Please note that there are more tool functions you can define, GaussForHomalg just provides homalg with a sufficient subset. This varies with the type and complexity of the rings you want to define. On the other hand, ImportMatrix
(3.1-4) is a function specifically designed for GaussForHomalg.
> ZeroMatrix ( C ) | ( function ) |
Returns: a sparse matrix
This returns a sparse matrix with the same dimensions and base ring as the homalg matrix C.
> IdentityMatrix ( C ) | ( function ) |
Returns: a sparse matrix
This returns a sparse n x n identity matrix with the same ring as the homalg matrix C, n being the number of rows of C.
> CopyMatrix ( C ) | ( function ) |
Returns: a sparse matrix
This returns a sparse matrix which is a shallow copy of the sparse matrix stored in the Eval
attribute of the homalg matrix C.
> ImportMatrix ( M, R ) | ( function ) |
Returns: a sparse matrix
This returns the sparse version of the GAP matrix M over the ring R. It prevents homalg from calling sparse matrix algorithms on dense GAP matrices. Note that this is not a "standard" tool but neccessary because of the new data type.
> Involution ( M ) | ( function ) |
Returns: a sparse matrix
This returns a sparse matrix which is the transpose of the sparse matrix stored in the Eval
attribute of the homalg matrix M.
> CertainRows ( M, plist ) | ( function ) |
Returns: a sparse matrix
This returns the rows in plist of the sparse matrix stored in the Eval
attribute of the homalg matrix M as a new matrix.
> CertainColumns ( M, plist ) | ( function ) |
Returns: a sparse matrix
This returns the columns in plist of the sparse matrix stored in the Eval
attribute of the homalg matrix M as a new matrix.
> UnionOfRows ( A, B ) | ( function ) |
Returns: a sparse matrix
This returns the sparse matrix created by concatenating the rows of the sparse matrices stored in the Eval
attributes of the homalg matrices A and B.
> UnionOfColumns ( A, B ) | ( function ) |
Returns: a sparse matrix
This returns the sparse matrix created by concatenating the columns of the sparse matrices stored in the Eval
attributes of the homalg matrices A and B.
> DiagMat ( e ) | ( function ) |
Returns: a sparse matrix
This method takes a list e of homalg matrices and returns the sparse block matrix of the matrices stored in the Eval
attributes of the matrices in e.
> KroneckerMat ( A, B ) | ( function ) |
Returns: a sparse matrix
This returns the sparse Kronecker matrix of the matrices stored in the Eval
attributes of the homalg matrices A and B.
> Compose ( A, B ) | ( function ) |
Returns: a sparse matrix
This returns the matrix product of the sparse matrices stored in the Eval
attributes of the homalg matrices A and B.
> NrRows ( C ) | ( function ) |
Returns: an integer
This returns the number of rows of the sparse matrix stored in the Eval
attribute of the homalg matrix C.
> NrColumns ( C ) | ( function ) |
Returns: an integer
This returns the number of columns of the sparse matrix stored in the Eval
attribute of the homalg matrix C.
> IsZeroMatrix ( C ) | ( function ) |
Returns: true or false
This returns true if the sparse matrix stored in the Eval
attribute of the homalg matrix C is a zero matrix, and false otherwise.
> IsDiagonalMatrix ( C ) | ( function ) |
Returns: true or false
This returns true if the sparse matrix stored in the Eval
attribute of the homalg matrix C is a diagonal matrix, and false otherwise.
> ZeroRows ( C ) | ( function ) |
Returns: a list
This returns the list of zero rows of the sparse matrix stored in the Eval
attribute of the homalg matrix C.
> ZeroColumns ( C ) | ( function ) |
Returns: a list
This returns the list of zero columns of the sparse matrix stored in the Eval
attribute of the homalg matrix C.
> DecideZeroRows ( A, B ) | ( function ) |
Returns: a homalg matrix
This returns the homalg matrix you get by row reducing the homalg matrix A with the homalg matrix B.
> DecideZeroRowsEffectively ( A, B, T ) | ( function ) |
Returns: a homalg matrix M
This returns the homalg matrix M you get by row reducing the homalg matrix A with the homalg matrix B. The transformation matrix is stored in the void homalg matrix T as a side effect. The matrices satisfy M = A + T * B.
> SyzygiesGeneratorsOfRows ( M ) | ( function ) |
Returns: a homalg matrix
This returns the row syzygies of the homalg matrix M, again as a homalg matrix.
> RelativeSyzygiesGeneratorsOfRows ( M, N ) | ( function ) |
Returns: a homalg matrix
The row syzygies of M are returned, but now the computation interpretes the rows of the homalg matrix N as additional zero relations.
> RowReducedEchelonForm ( M[, U] ) | ( function ) |
Returns: a homalg matrix N
If one argument is given, this returns the triangular basis (reduced row echelon form) of the homalg matrix M, again as a homalg matrix. In case of two arguments, still only the triangular basis of M is returned, but the transformation matrix is stored in the void homalg matrix U as a side effect. The matrices satisfy N = U * M.
> CreateHomalgTable ( R ) | ( function ) |
Returns: a homalg table
This returns the homalg table of what will become the homalg ring R (at this point R is just a homalg object with some properties for the method selection of CreateHomalgTable
). This method includes the needed functions stored in the global variables CommonHomalgTableForGaussTools
and CommonHomalgTableForGaussBasic
, and can add some more to the record that will become the homalg table.
This is just support for the sparse matrix data type.
> GetEntryOfHomalgMatrix ( M, r, c, R ) | ( method ) |
Returns: M[r,c]
If the Eval attribute of the homalg matrix M over the homalg ring R is sparse, this calls the corresponding Gauss command GetEntry
.
> SetEntryOfHomalgMatrix ( M, r, c, e, R ) | ( method ) |
Returns: nothing
If the Eval attribute of the homalg matrix M over the homalg ring R is sparse, this calls the corresponding Gauss command GetEntry
, to achieve M[r,c]:=e
.
> AddToEntryOfHomalgMatrix ( M, r, c, e, R ) | ( method ) |
Returns: nothing
If the Eval attribute of the homalg matrix M over the homalg ring R is sparse, this calls the corresponding Gauss command AddToEntry
, to achieve M[r,c] := M[r,c] + e
.
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