Sparse Matrices
- Introduction
- Creation of Sparse Matrices
- Construction of Initialized Sparse Matrices
SparseMatrix(R, m, n, Q): Rng, RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] → MtrxSprsSparseMatrix(m, n, Q): RngIntElt, RngIntElt, [ <RngIntElt, RngIntElt, RngElt> ] → MtrxSprsSparseMatrix(R, m, n): Rng, RngIntElt, RngIntElt → MtrxSprsSparseMatrix(m, n): RngIntElt, RngIntElt → MtrxSprs
- Construction of Trivial Sparse Matrices
- Construction of Structured Matrices
IdentitySparseMatrix(R, n): Rng, RngElt → MtrxSprsScalarSparseMatrix(n, s): RngIntElt, RngElt → MtrxSprsScalarSparseMatrix(R, n, s): Rng, RngIntElt, RngElt → MtrxSprsDiagonalSparseMatrix(R, n, Q): Rng, RngIntElt, [ RngElt ] → MtrxSprsDiagonalSparseMatrix(R, Q): Rng, [ RngElt ] → MtrxSprsDiagonalSparseMatrix(Q): [ RngElt ] → MtrxSprsSparseMonomialMatrix(g): GrpPermElt → MtrxSprs
- Parents of Sparse Matrices
- Accessing Sparse Matrices
- Accessing or Modifying Entries
A[i]: MtrxSprs, RngIntElt → ModTupRngEltA[i, j]: MtrxSprs, RngIntElt, RngIntElt → RngEltA[i, j] := x: MtrxSprs, RngIntElt, RngIntElt, RngEltSetEntry(~A, i, j, x): MtrxSprs, RngIntElt, RngIntElt, RngEltExample: Indexing- Extracting and Inserting Blocks
Submatrix(A, i, j, p, q): MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt → MtrxSprsExtractBlock(A, i, j, p, q): MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt → MtrxSprsSubmatrixRange(A, i, j, r, s): MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt → MtrxSprsExtractBlockRange(A, i, j, r, s): MtrxSprs, RngIntElt, RngIntElt, RngIntElt, RngIntElt → MtrxSprsSubmatrix(A, I, J): MtrxSprs, [RngIntElt], [RngIntElt] → MtrxSprsInsertBlock(A, B, i, j): MtrxSprs, MtrxSprs, RngIntElt, RngIntElt → MtrxSprsInsertBlock(~A, B, i, j): MtrxSprs, MtrxSprs, RngIntElt, RngIntElt → MtrxSprsRowSubmatrix(A, i, k): MtrxSprs, RngIntElt, RngIntElt → MtrxSprsRowSubmatrix(A, i): MtrxSprs, RngIntElt → MtrxSprsRowSubmatrixRange(A, i, j): MtrxSprs, RngIntElt, RngIntElt → MtrxSprsColumnSubmatrix(A, i, k): MtrxSprs, RngIntElt, RngIntElt → MtrxSprsColumnSubmatrix(A, i): MtrxSprs, RngIntElt → MtrxSprsColumnSubmatrixRange(A, i, j): MtrxSprs, RngIntElt, RngIntElt → MtrxSprs
- Row and Column Operations
SwapRows(A, i, j): MtrxSprs, RngIntElt, RngIntElt → MtrxSprsSwapRows(~A, i, j): MtrxSprs, RngIntElt, RngIntEltSwapColumns(A, i, j): MtrxSprs, RngIntElt, RngIntElt → MtrxSprsSwapColumns(~A, i, j): MtrxSprs, RngIntElt, RngIntEltReverseRows(A): MtrxSprs → MtrxSprsReverseRows(~A): MtrxSprsReverseColumns(A): MtrxSprs → MtrxSprsReverseColumns(~A): MtrxSprsAddRow(A, c, i, j): MtrxSprs, RngElt, RngIntElt, RngIntElt → MtrxSprsAddRow(~A, c, i, j): MtrxSprs, RngElt, RngIntElt, RngIntEltAddColumn(A, c, i, j): MtrxSprs, RngElt, RngIntElt, RngIntElt → MtrxSprsAddColumn(~A, c, i, j): MtrxSprs, RngElt, RngIntElt, RngIntEltMultiplyRow(A, c, i): MtrxSprs, RngElt, RngIntElt → MtrxSprsMultiplyRow(~A, c, i): MtrxSprs, RngElt, RngIntEltMultiplyColumn(A, c, i): MtrxSprs, RngElt, RngIntElt → MtrxSprsMultiplyColumn(~A, c, i): MtrxSprs, RngElt, RngIntEltRemoveRow(A, i): MtrxSprs, RngIntElt → MtrxSprsRemoveRow(~A, i): MtrxSprs, RngIntEltRemoveColumn(A, j): MtrxSprs, RngIntElt → MtrxSprsRemoveColumn(~A, j): MtrxSprs, RngIntEltRemoveRowColumn(A, i, j): MtrxSprs, RngIntElt → MtrxSprsRemoveRowColumn(~A, i, j): MtrxSprs, RngIntEltRemoveZeroRows(A): MtrxSprs → MtrxSprsRemoveZeroRows(~A): MtrxSprs
- Building Block Matrices
- Conversion to and from Dense Matrices
- Changing Ring
- Predicates
- Elementary Arithmetic
- Multiplying Vectors or Matrices by Sparse Matrices
- Non-trivial Properties
- Determinant and Other Properties
- Minimal and Characteristic Polynomials and Eigenvalues
MinimalPolynomial(A: parameters): MtrxSprs → RngUPolEltCharacteristicPolynomial(A: parameters): MtrxSprs → RngUPolEltMinimalAndCharacteristicPolynomials(A: parameters): MtrxSprs → RngUPolElt, RngUPolEltMCPolynomials(A): MtrxSprs → RngUPolElt, RngUPolEltFactoredMinimalPolynomial(A: parameters): MtrxSprs → [ <RngUPolElt, RngIntElt>]FactoredCharacteristicPolynomial(A: parameters): MtrxSprs → [ <RngUPolElt, RngIntElt>]FactoredMinimalAndCharacteristicPolynomials(A: parameters): MtrxSprs → [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]FactoredMCPolynomials(A: parameters): MtrxSprs → [<RngUPolElt, RngIntElt>], [<RngUPolElt, RngIntElt>]Eigenvalues(A): MtrxSprs → { <FldElt, RngIntElt> }Eigenspace(A, e): AlgMatElt, FldElt → ModTup- Elementary Divisors (Smith Form)
- Verbosity
- Linear Systems (Structured Gaussian Elimination)
