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Magma V2.28-5 Patch Notes

Patch release for Magma V2.28-5. Updated areas: Cohomology, Commutative Algebra, FP Groups, Finite Fields, Finite Groups and 4 more.

21 December 2023 9 areas

Cohomology

• The function SplitExtension has been improved.

Commutative Algebra

• A problem when computing Groebner bases over prime finite fields with size between 32 and 61 bits has been fixed.

FP Groups

• A crash using Kernel on a homomorphism with codomain an fp-group has been adjusted to a runtime error. Bug reported by A. Previtali.

Finite Fields

• A crash when computing square roots of elements in non-standard double extension fields (arising from computing the order of jacobians of hyperelliptic curves) has been fixed. Reported by Y. Uesato.

Finite Groups

• New function SmallestGeneratingSet(G) which returns a generating set of smallest size for the finite group \(G\) (the algorithm is based on that described in: Andrea Lucchini and Dhara Thakkar, The Minimum Generating Set Problem [arXiv:2306.07633]).

• New function PermutationRepresentationQuotient(G, N) to compute a faithful permutation representation of \(G/N\).

• New function IsAbstractFrobeniusGroup(G), which decides whether the finite group \(G\) has a faithful permutation represention with image equal to a Frobenius group. If so, then a Frobenius kernel and complement for this representation are returned in addition to true.

• New options for the type input parameter in the intrinsic ClassicalMaximals(type, d, q) have been introduced. These are: “SL”, “GL”, “Sp”, “SU”, “GU”, “Omega+”, “Omega-”, “Omega”, “SO+”, “SO-”, “SO”, “GO+”, “GO-” (which are the same as the options for ClassicalClasses(type, d, q) ). Their meaning is as expected. For example, ClassicalMaximals(“SO+”,8,5) returns representatives of the conjugacy classes of the maximal subgroups of the group returned by the intrinsic SOPlus(8,5).

• The function SearchForIsomorphism now has the parameter MaxStates.

• The database of primitive groups has been extended to degree 8191.

• Bugs in MaximalSubgroups for some special cases have been fixed.

Matrices

• A better error message is given when matrix inversion fails because an algorithm is not supported for the base ring.

• A crash in commutator computation where the base ring is not a field has been fixed.

Matrix Groups

• The algorithm for computing centralisers or conjugacy testing for elements of matrix groups now uses special algorithms for classical groups when applicable.

• New functions SpinClasses, SpinConjugacyClasses, SpinIsConjugate, SpinCentraliser, SpinCentralizer, SpinClassMap for spin groups.

• The function NameSimple now applies to matrix groups as well as permutation groups. Request of R. Keith Dennis.

PC Groups

• The function AutomorphismGroup for PC groups uses a new special algorithm by default when applicable.

• A bug in IrreducibleModules of a PC group has been fixed. Bug reported by E. O’Brien.

System

• New function Fork() which calls the Unix/Linux system call fork() and returns the process ID of the child (if now running as the parent), or returns 0 (if now running as the child).

• New function WaitForAllChildren() which waits until all children (created via Fork()) have exited.

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