Construction of Initialized Sparse Matrices
SparseMatrix(R, m, n, Q) : Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] -> MtrxSprs
SparseMatrix(R, m, n) : Rng, RngIntElt, RngIntElt -> MtrxSprs
SparseMatrix(m, n) : RngIntElt, RngIntElt -> MtrxSprs
Construction of Trivial Sparse Matrices
SparseMatrix(R) : Rng -> MtrxSprs
Example SMat_Create (H27E1)
Construction of Structured Matrices
IdentitySparseMatrix(R, n) : Rng, RngElt -> MtrxSprs
ScalarSparseMatrix(n, s) : RngIntElt, RngElt -> MtrxSprs
ScalarSparseMatrix(R, n, s) : Rng, RngIntElt, RngElt -> MtrxSprs
DiagonalSparseMatrix(R, n, Q) : Rng, RngIntElt, [ RngElt ] -> MtrxSprs
DiagonalSparseMatrix(R, Q) : Rng, [ RngElt ] -> MtrxSprs
DiagonalSparseMatrix(Q) : [ RngElt ] -> MtrxSprs
Parents of Sparse Matrices
SparseMatrixStructure(R) : [ Rng ] -> MtrxSprsStr
Elementary Properties
BaseRing(A) : MtrxSprs -> Rng
NumberOfRows(A) : MtrxSprs -> RngIntElt
NumberOfColumns(A) : MtrxSprs -> RngIntElt
ElementToSequence(A) : Mtrx -> [ <RngIntElt, RngIntElt, RngElt> ]
NumberOfNonZeroEntries(A) : MtrxSprs -> RngIntElt
Density(A) : MtrxSprs -> FldRe
Support(A, i) : MtrxSprs, RngIntElt -> [RngIntElt]
Support(A) : MtrxSprs -> [ <RngIntElt, RngIntElt, RngElt> ]
Weights
RowWeight(A, i) : MtrxSprs, RngIntElt -> RngIntElt
RowWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWeight(A, j) : MtrxSprs, RngIntElt -> RngIntElt
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
ColumnWeights(A) : MtrxSprs -> [RngIntElt]
Accessing or Modifying Entries
A[i] : MtrxSprs, RngIntElt -> ModTupRngElt
A[i, j] : MtrxSprs, RngIntElt, RngIntElt -> RngElt
A[i, j] := x : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
SetEntry(~A, i, j, x) : MtrxSprs, RngIntElt, RngIntElt, RngElt ->
Example SMat_Indexing (H27E2)
Extracting and Inserting Blocks
Submatrix(A, i, j, p, q) : MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> MtrxSprs
SubmatrixRange(A, i, j, r, s) : MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> MtrxSprs
Submatrix(A, I, J) : MtrxSprs, [RngIntElt], [RngIntElt] -> MtrxSprs
InsertBlock(A, B, i, j) : MtrxSprs, MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
RowSubmatrix(A, i, k) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
RowSubmatrix(A, i) : MtrxSprs, RngIntElt -> MtrxSprs
RowSubmatrixRange(A, i, j) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
ColumnSubmatrix(A, i, k) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
ColumnSubmatrix(A, i) : MtrxSprs, RngIntElt -> MtrxSprs
ColumnSubmatrixRange(A, i, j) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
Row and Column Operations
SwapRows(A, i, j) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
SwapColumns(A, i, j) : MtrxSprs, RngIntElt, RngIntElt -> MtrxSprs
ReverseRows(A) : MtrxSprs -> MtrxSprs
ReverseColumns(A) : MtrxSprs -> MtrxSprs
AddRow(A, c, i, j) : MtrxSprs, RngElt, RngIntElt, RngIntElt -> MtrxSprs
AddColumn(A, c, i, j) : MtrxSprs, RngElt, RngIntElt, RngIntElt -> MtrxSprs
MultiplyRow(A, c, i) : MtrxSprs, RngElt, RngIntElt -> MtrxSprs
MultiplyColumn(A, c, i) : MtrxSprs, RngElt, RngIntElt -> MtrxSprs
RemoveRow(A, i) : MtrxSprs, RngIntElt -> MtrxSprs
RemoveColumn(A, j) : MtrxSprs, RngIntElt -> MtrxSprs
RemoveRowColumn(A, i, j) : MtrxSprs, RngIntElt -> MtrxSprs
RemoveZeroRows(A) : MtrxSprs -> MtrxSprs
Building Block Matrices
HorizontalJoin(A, B) : MtrxSprs, MtrxSprs -> MtrxSprs
VerticalJoin(A, B) : MtrxSprs, MtrxSprs -> MtrxSprs
DiagonalJoin(A, B) : MtrxSprs, MtrxSprs -> MtrxSprs
Conversion to and from Dense Matrices
Matrix(A) : MtrxSprs -> Mtrx
SparseMatrix(A) : Mtrx -> MtrxSprs
Changing Ring
ChangeRing(A, R) : MtrxSprs, Rng -> MtrxSprs
Predicates
A eq B : MtrxSprs, MtrxSprs -> BoolElt
IsZero(A) : MtrxSprs -> BoolElt
IsOne(A) : MtrxSprs -> BoolElt
IsMinusOne(A) : MtrxSprs -> BoolElt
IsScalar(A) : MtrxSprs -> BoolElt
IsDiagonal(A) : MtrxSprs -> BoolElt
IsSymmetric(A) : MtrxSprs -> BoolElt
IsUpperTriangular(A) : MtrxSprs -> BoolElt
IsLowerTriangular(A) : MtrxSprs -> BoolElt
Elementary Arithmetic
A + B : MtrxSprs, MtrxSprs -> MtrxSprs
A - B : MtrxSprs, MtrxSprs -> MtrxSprs
A * B : MtrxSprs, MtrxSprs -> MtrxSprs
x * A : RngElt, MtrxSprs -> MtrxSprs
-A : MtrxSprs -> MtrxSprs
A ^-1 : MtrxSprs, RngIntElt -> MtrxSprs
A ^ n : MtrxSprs, RngIntElt -> MtrxSprs
Transpose(A) : MtrxSprs -> MtrxSprs
Multiplying Vectors or Matrices by Sparse Matrices
v * A : ModTupRng, MtrxSprs -> ModTupRng
MultiplyByTranspose(v, A) : ModTupRng, MtrxSprs -> ModTupRng
Nullspace and Rowspace
Nullspace(A) : MtrxSprs -> ModTupRng
NullspaceMatrix(A) : MtrxSprs -> Mtrx
NullspaceOfTranspose(A) : MtrxSprs -> ModTupRng
Rowspace(A) : MtrxSprs -> ModTupRng
Rank
Rank(A) : MtrxSprs -> RngIntElt
Determinant and Other Properties
Determinant(A: parameters) : MtrxSprs -> RngElt
Elementary Divisors (Smith Form)
ElementaryDivisors(A) : MtrxSprs -> [RngElt]
Verbosity
SetVerbose("SparseMatrix", v) : MonStgElt, RngIntElt ->
Linear Systems (Structured Gaussian Elimination)
ModularSolution(A, M) : MtrxSprs, RngIntElt -> ModTupRng
Example SMat_DiscreteLog (H27E3)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012