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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.exceptions import NonSquareMatrixError |
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from sympy.matrices.matrixbase import MatrixBase |
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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, **hints): |
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arg = self.arg |
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if hints.get('deep', True): |
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arg = arg.doit(**hints) |
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result = arg._eval_determinant() |
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if result is not None: |
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return result |
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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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if isinstance(self.arg, MatrixBase): |
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return self.arg.per() |
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else: |
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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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