Change log for Magma V2.26-10 (Released 22/11/2021)

Algebraic Function Fields

·The embeddings between fields in a tower and the direct extension between 2 of these fields have been fixed when non monic or non integral defining polynomials have been used. Reported by M. Zieve.

Algebraic Number Fields

·The embeddings of number fields using Embed, subset, IsSubfield and IsIsomorphic have been improved. Now, once an embedding has been added, no embedding that is inconsistent with it can be added, except using Embed with the new Overwrite parameter set to true. Reported by M. Grassl.

Arithmetic Geometry

·A serious error in the implementation of the rational version of the intrinsic LocalTwoSelmerMap has been fixed. Reported by M. Stoll and fixed by M. Stoll and N. Bruin.

·A bug where the computation of the L-series of a Hecke character group ignores the Precision parameter in the case of the trivial character has been fixed. Reported with fix by E. Costa.

Galois Theory

·The reported return types of GaloisSubgroup and GaloisQuotient have been corrected to match the types of the values actually returned. Reported by A. Ferraguti.

·An error in the implementation of the intrinsic IsEasySnAn which is a quick test as to whether the Galois group of a given polynomial of degree n is the symmetric or alternating group of degree n has been fixed. Reported and fixed by Raymond van Bommel.

Group Theory

·Crashes when computing ClassicalMaximals of O-(4,q) and O+(8,5) have been fixed (thanks to Derek Holt). Crashes reported by E. O'Brien and S. Freedman.

·A bug when computing the maximal subgroups of PSO+(8,3) has been fixed. Two subgroups of shape PSL(4,3):2x2 were missing. Bug reported by S. Freedman.

·The definitions of some small projective orthogonal groups were found to be incorrect. To fix this the constructions of the groups PGOPlus(2,q), PSOPLus(2,q), POmegaPlus(2,q), for q <= 5, and of PGOMinus(2,3), PSOMinus(2,3), and POmegaMinus(2,3) have all been changed to correct the definitions of these projective orthogonal groups, and to maintain the containments POmega subset PSO subset PGO.

·Recent errors in computing classes of classical matrix groups have beenr fixed. The errors came with using a classes algorithm specific to classical groups, and there were errors reported with some small cases.

Linear Codes

·A crash when testing equivalence of two linear codes has been fixed.

Modular Arithmetic Geometry

·ClassicalModularPolynomial(1) has been fixed so it returns the symmetric polynomial x â€“ y. Reported by Yan Bo Ti.

Polynomial Rings

·An incorrect result when computing n-th roots of recursively defined polynomials has been fixed. Reported by M. Zieve.

Representation Theory

·A bug in DirectSumDecomposition for G-modules where G was an unconditioned PC group has been fixed. Reported by J. Jones.

Series Rings

·Improvements have been made to the Factorization of inseparable polynomials over series rings and extensions of series rings. It is also now possible to take p-th power roots of elements of extensions of series rings of characteristic p. Reported by A. Zervou.

Sparse Matrices

·The procedure SetEntry has been fixed to extend the matrix to the correct number of rows when the last argument is zero and the existing row is zero. Reported by J. Gibson.

Symmetric Function Algebras

·Calling Ngens on a symmetric function algebra now returns Infinity instead of crashing.

·Coercion into a power symmetric function algebra now gives an error instead of crashing if the coefficients of the coerced result would not lie in the required ring. (For instance, if they are fractions and the ring is the integers.) Reported by E. Assaf.