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NZMATH
1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
 Fossies Dox: NZMATH-1.2.0.tar.gz ("inofficial" and yet experimental doxygen-generated source code documentation)  |
|
NZMATH
1.2.0
About: NZMATH is a Python based number theory oriented calculation system.
Fossies Dox: NZMATH-1.2.0.tar.gz ("inofficial" and yet experimental doxygen-generated source code documentation) |
Public Member Functions | |
| def | __init__ (self, row, column=0, compo=0, coeff_ring=0) |
| def | triangulate (self) |
| def | determinant (self) |
| def | inverse (self, V=1) |
| def | hessenbergForm (self) |
| def | LUDecomposition (self) |
 Public Member Functions inherited from nzmath.matrix.RingSquareMatrix | |
| def | __pow__ (self, other) |
| def | toFieldMatrix (self) |
| def | getRing (self) |
| def | isOrthogonalMatrix (self) |
| def | isAlternatingMatrix (self) |
| def | isSingular (self) |
| def | trace (self) |
| def | cofactor (self, i, j) |
| def | commutator (self, other) |
| def | characteristicMatrix (self) |
| def | characteristicPolynomial (self) |
| def | adjugateMatrix (self) |
| def | cofactorMatrix (self) |
| def | smithNormalForm (self) |
| def | extsmithNormalForm (self) |
| Public Member Functions inherited from nzmath.matrix.SquareMatrix | |
| def | isUpperTriangularMatrix (self) |
| def | isLowerTriangularMatrix (self) |
| def | isDiagonalMatrix (self) |
| def | isScalarMatrix (self) |
| def | isSymmetricMatrix (self) |
| Public Member Functions inherited from nzmath.matrix.Matrix | |
| def | __getitem__ (self, index) |
| def | __setitem__ (self, key, value) |
| def | __eq__ (self, other) |
| def | __hash__ (self) |
| def | __ne__ (self, other) |
| def | __nonzero__ (self) |
| def | __contains__ (self, item) |
| def | __repr__ (self) |
| def | __str__ (self) |
| def | __call__ (self, arg) |
| def | map (self, function) |
| def | reduce (self, function, initializer=None) |
| def | copy (self) |
| def | set (self, compo) |
| def | setRow (self, m, arg) |
| def | setColumn (self, n, arg) |
| def | getRow (self, i) |
| def | getColumn (self, j) |
| def | swapRow (self, m1, m2) |
| def | swapColumn (self, n1, n2) |
| def | insertRow (self, i, arg) |
| def | insertColumn (self, j, arg) |
| def | extendRow (self, arg) |
| def | extendColumn (self, arg) |
| def | deleteRow (self, i) |
| def | deleteColumn (self, j) |
| def | transpose (self) |
| def | getBlock (self, i, j, row, column=None) |
| def | subMatrix (self, I, J=None) |
| def | toMatrix (self, flag=True) |
| Public Member Functions inherited from nzmath.matrix.RingMatrix | |
| def | __add__ (self, other) |
| def | __sub__ (self, other) |
| def | __mul__ (self, other) |
| def | __rmul__ (self, other) |
| def | __mod__ (self, other) |
| def | __pos__ (self) |
| def | __neg__ (self) |
| def | getCoefficientRing (self) |
| def | hermiteNormalForm (self, non_zero=False) |
| def | exthermiteNormalForm (self, non_zero=False) |
| def | kernelAsModule (self) |
| Public Member Functions inherited from nzmath.ring.RingElement | |
| def | __init__ (self, *args, **kwd) |
| def | __eq__ (self, other) |
| def | __hash__ (self) |
| def | __ne__ (self, other) |
| Public Member Functions inherited from nzmath.matrix.FieldMatrix | |
| def | __truediv__ (self, other) |
| def | toSubspace (self, isbasis=None) |
| def | kernel (self) |
| def | image (self) |
| def | rank (self) |
| def | inverseImage (self, V) |
| def | solve (self, B) |
| def | columnEchelonForm (self) |
Additional Inherited Members | |
| Public Attributes inherited from nzmath.matrix.RingSquareMatrix | |
| coeff_ring | |
| row | |
| Public Attributes inherited from nzmath.matrix.Matrix | |
| row | |
| column | |
| compo | |
| coeff_ring | |
| Public Attributes inherited from nzmath.matrix.RingMatrix | |
| row | |
| coeff_ring | |
| Public Attributes inherited from nzmath.matrix.FieldMatrix | |
| coeff_ring | |
| row | |
| isbasis | |
| Static Public Attributes inherited from nzmath.matrix.RingSquareMatrix | |
| def | isAntisymmetricMatrix = isAlternatingMatrix |
| def | isSkewsymmetricMatrix = isAlternatingMatrix |
| def | cofactors = cofactorMatrix |
| def | SNF = smithNormalForm |
| def | elementary_divisor = smithNormalForm |
| def | extSNF = extsmithNormalForm |
| Static Public Attributes inherited from nzmath.matrix.RingMatrix | |
| def | HNF = hermiteNormalForm |
| def | extHNF = exthermiteNormalForm |
FieldSquareMatrix is a class for square matrices in field.
| def nzmath.matrix.FieldSquareMatrix.__init__ | ( | self, | |
| row, | |||
column = 0, |
|||
compo = 0, |
|||
coeff_ring = 0 |
|||
| ) |
FieldSquareMatrix(row [, column, components, coeff_ring]) FieldSquareMatrix must be row == column .
Reimplemented from nzmath.matrix.RingSquareMatrix.
Definition at line 1436 of file matrix.py.
References nzmath.matrix.Matrix._initialize().
| def nzmath.matrix.FieldSquareMatrix.determinant | ( | self | ) |
Return determinant of self.
Reimplemented from nzmath.matrix.RingSquareMatrix.
Definition at line 1469 of file matrix.py.
References nzmath.matrix.Matrix.coeff_ring, nzmath.bigrange.range(), nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, and nzmath.matrix.FieldSquareMatrix.triangulate().
| def nzmath.matrix.FieldSquareMatrix.hessenbergForm | ( | self | ) |
Return a Matrix in Hessenberg Form.
Definition at line 1534 of file matrix.py.
References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), nzmath.bigrange.range(), nzmath.matrix.Matrix.row, and nzmath.lattice.LatticeElement.row.
| def nzmath.matrix.FieldSquareMatrix.inverse | ( | self, | |
V = 1 |
|||
| ) |
Return inverse matrix of self or self.inverse() * V. If inverse does not exist, raise NoInverse error.
Definition at line 1479 of file matrix.py.
References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), nzmath.matrix.createMatrix(), nzmath.bigrange.range(), nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, nzmath.matrix.unitMatrix(), and nzmath.matrix.zeroMatrix().
Referenced by nzmath.permute.Permute.__pow__(), nzmath.permute.ExPermute.__pow__(), nzmath.module.Ideal.__pow__(), nzmath.matrix.RingSquareMatrix.__pow__(), nzmath.permute.Permute.__rdiv__(), nzmath.permute.ExPermute.__rdiv__(), and nzmath.ring.QuotientFieldElement.__rtruediv__().
| def nzmath.matrix.FieldSquareMatrix.LUDecomposition | ( | self | ) |
LUDecomposition() -> (L, U)
L and U are matrices such that
self == L * U
L : lower triangular matrix
U : upper triangular matrix
Definition at line 1564 of file matrix.py.
References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), nzmath.bigrange.range(), nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, and nzmath.matrix.unitMatrix().
| def nzmath.matrix.FieldSquareMatrix.triangulate | ( | self | ) |
Return triangulated matrix of self.
Definition at line 1443 of file matrix.py.
References nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), and nzmath.bigrange.range().
Referenced by nzmath.matrix.FieldSquareMatrix.determinant().
1.8.16