Magma V2.25-7 Patch Notes

Algebraic Function Fields¶

• A bug arising when testing whether two function fields are isomorphic using the intrinsic IsIsomorphic has been fixed. Reported by X. Xarles and fixed by F. Hess.

Algebraic Geometry¶

• A bug in PointSearch caused by recent changes to the intrinsic JacobianMatrix (which can now use a minimal basis) has been fixed. Reported by S. Elsenhans.
• A crash in the intrinsic DesingulariseSurfaceByBlowUp has been fixed. Reported by S. Elsenhans.
• A bug, involving denominator handling, in the intrinsic Reduction at a place has been fixed. Reported and fixed by R. van Bommel.
• A code regression which caused the intrinsic AutomorphismGroup applied to algebraic curves to fail has been fixed. Reported by D. Zureick-Brown.
• A bug when testing isomorphism of two curves using intrinsic IsIsomorphic has been fixed. Reported by X. Xarles and fixed by F. Hess.
• A bug in the code for homogenising maps between maps to toric ambient spaces has been fixed. Reported by A. Laface.

Algebraic Number Fields¶

• A bug in computing Automorphisms of a degree 2 field defined by a non-monic or non-integral polynomial has been fixed. Reported by S. Hashimoto.
• Memory handling in MaximalOrder when the Discriminant or Ramification parameter is set has been fixed. Reported by A. Brumer.
• Improvements have been made to MaximalOrder when the Discriminant or Ramification parameter is set. Reported by Juergen Klueners (among others).
• Decomposition of ramified primes in non-maximal orders of Kummer and Artin--Schreier extensions has been fixed. Reported by P. Koprowski.
• Error checking has been improved for the intersection intrinsic meet for two number fields to ensure both are defined by the same polynomial.
• A bug affecting pSelmerGroup, PrincipalUnitGroupGenerators and ResidueSystem for local rings containing more than one unramified extension has been fixed. Reported by W. Bley.
• A bug in the code for intrinsic RingClassGroup for orders of quadratic fields has been fixed. Reported by G. McConnell.

Arithmetic Geometry¶

• A bug which sometimes caused the intrinsic MordellWeilGroup to crash has been fixed. Reported by Alex Bartel.
• An error that caused code for constructing defining equations for modular curves X_0(N) to crash for certain curves has been fixed. Reported by D. Zureick-Brown.

Artin Representations¶

• The code for computing non-maximal orders using the intrinsic Minimize has been revised, so as to avoid some expensive optimizations. Reported by J. Jones.

Bilinear Forms¶

• The number of variants of standard quadratic and symmetric forms has been reduced from three to two: "Default" and "Revised". This is for consistency with the changes to the generators of the even dimensional orthogonal groups of minus type. The "Revised" variant returns the form preserved by the groups AltOmegaMinus, AltSOMinus, AltGOMinus.
• The intrinsic InvariantBilinearForms is no longer restricted to finite fields.
• The intrinsics SemilinearDual, TwistedDual and TwistedSemilinearDaul no longer call GModuleAction. This avoids calling RandomSchreier and so produces a considerable speed improvement. (Problem reported by Eamonn O'Brien.)
• A new intrinsic GramSchmidtPair is provided which given the matrix J of a reflexive form, applies a Gram-Schmidt algorithm to return a pair of matrices D and A such that AJA' = D, where D is almost diagonal and A' is either the transposed conjugate of A (when J is hermitian) or the transpose of A.
• A new intrinsic IsReflexive determines whether a matrix J represents a reflexive form and if so determines its type and multiplier.

Finite Fields¶

• The intrinsic Basis has been changed to create a relative basis. Reported by W. Bley.
• A bug in the finite field extension constructor ext< ... > which caused it to crash has been fixed. Reported by Eamonn O'Brien.

Galois Groups¶

• A bug in the code for intrinsic GaloisGroup which causes a failure for certain types of polynomial has been fixed. Reported by Martin Soderholm.
• A fix has been made when the Prime parameter to GaloisGroup is set. Reported by J. Voight.
• A fix has been made to the computation of the GaloisGroup of a reducible polynomial over a rational function field over $\mathbb{Q}$ having zero as a root. Reported by J. Voight.
• A bug in the intrinsic GaloisGroup when computing the Galois group of a polynomial defined over a number field has been fixed. Reported by Tim Dokchitser.

Group Theory: Classical Groups¶

• Several years ago the generators for the orthogonal groups of minus type in even dimensions (GOMinus and subgroups) were changed so that in odd characteristic the calculation of the generators involved calling the Sqrt function. Consequently even though the groups produced in different sessions of Magma were isomorphic, the generators were not necessarily the same. (Problem reported by Derek Holt.) In order to address this problem the original C code for the generators has been restored. (The code had been renamed OldOmegaMinus etc.)
• If needed, the groups which have been replaced by the above are returned by the intrinsics AltOmegaMinus, AltGOMinus and AltSOMinus.
• An error which sometimes occurred in the conjugacy classes of unitary groups, as constructed by the classical group machinery, has been fixed.
• A crash in ExtractGroups when internal limits are exceeded has been fixed. Reported by E. O'Brien.
• The code that converted the return value to the Zasasenhaus convention has been removed. This ensures that in charactersitic not 2 the spinor norm of an element x of the orthogonal group is consistent with SpinorNorm(V,x), where V is a quadratic or inner product space.
• An improved algorithm to compute the conjugacy invariants of classical groups has been installed. As a result there is a significant speed increase in computing the conjugacy classes of classical groups in odd characteristics.

Group Theory: General¶

• A crash in the intrinsic ExtractGroups when internal limits are exceeded has been fixed. Reported by E. O'Brien.
• An error in the intrinsic OuterFPGroup applied to the result returned by AutomorphismGroup (of a group) whereby it returned zero has been fixed. Reported by David Roe.

Invariant Theory¶

• Some major improvements in speed and memory usage have been added to the linear algebra method for computing monomials of given degree.

Lie Theory¶

• A crash when computing composition series of Lie Algebras has been fixed. Reported by D. Craven.

Linear Algebra¶

• A crash in the integer Hermite algorithm (arising from an AbelianQuotient call) has been fixed. Reported by T. Brown.
• A bug that occurred when taking projections of subspaces of a vector space over the rationals has been fixed. Reported by E. Assaf.

Polynomial Rings and Groebner Bases¶

• A crash in multivariate GCD for a large number of variables (arising out of a Lie group computation) has been fixed. Reported by A. Litterick.
• A hang in polynomial GCD over a certain class of high-degree number fields has been fixed. Reported by J. Voight.
• A slowdown in the F4 algorithm for dense HFE-like inputs, which was introduced in the previous patch release, has been fixed.

Representation Theory¶

• There is an important change when computing irreducible KG-modules, where K is a finite field and G is a matrix group:
• • For absolutely irreducible modules use AbsolutelyIrreducibleModules(G, p) where p is the characteristic of K. This returns the absolutely irreducible modules for G over the finite field GF(p);
• • For irreducible modules use IrreducibleModules(G, K) which will return the irreducible modules for G over the finite field K.
• A bug has been fixed which caused intrinsics such as IrreducibleModules and AbsolutelyIrreducibleModules to crash in certain circumstances when computing irreducible modules for a group over a finite field has been fixed. Reported by Melissa Lee (among others).
• A bug in the code for the intrinsic IrreducibleModulesSchur which occurs when computing KG-modules, K a finite field and G is a soluble group, has been fixed.
• A bug in the characteristic 0 Meataxe which caused it to hang in the case of some small KG-modules has been fixed. Reported by U. Thiel.
• A bug in the characteristic 0 Meataxe which caused it to crash when splitting a module over a cyclotomic field has been fixed. Reported by U. Thiel.

Series Rings¶

• A crash in the intrinsic Factorization with the Extensions parameter set to true has been fixed. Reported by A. Zervou.