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

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

General arithmetic sped up for larger fields.
Fields of size up to about 2^100 have optimal representation.
Fields with non-primitive defining polynomials now fully optimized.

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

Memory usage improved.

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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
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

General arithmetic sped up for larger fields.
Fields of size up to about 2^100 have optimal representation.
Fields with non-primitive defining polynomials now fully optimized.

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

Memory usage improved.

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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
Finite Fields: General arithmetic sped up for larger fields.
Fields of size up to about 2^100 have optimal representation.
Fields with non-primitive defining polynomials now fully optimized.

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

Memory usage improved.

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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
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

Memory usage improved.

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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
Graphs: Memory usage improved.

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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
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

Generator names for PC groups are now used in the printing.
SystemNormalizer installed.
Access functions for elements of a conditioned PC group updated.
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.
Bug in union for graphs and digraphs fixed.

Soluble groups

Bug in ChiefSeries fixed.
Graphs: Bug in Girth fixed.
Bug in InsertVertex fixed.
Bug in union for graphs and digraphs fixed.

Soluble groups

Bug in ChiefSeries fixed.
Soluble groups: Bug in ChiefSeries fixed.

Next: Release notes index Previous: V1.00-5 (10 June 1994)

Up: Release Notes index

V1.00-4 (19 May 1994)

Recent Changes and Improvements

Magma licence

Character Theory

Finite Fields

Modules and Matrix Structures

Graphs

Polynomials

Soluble groups

Recent Bug Fixes

Character Theory

Graphs

Soluble groups