Magma V2.18-4 Patch Notes

Algebraic Curves¶

• A bug that was causing sporadic crashes after a Runtime Error in Place(s) has been fixed. Reported by Emmanuel Thome.

Algebraic Fields¶

• Improvements to GaloisGroup computations for polynomials over number fields (including $\mathbb{Q}$) and rational and algebraic function fields have been made.
• NumberOfOperations counting multiplications in a Galois invariant involving a powering operation has been fixed. Reported by A-S. Elsenhans.

Algebras¶

• An error in DirectSum for left algebra modules has been fixed. Reported by M. Towers.
• A crash in the ideal< | > constructor when less elements than the dimension of the algebra were given in the right hand side has been fixed.

Coding Theory¶

• A bug that could cause MinimumWords to return spurious words not in the code has been fixed. This bug could be triggered by some quasicyclic codes. Reported by M. Grassl.
• A rare minor leak in the minimum weight algorithm has been fixed.
• Fixed a bug that would cause the weight distribution of a self-dual quantum code to be set to all zero on creation if the weight distribution of the stablizer code was already known. Reported by M. Grassl.
• Corrected the result of BCHBound when called on a code with generator polynomial $(x^n - 1)/(x - 1)$. (Should have been $n$, was returning 1.) Reported by T. Feulner.

Continued Fractions¶

• A large memory usage with ContinuedFraction of 0.0 has been fixed.

Elliptic Curves¶

• A bug has been fixed that could cause the order of a torsion point on a non-integral elliptic curve over the rationals to be erroneously reported as infinite.
• A rare crash when deleting an elliptic curve over a finite field has been fixed.

Function Fields¶

• Extra printing which occurred when computing a GaloisGroup of a polynomial over a rational function field with characteristic 0 or a global algebraic function field has been removed.
• Extra printing which occurred when computing Subfields of a global function field has been removed.
• The precision used in the computation of the roots in a GaloisGroup computation for a polynomial over an algebraic function field has been adjusted.

Groebner Bases¶

• A problem in verbose printing for the F4 algorithm has been fixed. Reported by M. Grassl.

Groups¶

• A crash in the GrowthFunction of an automatic group has been fixed.
• More access to information about an automatic group has been given. New intrinsic functions applying to automatic groups are: FPGroup, WordDifferenceSize, WordAcceptorSize, WordDifferenceAutomaton, GeneratorOrder.
• The function HasInfiniteComputableAbelianQuotient has been given a 4th return value, of boolean type, to distinguish between finding that the group has a finite derived quotient (true), and failing to compute the derived quotient (false). In both of these cases the 1st return value is false. Request of E. O'Brien.
• A bug to do with the printing of an empty sequence after applying Subgroups to an abelian group and (correctly) finding empty result has been fixed. Reported by D. Gruenewald.
• A bug in HomomorphismsProcess has been fixed. The process could, in some situations, return maps that were not homomorphisms. The closely related Homomorphisms function was not affected by this bug. Reported by E. O'Brien.

Hyperelliptic Curves¶

• The intrinsic function IsDeficient was incorrectly returning false in a particular (and rare) situation, also causing IsOdd and IsEven to return incorrect values. This has been corrected
• IsDeficient, IsOdd and IsEven have been extended to cover all hyperelliptic curves of genus up to 6 defined over the rationals.
• A problem computing resolvents which caused TwoSelmerGroup to crash in certain odd genus examples has been corrected.
• In TwoSelmerGroup and TwoCoverDescent primes dividing the leading coefficient of the defining polynomial were not always included in the set of bad primes, leading to incorrect results. This has been corrected.
• TwoSelmerGroup has been improved for curves of genus > 2 over the rationals. In particular it is now possible to compute 2-Selmer groups in cases where the previous algorithm would never terminate.
• RankBounds is now implemented for hyperelliptic curves of any genus over the rationals (it was previously only for genus 2).
• RankBounds now provides a sharper upper bound for certain even degree hyperelliptic curves. This is achieved by checking for certain nontrivial elements in Sha[2] using an algorithm of Creutz.
• A bug in IsIsomorphic when comparing hyperelliptic curves of differing degrees over p-adic fields. Reported by J.S. Mueller.
• New intrinsic functions HasIndexOne and HasIndexOneEverywhereLocally have been added. These test the existence of divisors of degree 1 on cyclic covers of P^1 defined over p-adic fields.
• HasPointsEverywhereLocally now checks for points over the reals.
• TorsionSubgroup is now implemented for higher genus curves of odd degree over the rationals. Previously this was only for genus 2.
• A error in IsLocallySolvable causing a crash caused by coercion problems has been fixed.

L-series¶

• A runtime error for some Artin L-function calculations (to do with local splitting fields) has been fixed.

Lattices¶

• A memory leak when testing two lattices for isometry has been fixed. Reported by G. Bellot.

Lie Theory¶

• Fixed a problem with W-Graph representation and Hecke representations. Also fixed the return types for ComplexRootDatum.

Matrices¶

• A problem with long vectors over integer residue class rings has been fixed. Reported by A. Lauder.

Number Fields¶

• A crash in the construction of an ideal from an ideal of the coefficient ring has been fixed. Reported by E. Thome.
• Incorrect errors in RayClassGroup have been fixed. Reported by K. Matsuno.
• A crash in some computations with large units has been replaced with an error. Reported by K. Matsuno.

Polynomial Rings¶

• A crash in IsSquare for recursive polynomial rings has been fixed. Reported by M. Zieve.

Quadratic Fields¶

• div and IsQuadratic have been improved so that many calls do not increase memory usage substantially and subsequently slow down further computations.

Sets¶

• The speed of RandomSubsets has been improved for large sets. Thanks to U. Thiel for the report.

Transcendental Functions¶

• A bug triggered by purely imaginary input to Psi was fixed.
• A bug triggered by low-precision input to Psi was fixed.