgroups of $GL(n, Z)$. I. The five and seven dimensional cases
On maximal finite irreducible subgroups of $GL(n, Z)$. II. The six dimensional case
$p$-groups with an abelian maximal subgroup and cyclic center
Addendum: ``A computer aided study of a group defined by fourth powers'' (Bull. Austral. Math. Soc. 14 (1976), no. 2, 293--297)
Self-dual codes over $GF(3)$
Finite groups with a Sylow 2-subgroup of type $M_24$. I, II
Groups generated by a class of elements of order 3
We programmed the HFE key-generation and encryption, as well as the attack, in the MAGMA computer-algebra system
A Modular Algorithm for Computing Polynomial GCDs over Number Fields presented with Multiple Extensions
We acknowledge John Cannon and the Magma group for hosting in Sydney in 2003 and Allan Steel for helping us with our Magma implementation.write up of implementation of algorithm in Magma which has not been published
A Point Halving Algorithm for Hyperelliptic Curves
Magma used to generate curves.
A remarkable Mathieu graph tower
The class decompositions for these have been given in [4]. The character tables of the full, reflective polytope groups, [p, q, r], were computed using the CAYLEY computer algebra system (this was superseded by MAGMA in 1993) from their Coxeter presentations and the required subgroup of index two selected.
Enumeration of the Equisymmetric Strata of the Moduli Space of Surfaces of Low Genus
Comment on the availability of an extensive library in...Magma.
Representatives of these conjugacy classes are available online in a MAGMA [Bosma et al., 1997] readable format from http://www.math.rwth-aachen.de/Markus.Kirschmer/symplectic/ .
First Steps Toward a Cryptography-Aware Language and Compiler
In discussion: Unlike languages such as Magma [46] or Maple [47] which allow the description of high-level mathematical constructions, we restrict our focus to the implementation of cryptography kernels such as block ciphers; hash functions;and sequences of finite field arithmetic used to implement systems such as ellipticcurve cryptography (ECC).
Our proof of Theorem 1.2 depends on computer calculations. The programs we used, some written in Magma [5] and some in C, can be found on the second author's web site: start at http://www.alumni.caltech.edu/~however/biblio.html and follow the links to this paper. ... Magma code for doing this can be found in the file DoubleBase.magma, available at the URL mentioned in the introduction.
Slid Pairs in Salsa$20$ and Trivium
for computations
The genera, reflexibility and simplicity of regular maps
The poset of elementary abelian $p$-subgroups having rank at least 2
Unable to view, but confirmed by J.F.Carlson.
The trace of special values of modular $L$-functions
"I thank Lloyd Kilford for performing these calculations using the Magma computing package."
Two new symmetric 2-$(144,66,30)$ designs
Magma used in computations.
Type I Codes over GF$(4)$
Verification of the Birch and Swinnerton-Dyer conjecture for specific elliptic curves
Used in computations