Release Notes V1.00-4

Magma V1.00-4 (19/5/94)

Recent Changes and Improvements

Magma licence

Typing "magma -d" at the shell prompt dumps the Magma licence for the current magmapassfile.

Character Theory

Improved version of the Dixon-Schneider algorithm implemented and installed.
New functions LinearCharacters and PrincipalCharacter.
All basic character functions re-engineered and many errors and limitations removed.
New functions SymmetricComponents, SymplecticComponents, OrthogonalComponents.

Finite Fields

Modules and Matrix Structures

CambridgeMatrix for large matrices in Cambridge format.
MatrixGroup(G-module) for constructing a matrix from the acting generators of a G-module.
ChangeRing(M, R) for any module M, ring R.
ChangeRing(A, R) for matrix algebra A, ring R.
DirectSum(M, N) for modules M, N returns embedding maps.
DirectSum(Q) for sequence Q of modules, returns sequences of maps.
ChangeRing(M, S, f) for any module M, ring S, hom f: ring(M) -> S.
ChangeRing(A, S, f) for matrix algebra A, ring S, hom f: ring(A) -> S.
RestrictField(G, S) for matrix group G (over K), and S subfield of K.
ExtendField(G, L) for matrix group G (over L), and L extension field of K.
ChangeRing(G, S) for matrix group G (over R), and S any ring.
ChangeRing(G, S, f) for matrix group G over R, S any ring, hom f: R -> S.
hom<A -> B | f> for full matrix algebras A & B, map f: ring(A) -> ring(B).
IsSymmetric(X), IsDiagonal(X) for matrix ring element X.
G-homomorphisms added -- types ModMatGrp and ModMatGrpElt.
IsGHom(X) - is X a GHom, for matrix X with dom and codom G-modules?
Hom(M, N) for RG-modules M and N, the module of all R-homs.
GHom(M, N) for RG-modules M and N, the module of all G-homs.
hom<M -> N | matrix> for modules M and N, the (map) hom given by matrix.
(H ! map) given hom module H and map, return matrix of map.

Graphs

Polynomials

SplittingField(F) for univariate polynomial over a finite field.
SplittingField(S) for set of polynomials. Arrow pairs allowed in polynomial homomorphism constructor.
ChangeRing(A, S) for polynomial algebra A (over R), and S any ring.
ChangeRing(A, S, f) for polynomial algebra A (over R), and S any ring, map f: R -> S.

Soluble groups

------- Recent Bug Fixes

Character Theory

Graphs

Soluble groups