add read me

venv/lib/python3.12/site-packages/sympy/matrices/expressions/determinant.py

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+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.singleton import S
+from sympy.core.sympify import sympify
+from sympy.matrices.exceptions import NonSquareMatrixError
+from sympy.matrices.matrixbase import MatrixBase
+
+
+class Determinant(Expr):
+    """Matrix Determinant
+
+    Represents the determinant of a matrix expression.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Determinant, eye
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> Determinant(A)
+    Determinant(A)
+    >>> Determinant(eye(3)).doit()
+    1
+    """
+    is_commutative = True
+
+    def __new__(cls, mat):
+        mat = sympify(mat)
+        if not mat.is_Matrix:
+            raise TypeError("Input to Determinant, %s, not a matrix" % str(mat))
+
+        if mat.is_square is False:
+            raise NonSquareMatrixError("Det of a non-square matrix")
+
+        return Basic.__new__(cls, mat)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    @property
+    def kind(self):
+        return self.arg.kind.element_kind
+
+    def doit(self, **hints):
+        arg = self.arg
+        if hints.get('deep', True):
+            arg = arg.doit(**hints)
+
+        result = arg._eval_determinant()
+        if result is not None:
+            return result
+
+        return self
+
+
+def det(matexpr):
+    """ Matrix Determinant
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, det, eye
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> det(A)
+    Determinant(A)
+    >>> det(eye(3))
+    1
+    """
+
+    return Determinant(matexpr).doit()
+
+class Permanent(Expr):
+    """Matrix Permanent
+
+    Represents the permanent of a matrix expression.
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Permanent, ones
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> Permanent(A)
+    Permanent(A)
+    >>> Permanent(ones(3, 3)).doit()
+    6
+    """
+
+    def __new__(cls, mat):
+        mat = sympify(mat)
+        if not mat.is_Matrix:
+            raise TypeError("Input to Permanent, %s, not a matrix" % str(mat))
+
+        return Basic.__new__(cls, mat)
+
+    @property
+    def arg(self):
+        return self.args[0]
+
+    def doit(self, expand=False, **hints):
+        if isinstance(self.arg, MatrixBase):
+            return self.arg.per()
+        else:
+            return self
+
+def per(matexpr):
+    """ Matrix Permanent
+
+    Examples
+    ========
+
+    >>> from sympy import MatrixSymbol, Matrix, per, ones
+    >>> A = MatrixSymbol('A', 3, 3)
+    >>> per(A)
+    Permanent(A)
+    >>> per(ones(5, 5))
+    120
+    >>> M = Matrix([1, 2, 5])
+    >>> per(M)
+    8
+    """
+
+    return Permanent(matexpr).doit()
+
+from sympy.assumptions.ask import ask, Q
+from sympy.assumptions.refine import handlers_dict
+
+
+def refine_Determinant(expr, assumptions):
+    """
+    >>> from sympy import MatrixSymbol, Q, assuming, refine, det
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> det(X)
+    Determinant(X)
+    >>> with assuming(Q.orthogonal(X)):
+    ...     print(refine(det(X)))
+    1
+    """
+    if ask(Q.orthogonal(expr.arg), assumptions):
+        return S.One
+    elif ask(Q.singular(expr.arg), assumptions):
+        return S.Zero
+    elif ask(Q.unit_triangular(expr.arg), assumptions):
+        return S.One
+
+    return expr
+
+
+handlers_dict['Determinant'] = refine_Determinant