Change log for Magma V2.20-9 (Released 5/9/2014)

Algebraic Function Fields

·A fix has been made to coercion between orders of function fields in some cases.

·A parameter allowing the "Round 2" algorithm to be selected has been added to MaximalOrderFinite and MaximalOrderInfinite when the input is a FldFunAb.

Algebraic Number Fields

·A fix has been made to MinimalPolynomial given a element of a number field and a ring, for some rings.

·A fix has been made to coercion between orders of number fields in some cases.

·An improvement has been made to CoveringStructure of orders of number fields.

Elliptic Curves

·The Cremona database of all elliptic curves of small conductor has been updated to the most recent version (including several conductors that had previously been omitted).

·The reduction algorithm for 2-coverings occurring in TwoDescent for elliptic curves over number fields has been patched. (Previously the scaling by units was not optimal.)

Factorization

·The integer factorization had a couple of fixes applied, to ensure that that B1 limit for ECM was small enough (else all the prime factors could often be found at the same time, not leading to a nontrivial splitting).

Groebner Bases

·A hang in Groebner basis computation over number fields has been fixed. Reported by T. Fisher.

Groups

·A runtime error when AutomorphismGroup of a matrix containing only one value is computed has been fixed. Bug reporetd by Morgan Rodgers.

·A problem with IsSatisfied when the 2nd argument is empty has been fixed. If the length of the 2nd argument does not equal the number of generators of the fp-group relevant to the first argument, then there will now be a runtime error in all cases, not just some. Bug reported by JÃ¡n KarabÃ¡s.

·A crash when computing the socle of a permutation group has been fixed. Bug found as a result of a report by Gabi Nebe.

·A crash in LMGSylow has been fixed. Bug reported by E. O'Brien and fixed by D. Holt.

·A crash in ClassicalMaximals has been fixed. Bug reported by E. O'Brien and fixed by D. Holt.

Isotropic Subspaces

·The code for IsotropicSubspace has been slightly reordered, to apply LLLGram after each prime (rather than just at the end). The previous code would double the size of entries at each step, which could lead to coefficient blow-up when the determinant had many prime factors. Noted by T. A. Fisher.

Lattices

·A bug with the improper use of C-integers for an indefinite Gram matrix has been fixed. Noted by T. A. Fisher.

·The Coordinates intrinsic can now (sometimes) work over real fields.

Matrices

·A bug in the p-adic nullspace algorithm has been fixed. Reported by T. Fisher.

Polynomials

·A hang in multivariate factorization over the integers has been fixed. Reported by T. Fisher.

Real and Complex matrices

·A problem with randomisation in QLCDecomposition has been fixed. This should lead to superior performance with similar functions.

Schemes

·A crash involving scheme maps has been fixed. Reported by M. Stoll.

Special Functions

·The intrinsic HypergeometricSeries2F1 has a number of problems, noted by J. Detrey. Firstly the answer is wrong in cases where the parameters induce a zero in the Gamma-quotient (pole in the denominator) from the transformation law. Secondly, a bug (division by zero) can occur when the parameters form nonpositive integers upon transformation. However, even upon fixing this directly, there would still be numerical instability when the transformation leads to parameters which are nearly nonpositive integers. The first problem has been patched, while the second one has not yet been addressed in full.