142 lines
3.1 KiB
Python
142 lines
3.1 KiB
Python
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from sympy.core.basic import Basic
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from sympy.core.expr import Expr
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from sympy.core.singleton import S
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from sympy.core.sympify import sympify
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from sympy.matrices.common import NonSquareMatrixError
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class Determinant(Expr):
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"""Matrix Determinant
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Represents the determinant of a matrix expression.
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Examples
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========
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>>> from sympy import MatrixSymbol, Determinant, eye
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>>> A = MatrixSymbol('A', 3, 3)
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>>> Determinant(A)
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Determinant(A)
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>>> Determinant(eye(3)).doit()
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1
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"""
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is_commutative = True
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def __new__(cls, mat):
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mat = sympify(mat)
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if not mat.is_Matrix:
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raise TypeError("Input to Determinant, %s, not a matrix" % str(mat))
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if mat.is_square is False:
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raise NonSquareMatrixError("Det of a non-square matrix")
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return Basic.__new__(cls, mat)
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@property
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def arg(self):
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return self.args[0]
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@property
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def kind(self):
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return self.arg.kind.element_kind
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def doit(self, expand=False, **hints):
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try:
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return self.arg._eval_determinant()
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except (AttributeError, NotImplementedError):
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return self
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def det(matexpr):
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""" Matrix Determinant
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Examples
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========
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>>> from sympy import MatrixSymbol, det, eye
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>>> A = MatrixSymbol('A', 3, 3)
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>>> det(A)
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Determinant(A)
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>>> det(eye(3))
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1
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"""
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return Determinant(matexpr).doit()
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class Permanent(Expr):
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"""Matrix Permanent
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Represents the permanent of a matrix expression.
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Examples
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========
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>>> from sympy import MatrixSymbol, Permanent, ones
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>>> A = MatrixSymbol('A', 3, 3)
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>>> Permanent(A)
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Permanent(A)
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>>> Permanent(ones(3, 3)).doit()
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6
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"""
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def __new__(cls, mat):
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mat = sympify(mat)
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if not mat.is_Matrix:
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raise TypeError("Input to Permanent, %s, not a matrix" % str(mat))
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return Basic.__new__(cls, mat)
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@property
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def arg(self):
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return self.args[0]
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def doit(self, expand=False, **hints):
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try:
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return self.arg.per()
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except (AttributeError, NotImplementedError):
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return self
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def per(matexpr):
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""" Matrix Permanent
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Examples
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========
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>>> from sympy import MatrixSymbol, Matrix, per, ones
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>>> A = MatrixSymbol('A', 3, 3)
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>>> per(A)
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Permanent(A)
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>>> per(ones(5, 5))
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120
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>>> M = Matrix([1, 2, 5])
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>>> per(M)
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8
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"""
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return Permanent(matexpr).doit()
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from sympy.assumptions.ask import ask, Q
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from sympy.assumptions.refine import handlers_dict
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def refine_Determinant(expr, assumptions):
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"""
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>>> from sympy import MatrixSymbol, Q, assuming, refine, det
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>>> X = MatrixSymbol('X', 2, 2)
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>>> det(X)
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Determinant(X)
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>>> with assuming(Q.orthogonal(X)):
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... print(refine(det(X)))
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1
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"""
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if ask(Q.orthogonal(expr.arg), assumptions):
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return S.One
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elif ask(Q.singular(expr.arg), assumptions):
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return S.Zero
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elif ask(Q.unit_triangular(expr.arg), assumptions):
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return S.One
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return expr
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handlers_dict['Determinant'] = refine_Determinant
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