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Magma V1.00-4 (19 May 1994)
Recent Changes and Improvements
- Magma licence
-
-
Typing "magma -d" at the shell prompt dumps the Magma licence for the
current magmapassfile.
- Character Theory
-
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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
-
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General arithmetic sped up for larger fields.
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Fields of size up to about 2^100 have optimal representation.
-
Fields with non-primitive defining polynomials now fully optimized.
- Modules and Matrix Structures
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CambridgeMatrix for large matrices in Cambridge format.
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MatrixGroup(G-module) for constructing a matrix from the acting
generators of a G-module.
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ChangeRing(M, R) for any module M, ring R.
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ChangeRing(A, R) for matrix algebra A, ring R.
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DirectSum(M, N) for modules M, N returns embedding maps.
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DirectSum(Q) for sequence Q of modules, returns sequences of maps.
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ChangeRing(M, S, f) for any module M, ring S, hom f: ring(M) -> S.
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ChangeRing(A, S, f) for matrix algebra A, ring S, hom f: ring(A) -> S.
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RestrictField(G, S) for matrix group G (over K), and S subfield of K.
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ExtendField(G, L) for matrix group G (over L), and L extension field
of K.
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ChangeRing(G, S) for matrix group G (over R), and S any ring.
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ChangeRing(G, S, f) for matrix group G over R, S any ring,
hom f: R -> S.
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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.
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G-homomorphisms added -- types ModMatGrp and ModMatGrpElt.
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IsGHom(X) - is X a GHom, for matrix X with dom and codom G-modules?
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Hom(M, N) for RG-modules M and N, the module of all R-homs.
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GHom(M, N) for RG-modules M and N, the module of all G-homs.
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hom<M -> N | matrix> for modules M and N, the (map) hom
given by matrix.
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(H ! map) given hom module H and map, return matrix of map.
- Graphs
-
- Polynomials
-
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SplittingField(F) for univariate polynomial over a finite field.
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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
-
-
Generator names for PC groups are now used in the printing.
-
SystemNormalizer installed.
-
Access functions for elements of a conditioned PC group updated.
-------
Recent Bug Fixes
- Character Theory
-
-
Many bug fixes in CharacterTable and other functions.
- Graphs
-
-
Bug in Girth fixed.
-
Bug in InsertVertex fixed.
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Bug in union for graphs and digraphs fixed.
- Soluble groups
-
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Bug in ChiefSeries fixed.
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