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lib/python3.12/site-packages/sympy/assumptions/handlers/__init__.py

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+"""
+Multipledispatch handlers for ``Predicate`` are implemented here.
+Handlers in this module are not directly imported to other modules in
+order to avoid circular import problem.
+"""
+
+from .common import (AskHandler, CommonHandler,
+    test_closed_group)
+
+__all__ = [
+    'AskHandler', 'CommonHandler',
+    'test_closed_group'
+]

lib/python3.12/site-packages/sympy/assumptions/handlers/common.py

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+"""
+This module defines base class for handlers and some core handlers:
+``Q.commutative`` and ``Q.is_true``.
+"""
+
+from sympy.assumptions import Q, ask, AppliedPredicate
+from sympy.core import Basic, Symbol
+from sympy.core.logic import _fuzzy_group
+from sympy.core.numbers import NaN, Number
+from sympy.logic.boolalg import (And, BooleanTrue, BooleanFalse, conjuncts,
+    Equivalent, Implies, Not, Or)
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+from ..predicates.common import CommutativePredicate, IsTruePredicate
+
+
+class AskHandler:
+    """Base class that all Ask Handlers must inherit."""
+    def __new__(cls, *args, **kwargs):
+        sympy_deprecation_warning(
+            """
+            The AskHandler system is deprecated. The AskHandler class should
+            be replaced with the multipledispatch handler of Predicate
+            """,
+            deprecated_since_version="1.8",
+            active_deprecations_target='deprecated-askhandler',
+        )
+        return super().__new__(cls, *args, **kwargs)
+
+
+class CommonHandler(AskHandler):
+    # Deprecated
+    """Defines some useful methods common to most Handlers. """
+
+    @staticmethod
+    def AlwaysTrue(expr, assumptions):
+        return True
+
+    @staticmethod
+    def AlwaysFalse(expr, assumptions):
+        return False
+
+    @staticmethod
+    def AlwaysNone(expr, assumptions):
+        return None
+
+    NaN = AlwaysFalse
+
+
+# CommutativePredicate
+
+@CommutativePredicate.register(Symbol)
+def _(expr, assumptions):
+    """Objects are expected to be commutative unless otherwise stated"""
+    assumps = conjuncts(assumptions)
+    if expr.is_commutative is not None:
+        return expr.is_commutative and not ~Q.commutative(expr) in assumps
+    if Q.commutative(expr) in assumps:
+        return True
+    elif ~Q.commutative(expr) in assumps:
+        return False
+    return True
+
+@CommutativePredicate.register(Basic)
+def _(expr, assumptions):
+    for arg in expr.args:
+        if not ask(Q.commutative(arg), assumptions):
+            return False
+    return True
+
+@CommutativePredicate.register(Number)
+def _(expr, assumptions):
+    return True
+
+@CommutativePredicate.register(NaN)
+def _(expr, assumptions):
+    return True
+
+
+# IsTruePredicate
+
+@IsTruePredicate.register(bool)
+def _(expr, assumptions):
+    return expr
+
+@IsTruePredicate.register(BooleanTrue)
+def _(expr, assumptions):
+    return True
+
+@IsTruePredicate.register(BooleanFalse)
+def _(expr, assumptions):
+    return False
+
+@IsTruePredicate.register(AppliedPredicate)
+def _(expr, assumptions):
+    return ask(expr, assumptions)
+
+@IsTruePredicate.register(Not)
+def _(expr, assumptions):
+    arg = expr.args[0]
+    if arg.is_Symbol:
+        # symbol used as abstract boolean object
+        return None
+    value = ask(arg, assumptions=assumptions)
+    if value in (True, False):
+        return not value
+    else:
+        return None
+
+@IsTruePredicate.register(Or)
+def _(expr, assumptions):
+    result = False
+    for arg in expr.args:
+        p = ask(arg, assumptions=assumptions)
+        if p is True:
+            return True
+        if p is None:
+            result = None
+    return result
+
+@IsTruePredicate.register(And)
+def _(expr, assumptions):
+    result = True
+    for arg in expr.args:
+        p = ask(arg, assumptions=assumptions)
+        if p is False:
+            return False
+        if p is None:
+            result = None
+    return result
+
+@IsTruePredicate.register(Implies)
+def _(expr, assumptions):
+    p, q = expr.args
+    return ask(~p | q, assumptions=assumptions)
+
+@IsTruePredicate.register(Equivalent)
+def _(expr, assumptions):
+    p, q = expr.args
+    pt = ask(p, assumptions=assumptions)
+    if pt is None:
+        return None
+    qt = ask(q, assumptions=assumptions)
+    if qt is None:
+        return None
+    return pt == qt
+
+
+#### Helper methods
+def test_closed_group(expr, assumptions, key):
+    """
+    Test for membership in a group with respect
+    to the current operation.
+    """
+    return _fuzzy_group(
+        (ask(key(a), assumptions) for a in expr.args), quick_exit=True)

lib/python3.12/site-packages/sympy/assumptions/predicates/__init__.py

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+"""
+Module to implement predicate classes.
+
+Class of every predicate registered to ``Q`` is defined here.
+"""

lib/python3.12/site-packages/sympy/assumptions/predicates/calculus.py

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+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+class FinitePredicate(Predicate):
+    """
+    Finite number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.finite(x)`` is true if ``x`` is a number but neither an infinity
+    nor a ``NaN``. In other words, ``ask(Q.finite(x))`` is true for all
+    numerical ``x`` having a bounded absolute value.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, S, oo, I, zoo
+    >>> from sympy.abc import x
+    >>> ask(Q.finite(oo))
+    False
+    >>> ask(Q.finite(-oo))
+    False
+    >>> ask(Q.finite(zoo))
+    False
+    >>> ask(Q.finite(1))
+    True
+    >>> ask(Q.finite(2 + 3*I))
+    True
+    >>> ask(Q.finite(x), Q.positive(x))
+    True
+    >>> print(ask(Q.finite(S.NaN)))
+    None
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Finite
+
+    """
+    name = 'finite'
+    handler = Dispatcher(
+        "FiniteHandler",
+        doc=("Handler for Q.finite. Test that an expression is bounded respect"
+        " to all its variables.")
+    )
+
+
+class InfinitePredicate(Predicate):
+    """
+    Infinite number predicate.
+
+    ``Q.infinite(x)`` is true iff the absolute value of ``x`` is
+    infinity.
+
+    """
+    # TODO: Add examples
+    name = 'infinite'
+    handler = Dispatcher(
+        "InfiniteHandler",
+        doc="""Handler for Q.infinite key."""
+    )
+
+
+class PositiveInfinitePredicate(Predicate):
+    """
+    Positive infinity predicate.
+
+    ``Q.positive_infinite(x)`` is true iff ``x`` is positive infinity ``oo``.
+    """
+    name = 'positive_infinite'
+    handler = Dispatcher("PositiveInfiniteHandler")
+
+
+class NegativeInfinitePredicate(Predicate):
+    """
+    Negative infinity predicate.
+
+    ``Q.negative_infinite(x)`` is true iff ``x`` is negative infinity ``-oo``.
+    """
+    name = 'negative_infinite'
+    handler = Dispatcher("NegativeInfiniteHandler")

lib/python3.12/site-packages/sympy/assumptions/predicates/common.py

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+from sympy.assumptions import Predicate, AppliedPredicate, Q
+from sympy.core.relational import Eq, Ne, Gt, Lt, Ge, Le
+from sympy.multipledispatch import Dispatcher
+
+
+class CommutativePredicate(Predicate):
+    """
+    Commutative predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.commutative(x))`` is true iff ``x`` commutes with any other
+    object with respect to multiplication operation.
+
+    """
+    # TODO: Add examples
+    name = 'commutative'
+    handler = Dispatcher("CommutativeHandler", doc="Handler for key 'commutative'.")
+
+
+binrelpreds = {Eq: Q.eq, Ne: Q.ne, Gt: Q.gt, Lt: Q.lt, Ge: Q.ge, Le: Q.le}
+
+class IsTruePredicate(Predicate):
+    """
+    Generic predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.is_true(x))`` is true iff ``x`` is true. This only makes
+    sense if ``x`` is a boolean object.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q
+    >>> from sympy.abc import x, y
+    >>> ask(Q.is_true(True))
+    True
+
+    Wrapping another applied predicate just returns the applied predicate.
+
+    >>> Q.is_true(Q.even(x))
+    Q.even(x)
+
+    Wrapping binary relation classes in SymPy core returns applied binary
+    relational predicates.
+
+    >>> from sympy import Eq, Gt
+    >>> Q.is_true(Eq(x, y))
+    Q.eq(x, y)
+    >>> Q.is_true(Gt(x, y))
+    Q.gt(x, y)
+
+    Notes
+    =====
+
+    This class is designed to wrap the boolean objects so that they can
+    behave as if they are applied predicates. Consequently, wrapping another
+    applied predicate is unnecessary and thus it just returns the argument.
+    Also, binary relation classes in SymPy core have binary predicates to
+    represent themselves and thus wrapping them with ``Q.is_true`` converts them
+    to these applied predicates.
+
+    """
+    name = 'is_true'
+    handler = Dispatcher(
+        "IsTrueHandler",
+        doc="Wrapper allowing to query the truth value of a boolean expression."
+    )
+
+    def __call__(self, arg):
+        # No need to wrap another predicate
+        if isinstance(arg, AppliedPredicate):
+            return arg
+        # Convert relational predicates instead of wrapping them
+        if getattr(arg, "is_Relational", False):
+            pred = binrelpreds[type(arg)]
+            return pred(*arg.args)
+        return super().__call__(arg)

lib/python3.12/site-packages/sympy/assumptions/predicates/matrices.py

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+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+class SquarePredicate(Predicate):
+    """
+    Square matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.square(x)`` is true iff ``x`` is a square matrix. A square matrix
+    is a matrix with the same number of rows and columns.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('X', 2, 3)
+    >>> ask(Q.square(X))
+    True
+    >>> ask(Q.square(Y))
+    False
+    >>> ask(Q.square(ZeroMatrix(3, 3)))
+    True
+    >>> ask(Q.square(Identity(3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Square_matrix
+
+    """
+    name = 'square'
+    handler = Dispatcher("SquareHandler", doc="Handler for Q.square.")
+
+
+class SymmetricPredicate(Predicate):
+    """
+    Symmetric matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.symmetric(x)`` is true iff ``x`` is a square matrix and is equal to
+    its transpose. Every square diagonal matrix is a symmetric matrix.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.symmetric(X*Z), Q.symmetric(X) & Q.symmetric(Z))
+    True
+    >>> ask(Q.symmetric(X + Z), Q.symmetric(X) & Q.symmetric(Z))
+    True
+    >>> ask(Q.symmetric(Y))
+    False
+
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Symmetric_matrix
+
+    """
+    # TODO: Add handlers to make these keys work with
+    # actual matrices and add more examples in the docstring.
+    name = 'symmetric'
+    handler = Dispatcher("SymmetricHandler", doc="Handler for Q.symmetric.")
+
+
+class InvertiblePredicate(Predicate):
+    """
+    Invertible matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.invertible(x)`` is true iff ``x`` is an invertible matrix.
+    A square matrix is called invertible only if its determinant is 0.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.invertible(X*Y), Q.invertible(X))
+    False
+    >>> ask(Q.invertible(X*Z), Q.invertible(X) & Q.invertible(Z))
+    True
+    >>> ask(Q.invertible(X), Q.fullrank(X) & Q.square(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Invertible_matrix
+
+    """
+    name = 'invertible'
+    handler = Dispatcher("InvertibleHandler", doc="Handler for Q.invertible.")
+
+
+class OrthogonalPredicate(Predicate):
+    """
+    Orthogonal matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.orthogonal(x)`` is true iff ``x`` is an orthogonal matrix.
+    A square matrix ``M`` is an orthogonal matrix if it satisfies
+    ``M^TM = MM^T = I`` where ``M^T`` is the transpose matrix of
+    ``M`` and ``I`` is an identity matrix. Note that an orthogonal
+    matrix is necessarily invertible.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.orthogonal(Y))
+    False
+    >>> ask(Q.orthogonal(X*Z*X), Q.orthogonal(X) & Q.orthogonal(Z))
+    True
+    >>> ask(Q.orthogonal(Identity(3)))
+    True
+    >>> ask(Q.invertible(X), Q.orthogonal(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Orthogonal_matrix
+
+    """
+    name = 'orthogonal'
+    handler = Dispatcher("OrthogonalHandler", doc="Handler for key 'orthogonal'.")
+
+
+class UnitaryPredicate(Predicate):
+    """
+    Unitary matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.unitary(x)`` is true iff ``x`` is a unitary matrix.
+    Unitary matrix is an analogue to orthogonal matrix. A square
+    matrix ``M`` with complex elements is unitary if :math:``M^TM = MM^T= I``
+    where :math:``M^T`` is the conjugate transpose matrix of ``M``.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.unitary(Y))
+    False
+    >>> ask(Q.unitary(X*Z*X), Q.unitary(X) & Q.unitary(Z))
+    True
+    >>> ask(Q.unitary(Identity(3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Unitary_matrix
+
+    """
+    name = 'unitary'
+    handler = Dispatcher("UnitaryHandler", doc="Handler for key 'unitary'.")
+
+
+class FullRankPredicate(Predicate):
+    """
+    Fullrank matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.fullrank(x)`` is true iff ``x`` is a full rank matrix.
+    A matrix is full rank if all rows and columns of the matrix
+    are linearly independent. A square matrix is full rank iff
+    its determinant is nonzero.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> ask(Q.fullrank(X.T), Q.fullrank(X))
+    True
+    >>> ask(Q.fullrank(ZeroMatrix(3, 3)))
+    False
+    >>> ask(Q.fullrank(Identity(3)))
+    True
+
+    """
+    name = 'fullrank'
+    handler = Dispatcher("FullRankHandler", doc="Handler for key 'fullrank'.")
+
+
+class PositiveDefinitePredicate(Predicate):
+    r"""
+    Positive definite matrix predicate.
+
+    Explanation
+    ===========
+
+    If $M$ is a :math:`n \times n` symmetric real matrix, it is said
+    to be positive definite if :math:`Z^TMZ` is positive for
+    every non-zero column vector $Z$ of $n$ real numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, Identity
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> Y = MatrixSymbol('Y', 2, 3)
+    >>> Z = MatrixSymbol('Z', 2, 2)
+    >>> ask(Q.positive_definite(Y))
+    False
+    >>> ask(Q.positive_definite(Identity(3)))
+    True
+    >>> ask(Q.positive_definite(X + Z), Q.positive_definite(X) &
+    ...     Q.positive_definite(Z))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Positive-definite_matrix
+
+    """
+    name = "positive_definite"
+    handler = Dispatcher("PositiveDefiniteHandler", doc="Handler for key 'positive_definite'.")
+
+
+class UpperTriangularPredicate(Predicate):
+    """
+    Upper triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A matrix $M$ is called upper triangular matrix if :math:`M_{ij}=0`
+    for :math:`i<j`.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, ZeroMatrix, Identity
+    >>> ask(Q.upper_triangular(Identity(3)))
+    True
+    >>> ask(Q.upper_triangular(ZeroMatrix(3, 3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/UpperTriangularMatrix.html
+
+    """
+    name = "upper_triangular"
+    handler = Dispatcher("UpperTriangularHandler", doc="Handler for key 'upper_triangular'.")
+
+
+class LowerTriangularPredicate(Predicate):
+    """
+    Lower triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A matrix $M$ is called lower triangular matrix if :math:`M_{ij}=0`
+    for :math:`i>j`.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, ZeroMatrix, Identity
+    >>> ask(Q.lower_triangular(Identity(3)))
+    True
+    >>> ask(Q.lower_triangular(ZeroMatrix(3, 3)))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/LowerTriangularMatrix.html
+
+    """
+    name = "lower_triangular"
+    handler = Dispatcher("LowerTriangularHandler", doc="Handler for key 'lower_triangular'.")
+
+
+class DiagonalPredicate(Predicate):
+    """
+    Diagonal matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.diagonal(x)`` is true iff ``x`` is a diagonal matrix. A diagonal
+    matrix is a matrix in which the entries outside the main diagonal
+    are all zero.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol, ZeroMatrix
+    >>> X = MatrixSymbol('X', 2, 2)
+    >>> ask(Q.diagonal(ZeroMatrix(3, 3)))
+    True
+    >>> ask(Q.diagonal(X), Q.lower_triangular(X) &
+    ...     Q.upper_triangular(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Diagonal_matrix
+
+    """
+    name = "diagonal"
+    handler = Dispatcher("DiagonalHandler", doc="Handler for key 'diagonal'.")
+
+
+class IntegerElementsPredicate(Predicate):
+    """
+    Integer elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.integer_elements(x)`` is true iff all the elements of ``x``
+    are integers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.integer(X[1, 2]), Q.integer_elements(X))
+    True
+
+    """
+    name = "integer_elements"
+    handler = Dispatcher("IntegerElementsHandler", doc="Handler for key 'integer_elements'.")
+
+
+class RealElementsPredicate(Predicate):
+    """
+    Real elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.real_elements(x)`` is true iff all the elements of ``x``
+    are real numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.real(X[1, 2]), Q.real_elements(X))
+    True
+
+    """
+    name = "real_elements"
+    handler = Dispatcher("RealElementsHandler", doc="Handler for key 'real_elements'.")
+
+
+class ComplexElementsPredicate(Predicate):
+    """
+    Complex elements matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.complex_elements(x)`` is true iff all the elements of ``x``
+    are complex numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.complex(X[1, 2]), Q.complex_elements(X))
+    True
+    >>> ask(Q.complex_elements(X), Q.integer_elements(X))
+    True
+
+    """
+    name = "complex_elements"
+    handler = Dispatcher("ComplexElementsHandler", doc="Handler for key 'complex_elements'.")
+
+
+class SingularPredicate(Predicate):
+    """
+    Singular matrix predicate.
+
+    A matrix is singular iff the value of its determinant is 0.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.singular(X), Q.invertible(X))
+    False
+    >>> ask(Q.singular(X), ~Q.invertible(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/SingularMatrix.html
+
+    """
+    name = "singular"
+    handler = Dispatcher("SingularHandler", doc="Predicate fore key 'singular'.")
+
+
+class NormalPredicate(Predicate):
+    """
+    Normal matrix predicate.
+
+    A matrix is normal if it commutes with its conjugate transpose.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.normal(X), Q.unitary(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Normal_matrix
+
+    """
+    name = "normal"
+    handler = Dispatcher("NormalHandler", doc="Predicate fore key 'normal'.")
+
+
+class TriangularPredicate(Predicate):
+    """
+    Triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    ``Q.triangular(X)`` is true if ``X`` is one that is either lower
+    triangular or upper triangular.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.triangular(X), Q.upper_triangular(X))
+    True
+    >>> ask(Q.triangular(X), Q.lower_triangular(X))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Triangular_matrix
+
+    """
+    name = "triangular"
+    handler = Dispatcher("TriangularHandler", doc="Predicate fore key 'triangular'.")
+
+
+class UnitTriangularPredicate(Predicate):
+    """
+    Unit triangular matrix predicate.
+
+    Explanation
+    ===========
+
+    A unit triangular matrix is a triangular matrix with 1s
+    on the diagonal.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, MatrixSymbol
+    >>> X = MatrixSymbol('X', 4, 4)
+    >>> ask(Q.triangular(X), Q.unit_triangular(X))
+    True
+
+    """
+    name = "unit_triangular"
+    handler = Dispatcher("UnitTriangularHandler", doc="Predicate fore key 'unit_triangular'.")

lib/python3.12/site-packages/sympy/assumptions/predicates/ntheory.py

@@ -0,0 +1,126 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class PrimePredicate(Predicate):
+    """
+    Prime number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.prime(x))`` is true iff ``x`` is a natural number greater
+    than 1 that has no positive divisors other than ``1`` and the
+    number itself.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask
+    >>> ask(Q.prime(0))
+    False
+    >>> ask(Q.prime(1))
+    False
+    >>> ask(Q.prime(2))
+    True
+    >>> ask(Q.prime(20))
+    False
+    >>> ask(Q.prime(-3))
+    False
+
+    """
+    name = 'prime'
+    handler = Dispatcher(
+        "PrimeHandler",
+        doc=("Handler for key 'prime'. Test that an expression represents a prime"
+        " number. When the expression is an exact number, the result (when True)"
+        " is subject to the limitations of isprime() which is used to return the "
+        "result.")
+    )
+
+
+class CompositePredicate(Predicate):
+    """
+    Composite number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.composite(x))`` is true iff ``x`` is a positive integer and has
+    at least one positive divisor other than ``1`` and the number itself.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask
+    >>> ask(Q.composite(0))
+    False
+    >>> ask(Q.composite(1))
+    False
+    >>> ask(Q.composite(2))
+    False
+    >>> ask(Q.composite(20))
+    True
+
+    """
+    name = 'composite'
+    handler = Dispatcher("CompositeHandler", doc="Handler for key 'composite'.")
+
+
+class EvenPredicate(Predicate):
+    """
+    Even number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.even(x))`` is true iff ``x`` belongs to the set of even
+    integers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, pi
+    >>> ask(Q.even(0))
+    True
+    >>> ask(Q.even(2))
+    True
+    >>> ask(Q.even(3))
+    False
+    >>> ask(Q.even(pi))
+    False
+
+    """
+    name = 'even'
+    handler = Dispatcher("EvenHandler", doc="Handler for key 'even'.")
+
+
+class OddPredicate(Predicate):
+    """
+    Odd number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.odd(x))`` is true iff ``x`` belongs to the set of odd numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, pi
+    >>> ask(Q.odd(0))
+    False
+    >>> ask(Q.odd(2))
+    False
+    >>> ask(Q.odd(3))
+    True
+    >>> ask(Q.odd(pi))
+    False
+
+    """
+    name = 'odd'
+    handler = Dispatcher(
+        "OddHandler",
+        doc=("Handler for key 'odd'. Test that an expression represents an odd"
+        " number.")
+    )

lib/python3.12/site-packages/sympy/assumptions/predicates/order.py

@@ -0,0 +1,390 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class NegativePredicate(Predicate):
+    r"""
+    Negative number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.negative(x)`` is true iff ``x`` is a real number and :math:`x < 0`, that is,
+    it is in the interval :math:`(-\infty, 0)`.  Note in particular that negative
+    infinity is not negative.
+
+    A few important facts about negative numbers:
+
+    - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
+        thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
+        whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
+        negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
+        ``Q.zero(x) | Q.positive(x)``.  So for example, ``~Q.negative(I)`` is
+        true, whereas ``Q.nonnegative(I)`` is false.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I
+    >>> x = symbols('x')
+    >>> ask(Q.negative(x), Q.real(x) & ~Q.positive(x) & ~Q.zero(x))
+    True
+    >>> ask(Q.negative(-1))
+    True
+    >>> ask(Q.nonnegative(I))
+    False
+    >>> ask(~Q.negative(I))
+    True
+
+    """
+    name = 'negative'
+    handler = Dispatcher(
+        "NegativeHandler",
+        doc=("Handler for Q.negative. Test that an expression is strictly less"
+        " than zero.")
+    )
+
+
+class NonNegativePredicate(Predicate):
+    """
+    Nonnegative real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonnegative(x))`` is true iff ``x`` belongs to the set of
+    positive numbers including zero.
+
+    - Note that ``Q.nonnegative`` and ``~Q.negative`` are *not* the same
+        thing. ``~Q.negative(x)`` simply means that ``x`` is not negative,
+        whereas ``Q.nonnegative(x)`` means that ``x`` is real and not
+        negative, i.e., ``Q.nonnegative(x)`` is logically equivalent to
+        ``Q.zero(x) | Q.positive(x)``.  So for example, ``~Q.negative(I)`` is
+        true, whereas ``Q.nonnegative(I)`` is false.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+    >>> ask(Q.nonnegative(1))
+    True
+    >>> ask(Q.nonnegative(0))
+    True
+    >>> ask(Q.nonnegative(-1))
+    False
+    >>> ask(Q.nonnegative(I))
+    False
+    >>> ask(Q.nonnegative(-I))
+    False
+
+    """
+    name = 'nonnegative'
+    handler = Dispatcher(
+        "NonNegativeHandler",
+        doc=("Handler for Q.nonnegative.")
+    )
+
+
+class NonZeroPredicate(Predicate):
+    """
+    Nonzero real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonzero(x))`` is true iff ``x`` is real and ``x`` is not zero.  Note in
+    particular that ``Q.nonzero(x)`` is false if ``x`` is not real.  Use
+    ``~Q.zero(x)`` if you want the negation of being zero without any real
+    assumptions.
+
+    A few important facts about nonzero numbers:
+
+    - ``Q.nonzero`` is logically equivalent to ``Q.positive | Q.negative``.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I, oo
+    >>> x = symbols('x')
+    >>> print(ask(Q.nonzero(x), ~Q.zero(x)))
+    None
+    >>> ask(Q.nonzero(x), Q.positive(x))
+    True
+    >>> ask(Q.nonzero(x), Q.zero(x))
+    False
+    >>> ask(Q.nonzero(0))
+    False
+    >>> ask(Q.nonzero(I))
+    False
+    >>> ask(~Q.zero(I))
+    True
+    >>> ask(Q.nonzero(oo))
+    False
+
+    """
+    name = 'nonzero'
+    handler = Dispatcher(
+        "NonZeroHandler",
+        doc=("Handler for key 'nonzero'. Test that an expression is not identically"
+        " zero.")
+    )
+
+
+class ZeroPredicate(Predicate):
+    """
+    Zero number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.zero(x))`` is true iff the value of ``x`` is zero.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, oo, symbols
+    >>> x, y = symbols('x, y')
+    >>> ask(Q.zero(0))
+    True
+    >>> ask(Q.zero(1/oo))
+    True
+    >>> print(ask(Q.zero(0*oo)))
+    None
+    >>> ask(Q.zero(1))
+    False
+    >>> ask(Q.zero(x*y), Q.zero(x) | Q.zero(y))
+    True
+
+    """
+    name = 'zero'
+    handler = Dispatcher(
+        "ZeroHandler",
+        doc="Handler for key 'zero'."
+    )
+
+
+class NonPositivePredicate(Predicate):
+    """
+    Nonpositive real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.nonpositive(x))`` is true iff ``x`` belongs to the set of
+    negative numbers including zero.
+
+    - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
+        thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
+        whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
+        positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
+        `Q.negative(x) | Q.zero(x)``.  So for example, ``~Q.positive(I)`` is
+        true, whereas ``Q.nonpositive(I)`` is false.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+
+    >>> ask(Q.nonpositive(-1))
+    True
+    >>> ask(Q.nonpositive(0))
+    True
+    >>> ask(Q.nonpositive(1))
+    False
+    >>> ask(Q.nonpositive(I))
+    False
+    >>> ask(Q.nonpositive(-I))
+    False
+
+    """
+    name = 'nonpositive'
+    handler = Dispatcher(
+        "NonPositiveHandler",
+        doc="Handler for key 'nonpositive'."
+    )
+
+
+class PositivePredicate(Predicate):
+    r"""
+    Positive real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.positive(x)`` is true iff ``x`` is real and `x > 0`, that is if ``x``
+    is in the interval `(0, \infty)`.  In particular, infinity is not
+    positive.
+
+    A few important facts about positive numbers:
+
+    - Note that ``Q.nonpositive`` and ``~Q.positive`` are *not* the same
+        thing. ``~Q.positive(x)`` simply means that ``x`` is not positive,
+        whereas ``Q.nonpositive(x)`` means that ``x`` is real and not
+        positive, i.e., ``Q.nonpositive(x)`` is logically equivalent to
+        `Q.negative(x) | Q.zero(x)``.  So for example, ``~Q.positive(I)`` is
+        true, whereas ``Q.nonpositive(I)`` is false.
+
+    - See the documentation of ``Q.real`` for more information about
+        related facts.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols, I
+    >>> x = symbols('x')
+    >>> ask(Q.positive(x), Q.real(x) & ~Q.negative(x) & ~Q.zero(x))
+    True
+    >>> ask(Q.positive(1))
+    True
+    >>> ask(Q.nonpositive(I))
+    False
+    >>> ask(~Q.positive(I))
+    True
+
+    """
+    name = 'positive'
+    handler = Dispatcher(
+        "PositiveHandler",
+        doc=("Handler for key 'positive'. Test that an expression is strictly"
+        " greater than zero.")
+    )
+
+
+class ExtendedPositivePredicate(Predicate):
+    r"""
+    Positive extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_positive(x)`` is true iff ``x`` is extended real and
+    `x > 0`, that is if ``x`` is in the interval `(0, \infty]`.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_positive(1))
+    True
+    >>> ask(Q.extended_positive(oo))
+    True
+    >>> ask(Q.extended_positive(I))
+    False
+
+    """
+    name = 'extended_positive'
+    handler = Dispatcher("ExtendedPositiveHandler")
+
+
+class ExtendedNegativePredicate(Predicate):
+    r"""
+    Negative extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_negative(x)`` is true iff ``x`` is extended real and
+    `x < 0`, that is if ``x`` is in the interval `[-\infty, 0)`.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_negative(-1))
+    True
+    >>> ask(Q.extended_negative(-oo))
+    True
+    >>> ask(Q.extended_negative(-I))
+    False
+
+    """
+    name = 'extended_negative'
+    handler = Dispatcher("ExtendedNegativeHandler")
+
+
+class ExtendedNonZeroPredicate(Predicate):
+    """
+    Nonzero extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonzero(x))`` is true iff ``x`` is extended real and
+    ``x`` is not zero.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonzero(-1))
+    True
+    >>> ask(Q.extended_nonzero(oo))
+    True
+    >>> ask(Q.extended_nonzero(I))
+    False
+
+    """
+    name = 'extended_nonzero'
+    handler = Dispatcher("ExtendedNonZeroHandler")
+
+
+class ExtendedNonPositivePredicate(Predicate):
+    """
+    Nonpositive extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonpositive(x))`` is true iff ``x`` is extended real and
+    ``x`` is not positive.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonpositive(-1))
+    True
+    >>> ask(Q.extended_nonpositive(oo))
+    False
+    >>> ask(Q.extended_nonpositive(0))
+    True
+    >>> ask(Q.extended_nonpositive(I))
+    False
+
+    """
+    name = 'extended_nonpositive'
+    handler = Dispatcher("ExtendedNonPositiveHandler")
+
+
+class ExtendedNonNegativePredicate(Predicate):
+    """
+    Nonnegative extended real number predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.extended_nonnegative(x))`` is true iff ``x`` is extended real and
+    ``x`` is not negative.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, I, oo, Q
+    >>> ask(Q.extended_nonnegative(-1))
+    False
+    >>> ask(Q.extended_nonnegative(oo))
+    True
+    >>> ask(Q.extended_nonnegative(0))
+    True
+    >>> ask(Q.extended_nonnegative(I))
+    False
+
+    """
+    name = 'extended_nonnegative'
+    handler = Dispatcher("ExtendedNonNegativeHandler")

lib/python3.12/site-packages/sympy/assumptions/predicates/sets.py

@@ -0,0 +1,399 @@
+from sympy.assumptions import Predicate
+from sympy.multipledispatch import Dispatcher
+
+
+class IntegerPredicate(Predicate):
+    """
+    Integer predicate.
+
+    Explanation
+    ===========
+
+    ``Q.integer(x)`` is true iff ``x`` belongs to the set of integer
+    numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, S
+    >>> ask(Q.integer(5))
+    True
+    >>> ask(Q.integer(S(1)/2))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Integer
+
+    """
+    name = 'integer'
+    handler = Dispatcher(
+        "IntegerHandler",
+        doc=("Handler for Q.integer.\n\n"
+        "Test that an expression belongs to the field of integer numbers.")
+    )
+
+
+class NonIntegerPredicate(Predicate):
+    """
+    Non-integer extended real predicate.
+    """
+    name = 'noninteger'
+    handler = Dispatcher(
+        "NonIntegerHandler",
+        doc=("Handler for Q.noninteger.\n\n"
+        "Test that an expression is a non-integer extended real number.")
+    )
+
+
+class RationalPredicate(Predicate):
+    """
+    Rational number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.rational(x)`` is true iff ``x`` belongs to the set of
+    rational numbers.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, pi, S
+    >>> ask(Q.rational(0))
+    True
+    >>> ask(Q.rational(S(1)/2))
+    True
+    >>> ask(Q.rational(pi))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Rational_number
+
+    """
+    name = 'rational'
+    handler = Dispatcher(
+        "RationalHandler",
+        doc=("Handler for Q.rational.\n\n"
+        "Test that an expression belongs to the field of rational numbers.")
+    )
+
+
+class IrrationalPredicate(Predicate):
+    """
+    Irrational number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.irrational(x)`` is true iff ``x``  is any real number that
+    cannot be expressed as a ratio of integers.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, pi, S, I
+    >>> ask(Q.irrational(0))
+    False
+    >>> ask(Q.irrational(S(1)/2))
+    False
+    >>> ask(Q.irrational(pi))
+    True
+    >>> ask(Q.irrational(I))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Irrational_number
+
+    """
+    name = 'irrational'
+    handler = Dispatcher(
+        "IrrationalHandler",
+        doc=("Handler for Q.irrational.\n\n"
+        "Test that an expression is irrational numbers.")
+    )
+
+
+class RealPredicate(Predicate):
+    r"""
+    Real number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.real(x)`` is true iff ``x`` is a real number, i.e., it is in the
+    interval `(-\infty, \infty)`.  Note that, in particular the
+    infinities are not real. Use ``Q.extended_real`` if you want to
+    consider those as well.
+
+    A few important facts about reals:
+
+    - Every real number is positive, negative, or zero.  Furthermore,
+        because these sets are pairwise disjoint, each real number is
+        exactly one of those three.
+
+    - Every real number is also complex.
+
+    - Every real number is finite.
+
+    - Every real number is either rational or irrational.
+
+    - Every real number is either algebraic or transcendental.
+
+    - The facts ``Q.negative``, ``Q.zero``, ``Q.positive``,
+        ``Q.nonnegative``, ``Q.nonpositive``, ``Q.nonzero``,
+        ``Q.integer``, ``Q.rational``, and ``Q.irrational`` all imply
+        ``Q.real``, as do all facts that imply those facts.
+
+    - The facts ``Q.algebraic``, and ``Q.transcendental`` do not imply
+        ``Q.real``; they imply ``Q.complex``. An algebraic or
+        transcendental number may or may not be real.
+
+    - The "non" facts (i.e., ``Q.nonnegative``, ``Q.nonzero``,
+        ``Q.nonpositive`` and ``Q.noninteger``) are not equivalent to
+        not the fact, but rather, not the fact *and* ``Q.real``.
+        For example, ``Q.nonnegative`` means ``~Q.negative & Q.real``.
+        So for example, ``I`` is not nonnegative, nonzero, or
+        nonpositive.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, symbols
+    >>> x = symbols('x')
+    >>> ask(Q.real(x), Q.positive(x))
+    True
+    >>> ask(Q.real(0))
+    True
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Real_number
+
+    """
+    name = 'real'
+    handler = Dispatcher(
+        "RealHandler",
+        doc=("Handler for Q.real.\n\n"
+        "Test that an expression belongs to the field of real numbers.")
+    )
+
+
+class ExtendedRealPredicate(Predicate):
+    r"""
+    Extended real predicate.
+
+    Explanation
+    ===========
+
+    ``Q.extended_real(x)`` is true iff ``x`` is a real number or
+    `\{-\infty, \infty\}`.
+
+    See documentation of ``Q.real`` for more information about related
+    facts.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, oo, I
+    >>> ask(Q.extended_real(1))
+    True
+    >>> ask(Q.extended_real(I))
+    False
+    >>> ask(Q.extended_real(oo))
+    True
+
+    """
+    name = 'extended_real'
+    handler = Dispatcher(
+        "ExtendedRealHandler",
+        doc=("Handler for Q.extended_real.\n\n"
+        "Test that an expression belongs to the field of extended real\n"
+        "numbers, that is real numbers union {Infinity, -Infinity}.")
+    )
+
+
+class HermitianPredicate(Predicate):
+    """
+    Hermitian predicate.
+
+    Explanation
+    ===========
+
+    ``ask(Q.hermitian(x))`` is true iff ``x`` belongs to the set of
+    Hermitian operators.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/HermitianOperator.html
+
+    """
+    # TODO: Add examples
+    name = 'hermitian'
+    handler = Dispatcher(
+        "HermitianHandler",
+        doc=("Handler for Q.hermitian.\n\n"
+        "Test that an expression belongs to the field of Hermitian operators.")
+    )
+
+
+class ComplexPredicate(Predicate):
+    """
+    Complex number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.complex(x)`` is true iff ``x`` belongs to the set of complex
+    numbers. Note that every complex number is finite.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, Symbol, ask, I, oo
+    >>> x = Symbol('x')
+    >>> ask(Q.complex(0))
+    True
+    >>> ask(Q.complex(2 + 3*I))
+    True
+    >>> ask(Q.complex(oo))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Complex_number
+
+    """
+    name = 'complex'
+    handler = Dispatcher(
+        "ComplexHandler",
+        doc=("Handler for Q.complex.\n\n"
+        "Test that an expression belongs to the field of complex numbers.")
+    )
+
+
+class ImaginaryPredicate(Predicate):
+    """
+    Imaginary number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.imaginary(x)`` is true iff ``x`` can be written as a real
+    number multiplied by the imaginary unit ``I``. Please note that ``0``
+    is not considered to be an imaginary number.
+
+    Examples
+    ========
+
+    >>> from sympy import Q, ask, I
+    >>> ask(Q.imaginary(3*I))
+    True
+    >>> ask(Q.imaginary(2 + 3*I))
+    False
+    >>> ask(Q.imaginary(0))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Imaginary_number
+
+    """
+    name = 'imaginary'
+    handler = Dispatcher(
+        "ImaginaryHandler",
+        doc=("Handler for Q.imaginary.\n\n"
+        "Test that an expression belongs to the field of imaginary numbers,\n"
+        "that is, numbers in the form x*I, where x is real.")
+    )
+
+
+class AntihermitianPredicate(Predicate):
+    """
+    Antihermitian predicate.
+
+    Explanation
+    ===========
+
+    ``Q.antihermitian(x)`` is true iff ``x`` belongs to the field of
+    antihermitian operators, i.e., operators in the form ``x*I``, where
+    ``x`` is Hermitian.
+
+    References
+    ==========
+
+    .. [1] https://mathworld.wolfram.com/HermitianOperator.html
+
+    """
+    # TODO: Add examples
+    name = 'antihermitian'
+    handler = Dispatcher(
+        "AntiHermitianHandler",
+        doc=("Handler for Q.antihermitian.\n\n"
+        "Test that an expression belongs to the field of anti-Hermitian\n"
+        "operators, that is, operators in the form x*I, where x is Hermitian.")
+    )
+
+
+class AlgebraicPredicate(Predicate):
+    r"""
+    Algebraic number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.algebraic(x)`` is true iff ``x`` belongs to the set of
+    algebraic numbers. ``x`` is algebraic if there is some polynomial
+    in ``p(x)\in \mathbb\{Q\}[x]`` such that ``p(x) = 0``.
+
+    Examples
+    ========
+
+    >>> from sympy import ask, Q, sqrt, I, pi
+    >>> ask(Q.algebraic(sqrt(2)))
+    True
+    >>> ask(Q.algebraic(I))
+    True
+    >>> ask(Q.algebraic(pi))
+    False
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Algebraic_number
+
+    """
+    name = 'algebraic'
+    AlgebraicHandler = Dispatcher(
+        "AlgebraicHandler",
+        doc="""Handler for Q.algebraic key."""
+    )
+
+
+class TranscendentalPredicate(Predicate):
+    """
+    Transcedental number predicate.
+
+    Explanation
+    ===========
+
+    ``Q.transcendental(x)`` is true iff ``x`` belongs to the set of
+    transcendental numbers. A transcendental number is a real
+    or complex number that is not algebraic.
+
+    """
+    # TODO: Add examples
+    name = 'transcendental'
+    handler = Dispatcher(
+        "Transcendental",
+        doc="""Handler for Q.transcendental key."""
+    )

lib/python3.12/site-packages/sympy/parsing/c/__init__.py

@@ -0,0 +1 @@
+"""Used for translating C source code into a SymPy expression"""

lib/python3.12/site-packages/sympy/parsing/c/c_parser.py

@@ -0,0 +1,1058 @@
+from sympy.external import import_module
+import os
+
+cin = import_module('clang.cindex', import_kwargs = {'fromlist': ['cindex']})
+
+"""
+This module contains all the necessary Classes and Function used to Parse C and
+C++ code into SymPy expression
+The module serves as a backend for SymPyExpression to parse C code
+It is also dependent on Clang's AST and SymPy's Codegen AST.
+The module only supports the features currently supported by the Clang and
+codegen AST which will be updated as the development of codegen AST and this
+module progresses.
+You might find unexpected bugs and exceptions while using the module, feel free
+to report them to the SymPy Issue Tracker
+
+Features Supported
+==================
+
+- Variable Declarations (integers and reals)
+- Assignment (using integer & floating literal and function calls)
+- Function Definitions and Declaration
+- Function Calls
+- Compound statements, Return statements
+
+Notes
+=====
+
+The module is dependent on an external dependency which needs to be installed
+to use the features of this module.
+
+Clang: The C and C++ compiler which is used to extract an AST from the provided
+C source code.
+
+References
+==========
+
+.. [1] https://github.com/sympy/sympy/issues
+.. [2] https://clang.llvm.org/docs/
+.. [3] https://clang.llvm.org/docs/IntroductionToTheClangAST.html
+
+"""
+
+if cin:
+    from sympy.codegen.ast import (Variable, Integer, Float,
+        FunctionPrototype, FunctionDefinition, FunctionCall,
+        none, Return, Assignment, intc, int8, int16, int64,
+        uint8, uint16, uint32, uint64, float32, float64, float80,
+        aug_assign, bool_, While, CodeBlock)
+    from sympy.codegen.cnodes import (PreDecrement, PostDecrement,
+        PreIncrement, PostIncrement)
+    from sympy.core import Add, Mod, Mul, Pow, Rel
+    from sympy.logic.boolalg import And, as_Boolean, Not, Or
+    from sympy.core.symbol import Symbol
+    from sympy.core.sympify import sympify
+    from sympy.logic.boolalg import (false, true)
+    import sys
+    import tempfile
+
+    class BaseParser:
+        """Base Class for the C parser"""
+
+        def __init__(self):
+            """Initializes the Base parser creating a Clang AST index"""
+            self.index = cin.Index.create()
+
+        def diagnostics(self, out):
+            """Diagostics function for the Clang AST"""
+            for diag in self.tu.diagnostics:
+                # tu = translation unit
+                print('%s %s (line %s, col %s) %s' % (
+                        {
+                            4: 'FATAL',
+                            3: 'ERROR',
+                            2: 'WARNING',
+                            1: 'NOTE',
+                            0: 'IGNORED',
+                        }[diag.severity],
+                        diag.location.file,
+                        diag.location.line,
+                        diag.location.column,
+                        diag.spelling
+                    ), file=out)
+
+    class CCodeConverter(BaseParser):
+        """The Code Convereter for Clang AST
+
+        The converter object takes the C source code or file as input and
+        converts them to SymPy Expressions.
+        """
+
+        def __init__(self):
+            """Initializes the code converter"""
+            super().__init__()
+            self._py_nodes = []
+            self._data_types = {
+                "void": {
+                    cin.TypeKind.VOID: none
+                },
+                "bool": {
+                    cin.TypeKind.BOOL: bool_
+                },
+                "int": {
+                    cin.TypeKind.SCHAR: int8,
+                    cin.TypeKind.SHORT: int16,
+                    cin.TypeKind.INT: intc,
+                    cin.TypeKind.LONG: int64,
+                    cin.TypeKind.UCHAR: uint8,
+                    cin.TypeKind.USHORT: uint16,
+                    cin.TypeKind.UINT: uint32,
+                    cin.TypeKind.ULONG: uint64
+                },
+                "float": {
+                    cin.TypeKind.FLOAT: float32,
+                    cin.TypeKind.DOUBLE: float64,
+                    cin.TypeKind.LONGDOUBLE: float80
+                }
+            }
+
+        def parse(self, filename, flags):
+            """Function to parse a file with C source code
+
+            It takes the filename as an attribute and creates a Clang AST
+            Translation Unit parsing the file.
+            Then the transformation function is called on the translation unit,
+            whose reults are collected into a list which is returned by the
+            function.
+
+            Parameters
+            ==========
+
+            filename : string
+                Path to the C file to be parsed
+
+            flags: list
+                Arguments to be passed to Clang while parsing the C code
+
+            Returns
+            =======
+
+            py_nodes: list
+                A list of SymPy AST nodes
+
+            """
+            filepath = os.path.abspath(filename)
+            self.tu = self.index.parse(
+                filepath,
+                args=flags,
+                options=cin.TranslationUnit.PARSE_DETAILED_PROCESSING_RECORD
+            )
+            for child in self.tu.cursor.get_children():
+                if child.kind == cin.CursorKind.VAR_DECL or child.kind == cin.CursorKind.FUNCTION_DECL:
+                    self._py_nodes.append(self.transform(child))
+            return self._py_nodes
+
+        def parse_str(self, source, flags):
+            """Function to parse a string with C source code
+
+            It takes the source code as an attribute, stores it in a temporary
+            file and creates a Clang AST Translation Unit parsing the file.
+            Then the transformation function is called on the translation unit,
+            whose reults are collected into a list which is returned by the
+            function.
+
+            Parameters
+            ==========
+
+            source : string
+                A string containing the C source code to be parsed
+
+            flags: list
+                Arguments to be passed to Clang while parsing the C code
+
+            Returns
+            =======
+
+            py_nodes: list
+                A list of SymPy AST nodes
+
+            """
+            file = tempfile.NamedTemporaryFile(mode = 'w+', suffix = '.cpp')
+            file.write(source)
+            file.seek(0)
+            self.tu = self.index.parse(
+                file.name,
+                args=flags,
+                options=cin.TranslationUnit.PARSE_DETAILED_PROCESSING_RECORD
+            )
+            file.close()
+            for child in self.tu.cursor.get_children():
+                if child.kind == cin.CursorKind.VAR_DECL or child.kind == cin.CursorKind.FUNCTION_DECL:
+                    self._py_nodes.append(self.transform(child))
+            return self._py_nodes
+
+        def transform(self, node):
+            """Transformation Function for Clang AST nodes
+
+            It determines the kind of node and calls the respective
+            transformation function for that node.
+
+            Raises
+            ======
+
+            NotImplementedError : if the transformation for the provided node
+            is not implemented
+
+            """
+            handler = getattr(self, 'transform_%s' % node.kind.name.lower(), None)
+
+            if handler is None:
+                print(
+                    "Ignoring node of type %s (%s)" % (
+                        node.kind,
+                        ' '.join(
+                            t.spelling for t in node.get_tokens())
+                        ),
+                    file=sys.stderr
+                )
+
+            return handler(node)
+
+        def transform_var_decl(self, node):
+            """Transformation Function for Variable Declaration
+
+            Used to create nodes for variable declarations and assignments with
+            values or function call for the respective nodes in the clang AST
+
+            Returns
+            =======
+
+            A variable node as Declaration, with the initial value if given
+
+            Raises
+            ======
+
+            NotImplementedError : if called for data types not currently
+            implemented
+
+            Notes
+            =====
+
+            The function currently supports following data types:
+
+            Boolean:
+                bool, _Bool
+
+            Integer:
+                8-bit: signed char and unsigned char
+                16-bit: short, short int, signed short,
+                    signed short int, unsigned short, unsigned short int
+                32-bit: int, signed int, unsigned int
+                64-bit: long, long int, signed long,
+                    signed long int, unsigned long, unsigned long int
+
+            Floating point:
+                Single Precision: float
+                Double Precision: double
+                Extended Precision: long double
+
+            """
+            if node.type.kind in self._data_types["int"]:
+                type = self._data_types["int"][node.type.kind]
+            elif node.type.kind in self._data_types["float"]:
+                type = self._data_types["float"][node.type.kind]
+            elif node.type.kind in self._data_types["bool"]:
+                type = self._data_types["bool"][node.type.kind]
+            else:
+                raise NotImplementedError("Only bool, int "
+                    "and float are supported")
+            try:
+                children = node.get_children()
+                child = next(children)
+
+                #ignoring namespace and type details for the variable
+                while child.kind == cin.CursorKind.NAMESPACE_REF or child.kind == cin.CursorKind.TYPE_REF:
+                    child = next(children)
+
+                val = self.transform(child)
+
+                supported_rhs = [
+                    cin.CursorKind.INTEGER_LITERAL,
+                    cin.CursorKind.FLOATING_LITERAL,
+                    cin.CursorKind.UNEXPOSED_EXPR,
+                    cin.CursorKind.BINARY_OPERATOR,
+                    cin.CursorKind.PAREN_EXPR,
+                    cin.CursorKind.UNARY_OPERATOR,
+                    cin.CursorKind.CXX_BOOL_LITERAL_EXPR
+                ]
+
+                if child.kind in supported_rhs:
+                    if isinstance(val, str):
+                        value = Symbol(val)
+                    elif isinstance(val, bool):
+                        if node.type.kind in self._data_types["int"]:
+                            value = Integer(0) if val == False else Integer(1)
+                        elif node.type.kind in self._data_types["float"]:
+                            value = Float(0.0) if val == False else Float(1.0)
+                        elif node.type.kind in self._data_types["bool"]:
+                            value = sympify(val)
+                    elif isinstance(val, (Integer, int, Float, float)):
+                        if node.type.kind in self._data_types["int"]:
+                            value = Integer(val)
+                        elif node.type.kind in self._data_types["float"]:
+                            value = Float(val)
+                        elif node.type.kind in self._data_types["bool"]:
+                            value = sympify(bool(val))
+                    else:
+                        value = val
+
+                    return Variable(
+                    node.spelling
+                    ).as_Declaration(
+                        type = type,
+                        value = value
+                    )
+
+                elif child.kind == cin.CursorKind.CALL_EXPR:
+                    return Variable(
+                        node.spelling
+                        ).as_Declaration(
+                            value = val
+                        )
+
+                else:
+                    raise NotImplementedError("Given "
+                        "variable declaration \"{}\" "
+                        "is not possible to parse yet!"
+                        .format(" ".join(
+                            t.spelling for t in node.get_tokens()
+                            )
+                        ))
+
+            except StopIteration:
+                return Variable(
+                node.spelling
+                ).as_Declaration(
+                    type = type
+                )
+
+        def transform_function_decl(self, node):
+            """Transformation Function For Function Declaration
+
+            Used to create nodes for function declarations and definitions for
+            the respective nodes in the clang AST
+
+            Returns
+            =======
+
+            function : Codegen AST node
+                - FunctionPrototype node if function body is not present
+                - FunctionDefinition node if the function body is present
+
+
+            """
+
+            if node.result_type.kind in self._data_types["int"]:
+                ret_type = self._data_types["int"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["float"]:
+                ret_type = self._data_types["float"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["bool"]:
+                ret_type = self._data_types["bool"][node.result_type.kind]
+            elif node.result_type.kind in self._data_types["void"]:
+                ret_type = self._data_types["void"][node.result_type.kind]
+            else:
+                raise NotImplementedError("Only void, bool, int "
+                    "and float are supported")
+            body = []
+            param = []
+
+            # Subsequent nodes will be the parameters for the function.
+            for child in node.get_children():
+                decl = self.transform(child)
+                if child.kind == cin.CursorKind.PARM_DECL:
+                    param.append(decl)
+                elif child.kind == cin.CursorKind.COMPOUND_STMT:
+                    for val in decl:
+                        body.append(val)
+                else:
+                    body.append(decl)
+
+            if body == []:
+                function = FunctionPrototype(
+                    return_type = ret_type,
+                    name = node.spelling,
+                    parameters = param
+                )
+            else:
+                function = FunctionDefinition(
+                    return_type = ret_type,
+                    name = node.spelling,
+                    parameters = param,
+                    body = body
+                )
+            return function
+
+        def transform_parm_decl(self, node):
+            """Transformation function for Parameter Declaration
+
+            Used to create parameter nodes for the required functions for the
+            respective nodes in the clang AST
+
+            Returns
+            =======
+
+            param : Codegen AST Node
+                Variable node with the value and type of the variable
+
+            Raises
+            ======
+
+            ValueError if multiple children encountered in the parameter node
+
+            """
+            if node.type.kind in self._data_types["int"]:
+                type = self._data_types["int"][node.type.kind]
+            elif node.type.kind in self._data_types["float"]:
+                type = self._data_types["float"][node.type.kind]
+            elif node.type.kind in self._data_types["bool"]:
+                type = self._data_types["bool"][node.type.kind]
+            else:
+                raise NotImplementedError("Only bool, int "
+                    "and float are supported")
+            try:
+                children = node.get_children()
+                child = next(children)
+
+                # Any namespace nodes can be ignored
+                while child.kind in [cin.CursorKind.NAMESPACE_REF,
+                                     cin.CursorKind.TYPE_REF,
+                                     cin.CursorKind.TEMPLATE_REF]:
+                    child = next(children)
+
+                # If there is a child, it is the default value of the parameter.
+                lit = self.transform(child)
+                if node.type.kind in self._data_types["int"]:
+                    val = Integer(lit)
+                elif node.type.kind in self._data_types["float"]:
+                    val = Float(lit)
+                elif node.type.kind in self._data_types["bool"]:
+                    val = sympify(bool(lit))
+                else:
+                    raise NotImplementedError("Only bool, int "
+                        "and float are supported")
+
+                param = Variable(
+                    node.spelling
+                ).as_Declaration(
+                    type = type,
+                    value = val
+                )
+            except StopIteration:
+                param = Variable(
+                    node.spelling
+                ).as_Declaration(
+                    type = type
+                )
+
+            try:
+                self.transform(next(children))
+                raise ValueError("Can't handle multiple children on parameter")
+            except StopIteration:
+                pass
+
+            return param
+
+        def transform_integer_literal(self, node):
+            """Transformation function for integer literal
+
+            Used to get the value and type of the given integer literal.
+
+            Returns
+            =======
+
+            val : list
+                List with two arguments type and Value
+                type contains the type of the integer
+                value contains the value stored in the variable
+
+            Notes
+            =====
+
+            Only Base Integer type supported for now
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except StopIteration:
+                # No tokens
+                value = node.literal
+            return int(value)
+
+        def transform_floating_literal(self, node):
+            """Transformation function for floating literal
+
+            Used to get the value and type of the given floating literal.
+
+            Returns
+            =======
+
+            val : list
+                List with two arguments type and Value
+                type contains the type of float
+                value contains the value stored in the variable
+
+            Notes
+            =====
+
+            Only Base Float type supported for now
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                # No tokens
+                value = node.literal
+            return float(value)
+
+        def transform_string_literal(self, node):
+            #TODO: No string type in AST
+            #type =
+            #try:
+            #    value = next(node.get_tokens()).spelling
+            #except (StopIteration, ValueError):
+                # No tokens
+            #    value = node.literal
+            #val = [type, value]
+            #return val
+            pass
+
+        def transform_character_literal(self, node):
+            """Transformation function for character literal
+
+            Used to get the value of the given character literal.
+
+            Returns
+            =======
+
+            val : int
+                val contains the ascii value of the character literal
+
+            Notes
+            =====
+
+            Only for cases where character is assigned to a integer value,
+            since character literal is not in SymPy AST
+
+            """
+            try:
+               value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                # No tokens
+               value = node.literal
+            return ord(str(value[1]))
+
+        def transform_cxx_bool_literal_expr(self, node):
+            """Transformation function for boolean literal
+
+            Used to get the value of the given boolean literal.
+
+            Returns
+            =======
+
+            value : bool
+                value contains the boolean value of the variable
+
+            """
+            try:
+                value = next(node.get_tokens()).spelling
+            except (StopIteration, ValueError):
+                value = node.literal
+            return True if value == 'true' else False
+
+        def transform_unexposed_decl(self,node):
+            """Transformation function for unexposed declarations"""
+            pass
+
+        def transform_unexposed_expr(self, node):
+            """Transformation function for unexposed expression
+
+            Unexposed expressions are used to wrap float, double literals and
+            expressions
+
+            Returns
+            =======
+
+            expr : Codegen AST Node
+                the result from the wrapped expression
+
+            None : NoneType
+                No childs are found for the node
+
+            Raises
+            ======
+
+            ValueError if the expression contains multiple children
+
+            """
+            # Ignore unexposed nodes; pass whatever is the first
+            # (and should be only) child unaltered.
+            try:
+                children = node.get_children()
+                expr = self.transform(next(children))
+            except StopIteration:
+                return None
+
+            try:
+                next(children)
+                raise ValueError("Unexposed expression has > 1 children.")
+            except StopIteration:
+                pass
+
+            return expr
+
+        def transform_decl_ref_expr(self, node):
+            """Returns the name of the declaration reference"""
+            return node.spelling
+
+        def transform_call_expr(self, node):
+            """Transformation function for a call expression
+
+            Used to create function call nodes for the function calls present
+            in the C code
+
+            Returns
+            =======
+
+            FunctionCall : Codegen AST Node
+                FunctionCall node with parameters if any parameters are present
+
+            """
+            param = []
+            children = node.get_children()
+            child = next(children)
+
+            while child.kind == cin.CursorKind.NAMESPACE_REF:
+                child = next(children)
+            while child.kind == cin.CursorKind.TYPE_REF:
+                child = next(children)
+
+            first_child = self.transform(child)
+            try:
+                for child in children:
+                    arg = self.transform(child)
+                    if child.kind == cin.CursorKind.INTEGER_LITERAL:
+                        param.append(Integer(arg))
+                    elif child.kind == cin.CursorKind.FLOATING_LITERAL:
+                        param.append(Float(arg))
+                    else:
+                        param.append(arg)
+                return FunctionCall(first_child, param)
+
+            except StopIteration:
+                return FunctionCall(first_child)
+
+        def transform_return_stmt(self, node):
+            """Returns the Return Node for a return statement"""
+            return Return(next(node.get_children()).spelling)
+
+        def transform_compound_stmt(self, node):
+            """Transformation function for compond statemets
+
+            Returns
+            =======
+
+            expr : list
+                list of Nodes for the expressions present in the statement
+
+            None : NoneType
+                if the compound statement is empty
+
+            """
+            expr = []
+            children = node.get_children()
+
+            for child in children:
+                expr.append(self.transform(child))
+            return expr
+
+        def transform_decl_stmt(self, node):
+            """Transformation function for declaration statements
+
+            These statements are used to wrap different kinds of declararions
+            like variable or function declaration
+            The function calls the transformer function for the child of the
+            given node
+
+            Returns
+            =======
+
+            statement : Codegen AST Node
+                contains the node returned by the children node for the type of
+                declaration
+
+            Raises
+            ======
+
+            ValueError if multiple children present
+
+            """
+            try:
+                children = node.get_children()
+                statement = self.transform(next(children))
+            except StopIteration:
+                pass
+
+            try:
+                self.transform(next(children))
+                raise ValueError("Don't know how to handle multiple statements")
+            except StopIteration:
+                pass
+
+            return statement
+
+        def transform_paren_expr(self, node):
+            """Transformation function for Parenthesized expressions
+
+            Returns the result from its children nodes
+
+            """
+            return self.transform(next(node.get_children()))
+
+        def transform_compound_assignment_operator(self, node):
+            """Transformation function for handling shorthand operators
+
+            Returns
+            =======
+
+            augmented_assignment_expression: Codegen AST node
+                    shorthand assignment expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If the shorthand operator for bitwise operators
+                (~=, ^=, &=, |=, <<=, >>=) is encountered
+
+            """
+            return self.transform_binary_operator(node)
+
+        def transform_unary_operator(self, node):
+            """Transformation function for handling unary operators
+
+            Returns
+            =======
+
+            unary_expression: Codegen AST node
+                    simplified unary expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If dereferencing operator(*), address operator(&) or
+                bitwise NOT operator(~) is encountered
+
+            """
+            # supported operators list
+            operators_list = ['+', '-', '++', '--', '!']
+            tokens = list(node.get_tokens())
+
+            # it can be either pre increment/decrement or any other operator from the list
+            if tokens[0].spelling in operators_list:
+                child = self.transform(next(node.get_children()))
+                # (decl_ref) e.g.; int a = ++b; or simply ++b;
+                if isinstance(child, str):
+                    if tokens[0].spelling == '+':
+                        return Symbol(child)
+                    if tokens[0].spelling == '-':
+                        return Mul(Symbol(child), -1)
+                    if tokens[0].spelling == '++':
+                        return PreIncrement(Symbol(child))
+                    if tokens[0].spelling == '--':
+                        return PreDecrement(Symbol(child))
+                    if tokens[0].spelling == '!':
+                        return Not(Symbol(child))
+                # e.g.; int a = -1; or int b = -(1 + 2);
+                else:
+                    if tokens[0].spelling == '+':
+                        return child
+                    if tokens[0].spelling == '-':
+                        return Mul(child, -1)
+                    if tokens[0].spelling == '!':
+                        return Not(sympify(bool(child)))
+
+            # it can be either post increment/decrement
+            # since variable name is obtained in token[0].spelling
+            elif tokens[1].spelling in ['++', '--']:
+                child = self.transform(next(node.get_children()))
+                if tokens[1].spelling == '++':
+                    return PostIncrement(Symbol(child))
+                if tokens[1].spelling == '--':
+                    return PostDecrement(Symbol(child))
+            else:
+                raise NotImplementedError("Dereferencing operator, "
+                    "Address operator and bitwise NOT operator "
+                    "have not been implemented yet!")
+
+        def transform_binary_operator(self, node):
+            """Transformation function for handling binary operators
+
+            Returns
+            =======
+
+            binary_expression: Codegen AST node
+                    simplified binary expression represented as Codegen AST
+
+            Raises
+            ======
+
+            NotImplementedError
+                If a bitwise operator or
+                unary operator(which is a child of any binary
+                operator in Clang AST) is encountered
+
+            """
+            # get all the tokens of assignment
+            # and store it in the tokens list
+            tokens = list(node.get_tokens())
+
+            # supported operators list
+            operators_list = ['+', '-', '*', '/', '%','=',
+            '>', '>=', '<', '<=', '==', '!=', '&&', '||', '+=', '-=',
+            '*=', '/=', '%=']
+
+            # this stack will contain variable content
+            # and type of variable in the rhs
+            combined_variables_stack = []
+
+            # this stack will contain operators
+            # to be processed in the rhs
+            operators_stack = []
+
+            # iterate through every token
+            for token in tokens:
+                # token is either '(', ')' or
+                # any of the supported operators from the operator list
+                if token.kind == cin.TokenKind.PUNCTUATION:
+
+                    # push '(' to the operators stack
+                    if token.spelling == '(':
+                        operators_stack.append('(')
+
+                    elif token.spelling == ')':
+                        # keep adding the expression to the
+                        # combined variables stack unless
+                        # '(' is found
+                        while (operators_stack
+                            and operators_stack[-1] != '('):
+                            if len(combined_variables_stack) < 2:
+                                raise NotImplementedError(
+                                    "Unary operators as a part of "
+                                    "binary operators is not "
+                                    "supported yet!")
+                            rhs = combined_variables_stack.pop()
+                            lhs = combined_variables_stack.pop()
+                            operator = operators_stack.pop()
+                            combined_variables_stack.append(
+                                self.perform_operation(
+                                lhs, rhs, operator))
+
+                        # pop '('
+                        operators_stack.pop()
+
+                    # token is an operator (supported)
+                    elif token.spelling in operators_list:
+                        while (operators_stack
+                            and self.priority_of(token.spelling)
+                            <= self.priority_of(
+                            operators_stack[-1])):
+                            if len(combined_variables_stack) < 2:
+                                raise NotImplementedError(
+                                    "Unary operators as a part of "
+                                    "binary operators is not "
+                                    "supported yet!")
+                            rhs = combined_variables_stack.pop()
+                            lhs = combined_variables_stack.pop()
+                            operator = operators_stack.pop()
+                            combined_variables_stack.append(
+                                self.perform_operation(
+                                lhs, rhs, operator))
+
+                        # push current operator
+                        operators_stack.append(token.spelling)
+
+                    # token is a bitwise operator
+                    elif token.spelling in ['&', '|', '^', '<<', '>>']:
+                        raise NotImplementedError(
+                            "Bitwise operator has not been "
+                            "implemented yet!")
+
+                    # token is a shorthand bitwise operator
+                    elif token.spelling in ['&=', '|=', '^=', '<<=',
+                    '>>=']:
+                        raise NotImplementedError(
+                            "Shorthand bitwise operator has not been "
+                            "implemented yet!")
+                    else:
+                        raise NotImplementedError(
+                            "Given token {} is not implemented yet!"
+                            .format(token.spelling))
+
+                # token is an identifier(variable)
+                elif token.kind == cin.TokenKind.IDENTIFIER:
+                    combined_variables_stack.append(
+                        [token.spelling, 'identifier'])
+
+                # token is a literal
+                elif token.kind == cin.TokenKind.LITERAL:
+                    combined_variables_stack.append(
+                        [token.spelling, 'literal'])
+
+                # token is a keyword, either true or false
+                elif (token.kind == cin.TokenKind.KEYWORD
+                    and token.spelling in ['true', 'false']):
+                    combined_variables_stack.append(
+                        [token.spelling, 'boolean'])
+                else:
+                    raise NotImplementedError(
+                        "Given token {} is not implemented yet!"
+                        .format(token.spelling))
+
+            # process remaining operators
+            while operators_stack:
+                if len(combined_variables_stack) < 2:
+                    raise NotImplementedError(
+                        "Unary operators as a part of "
+                        "binary operators is not "
+                        "supported yet!")
+                rhs = combined_variables_stack.pop()
+                lhs = combined_variables_stack.pop()
+                operator = operators_stack.pop()
+                combined_variables_stack.append(
+                    self.perform_operation(lhs, rhs, operator))
+
+            return combined_variables_stack[-1][0]
+
+        def priority_of(self, op):
+            """To get the priority of given operator"""
+            if op in ['=', '+=', '-=', '*=', '/=', '%=']:
+                return 1
+            if op in ['&&', '||']:
+                return 2
+            if op in ['<', '<=', '>', '>=', '==', '!=']:
+                return 3
+            if op in ['+', '-']:
+                return 4
+            if op in ['*', '/', '%']:
+                return 5
+            return 0
+
+        def perform_operation(self, lhs, rhs, op):
+            """Performs operation supported by the SymPy core
+
+            Returns
+            =======
+
+            combined_variable: list
+                contains variable content and type of variable
+
+            """
+            lhs_value = self.get_expr_for_operand(lhs)
+            rhs_value = self.get_expr_for_operand(rhs)
+            if op == '+':
+                return [Add(lhs_value, rhs_value), 'expr']
+            if op == '-':
+                return [Add(lhs_value, -rhs_value), 'expr']
+            if op == '*':
+                return [Mul(lhs_value, rhs_value), 'expr']
+            if op == '/':
+                return [Mul(lhs_value, Pow(rhs_value, Integer(-1))), 'expr']
+            if op == '%':
+                return [Mod(lhs_value, rhs_value), 'expr']
+            if op in ['<', '<=', '>', '>=', '==', '!=']:
+                return [Rel(lhs_value, rhs_value, op), 'expr']
+            if op == '&&':
+                return [And(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
+            if op == '||':
+                return [Or(as_Boolean(lhs_value), as_Boolean(rhs_value)), 'expr']
+            if op == '=':
+                return [Assignment(Variable(lhs_value), rhs_value), 'expr']
+            if op in ['+=', '-=', '*=', '/=', '%=']:
+                return [aug_assign(Variable(lhs_value), op[0], rhs_value), 'expr']
+
+        def get_expr_for_operand(self, combined_variable):
+            """Gives out SymPy Codegen AST node
+
+            AST node returned is corresponding to
+            combined variable passed.Combined variable contains
+            variable content and type of variable
+
+            """
+            if combined_variable[1] == 'identifier':
+                return Symbol(combined_variable[0])
+            if combined_variable[1] == 'literal':
+                if '.' in combined_variable[0]:
+                    return Float(float(combined_variable[0]))
+                else:
+                    return Integer(int(combined_variable[0]))
+            if combined_variable[1] == 'expr':
+                return combined_variable[0]
+            if combined_variable[1] == 'boolean':
+                    return true if combined_variable[0] == 'true' else false
+
+        def transform_null_stmt(self, node):
+            """Handles Null Statement and returns None"""
+            return none
+
+        def transform_while_stmt(self, node):
+            """Transformation function for handling while statement
+
+            Returns
+            =======
+
+            while statement : Codegen AST Node
+                contains the while statement node having condition and
+                statement block
+
+            """
+            children = node.get_children()
+
+            condition = self.transform(next(children))
+            statements = self.transform(next(children))
+
+            if isinstance(statements, list):
+                statement_block = CodeBlock(*statements)
+            else:
+                statement_block = CodeBlock(statements)
+
+            return While(condition, statement_block)
+
+
+
+else:
+    class CCodeConverter():  # type: ignore
+        def __init__(self, *args, **kwargs):
+            raise ImportError("Module not Installed")
+
+
+def parse_c(source):
+    """Function for converting a C source code
+
+    The function reads the source code present in the given file and parses it
+    to give out SymPy Expressions
+
+    Returns
+    =======
+
+    src : list
+        List of Python expression strings
+
+    """
+    converter = CCodeConverter()
+    if os.path.exists(source):
+        src = converter.parse(source, flags = [])
+    else:
+        src = converter.parse_str(source, flags = [])
+    return src

lib/python3.12/site-packages/sympy/parsing/latex/LICENSE.txt

@@ -0,0 +1,21 @@
+The MIT License (MIT)
+
+Copyright 2016, latex2sympy
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

lib/python3.12/site-packages/sympy/parsing/latex/LaTeX.g4

@@ -0,0 +1,312 @@
+/*
+ ANTLR4 LaTeX Math Grammar
+
+ Ported from latex2sympy by @augustt198 https://github.com/augustt198/latex2sympy See license in
+ LICENSE.txt
+ */
+
+/*
+ After changing this file, it is necessary to run `python setup.py antlr` in the root directory of
+ the repository. This will regenerate the code in `sympy/parsing/latex/_antlr/*.py`.
+ */
+
+grammar LaTeX;
+
+options {
+	language = Python3;
+}
+
+WS: [ \t\r\n]+ -> skip;
+THINSPACE: ('\\,' | '\\thinspace') -> skip;
+MEDSPACE: ('\\:' | '\\medspace') -> skip;
+THICKSPACE: ('\\;' | '\\thickspace') -> skip;
+QUAD: '\\quad' -> skip;
+QQUAD: '\\qquad' -> skip;
+NEGTHINSPACE: ('\\!' | '\\negthinspace') -> skip;
+NEGMEDSPACE: '\\negmedspace' -> skip;
+NEGTHICKSPACE: '\\negthickspace' -> skip;
+CMD_LEFT: '\\left' -> skip;
+CMD_RIGHT: '\\right' -> skip;
+
+IGNORE:
+	(
+		'\\vrule'
+		| '\\vcenter'
+		| '\\vbox'
+		| '\\vskip'
+		| '\\vspace'
+		| '\\hfil'
+		| '\\*'
+		| '\\-'
+		| '\\.'
+		| '\\/'
+		| '\\"'
+		| '\\('
+		| '\\='
+	) -> skip;
+
+ADD: '+';
+SUB: '-';
+MUL: '*';
+DIV: '/';
+
+L_PAREN: '(';
+R_PAREN: ')';
+L_BRACE: '{';
+R_BRACE: '}';
+L_BRACE_LITERAL: '\\{';
+R_BRACE_LITERAL: '\\}';
+L_BRACKET: '[';
+R_BRACKET: ']';
+
+BAR: '|';
+
+R_BAR: '\\right|';
+L_BAR: '\\left|';
+
+L_ANGLE: '\\langle';
+R_ANGLE: '\\rangle';
+FUNC_LIM: '\\lim';
+LIM_APPROACH_SYM:
+	'\\to'
+	| '\\rightarrow'
+	| '\\Rightarrow'
+	| '\\longrightarrow'
+	| '\\Longrightarrow';
+FUNC_INT:
+    '\\int'
+    | '\\int\\limits';
+FUNC_SUM: '\\sum';
+FUNC_PROD: '\\prod';
+
+FUNC_EXP: '\\exp';
+FUNC_LOG: '\\log';
+FUNC_LG: '\\lg';
+FUNC_LN: '\\ln';
+FUNC_SIN: '\\sin';
+FUNC_COS: '\\cos';
+FUNC_TAN: '\\tan';
+FUNC_CSC: '\\csc';
+FUNC_SEC: '\\sec';
+FUNC_COT: '\\cot';
+
+FUNC_ARCSIN: '\\arcsin';
+FUNC_ARCCOS: '\\arccos';
+FUNC_ARCTAN: '\\arctan';
+FUNC_ARCCSC: '\\arccsc';
+FUNC_ARCSEC: '\\arcsec';
+FUNC_ARCCOT: '\\arccot';
+
+FUNC_SINH: '\\sinh';
+FUNC_COSH: '\\cosh';
+FUNC_TANH: '\\tanh';
+FUNC_ARSINH: '\\arsinh';
+FUNC_ARCOSH: '\\arcosh';
+FUNC_ARTANH: '\\artanh';
+
+L_FLOOR: '\\lfloor';
+R_FLOOR: '\\rfloor';
+L_CEIL: '\\lceil';
+R_CEIL: '\\rceil';
+
+FUNC_SQRT: '\\sqrt';
+FUNC_OVERLINE: '\\overline';
+
+CMD_TIMES: '\\times';
+CMD_CDOT: '\\cdot';
+CMD_DIV: '\\div';
+CMD_FRAC:
+    '\\frac'
+    | '\\dfrac'
+    | '\\tfrac';
+CMD_BINOM: '\\binom';
+CMD_DBINOM: '\\dbinom';
+CMD_TBINOM: '\\tbinom';
+
+CMD_MATHIT: '\\mathit';
+
+UNDERSCORE: '_';
+CARET: '^';
+COLON: ':';
+
+fragment WS_CHAR: [ \t\r\n];
+DIFFERENTIAL: 'd' WS_CHAR*? ([a-zA-Z] | '\\' [a-zA-Z]+);
+
+LETTER: [a-zA-Z];
+DIGIT: [0-9];
+
+EQUAL: (('&' WS_CHAR*?)? '=') | ('=' (WS_CHAR*? '&')?);
+NEQ: '\\neq';
+
+LT: '<';
+LTE: ('\\leq' | '\\le' | LTE_Q | LTE_S);
+LTE_Q: '\\leqq';
+LTE_S: '\\leqslant';
+
+GT: '>';
+GTE: ('\\geq' | '\\ge' | GTE_Q | GTE_S);
+GTE_Q: '\\geqq';
+GTE_S: '\\geqslant';
+
+BANG: '!';
+
+SINGLE_QUOTES: '\''+;
+
+SYMBOL: '\\' [a-zA-Z]+;
+
+math: relation;
+
+relation:
+	relation (EQUAL | LT | LTE | GT | GTE | NEQ) relation
+	| expr;
+
+equality: expr EQUAL expr;
+
+expr: additive;
+
+additive: additive (ADD | SUB) additive | mp;
+
+// mult part
+mp:
+	mp (MUL | CMD_TIMES | CMD_CDOT | DIV | CMD_DIV | COLON) mp
+	| unary;
+
+mp_nofunc:
+	mp_nofunc (
+		MUL
+		| CMD_TIMES
+		| CMD_CDOT
+		| DIV
+		| CMD_DIV
+		| COLON
+	) mp_nofunc
+	| unary_nofunc;
+
+unary: (ADD | SUB) unary | postfix+;
+
+unary_nofunc:
+	(ADD | SUB) unary_nofunc
+	| postfix postfix_nofunc*;
+
+postfix: exp postfix_op*;
+postfix_nofunc: exp_nofunc postfix_op*;
+postfix_op: BANG | eval_at;
+
+eval_at:
+	BAR (eval_at_sup | eval_at_sub | eval_at_sup eval_at_sub);
+
+eval_at_sub: UNDERSCORE L_BRACE (expr | equality) R_BRACE;
+
+eval_at_sup: CARET L_BRACE (expr | equality) R_BRACE;
+
+exp: exp CARET (atom | L_BRACE expr R_BRACE) subexpr? | comp;
+
+exp_nofunc:
+	exp_nofunc CARET (atom | L_BRACE expr R_BRACE) subexpr?
+	| comp_nofunc;
+
+comp:
+	group
+	| abs_group
+	| func
+	| atom
+	| floor
+	| ceil;
+
+comp_nofunc:
+	group
+	| abs_group
+	| atom
+	| floor
+	| ceil;
+
+group:
+	L_PAREN expr R_PAREN
+	| L_BRACKET expr R_BRACKET
+	| L_BRACE expr R_BRACE
+	| L_BRACE_LITERAL expr R_BRACE_LITERAL;
+
+abs_group: BAR expr BAR;
+
+number: DIGIT+ (',' DIGIT DIGIT DIGIT)* ('.' DIGIT+)?;
+
+atom: (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?)
+	| number
+	| DIFFERENTIAL
+	| mathit
+	| frac
+	| binom
+	| bra
+	| ket;
+
+bra: L_ANGLE expr (R_BAR | BAR);
+ket: (L_BAR | BAR) expr R_ANGLE;
+
+mathit: CMD_MATHIT L_BRACE mathit_text R_BRACE;
+mathit_text: LETTER*;
+
+frac: CMD_FRAC (upperd = DIGIT | L_BRACE upper = expr R_BRACE)
+    (lowerd = DIGIT | L_BRACE lower = expr R_BRACE);
+
+binom:
+	(CMD_BINOM | CMD_DBINOM | CMD_TBINOM) L_BRACE n = expr R_BRACE L_BRACE k = expr R_BRACE;
+
+floor: L_FLOOR val = expr R_FLOOR;
+ceil: L_CEIL val = expr R_CEIL;
+
+func_normal:
+	FUNC_EXP
+	| FUNC_LOG
+	| FUNC_LG
+	| FUNC_LN
+	| FUNC_SIN
+	| FUNC_COS
+	| FUNC_TAN
+	| FUNC_CSC
+	| FUNC_SEC
+	| FUNC_COT
+	| FUNC_ARCSIN
+	| FUNC_ARCCOS
+	| FUNC_ARCTAN
+	| FUNC_ARCCSC
+	| FUNC_ARCSEC
+	| FUNC_ARCCOT
+	| FUNC_SINH
+	| FUNC_COSH
+	| FUNC_TANH
+	| FUNC_ARSINH
+	| FUNC_ARCOSH
+	| FUNC_ARTANH;
+
+func:
+	func_normal (subexpr? supexpr? | supexpr? subexpr?) (
+		L_PAREN func_arg R_PAREN
+		| func_arg_noparens
+	)
+	| (LETTER | SYMBOL) (subexpr? SINGLE_QUOTES? | SINGLE_QUOTES? subexpr?) // e.g. f(x), f_1'(x)
+	L_PAREN args R_PAREN
+	| FUNC_INT (subexpr supexpr | supexpr subexpr)? (
+		additive? DIFFERENTIAL
+		| frac
+		| additive
+	)
+	| FUNC_SQRT (L_BRACKET root = expr R_BRACKET)? L_BRACE base = expr R_BRACE
+	| FUNC_OVERLINE L_BRACE base = expr R_BRACE
+	| (FUNC_SUM | FUNC_PROD) (subeq supexpr | supexpr subeq) mp
+	| FUNC_LIM limit_sub mp;
+
+args: (expr ',' args) | expr;
+
+limit_sub:
+	UNDERSCORE L_BRACE (LETTER | SYMBOL) LIM_APPROACH_SYM expr (
+		CARET ((L_BRACE (ADD | SUB) R_BRACE) | ADD | SUB)
+	)? R_BRACE;
+
+func_arg: expr | (expr ',' func_arg);
+func_arg_noparens: mp_nofunc;
+
+subexpr: UNDERSCORE (atom | L_BRACE expr R_BRACE);
+supexpr: CARET (atom | L_BRACE expr R_BRACE);
+
+subeq: UNDERSCORE L_BRACE equality R_BRACE;
+supeq: UNDERSCORE L_BRACE equality R_BRACE;

lib/python3.12/site-packages/sympy/parsing/latex/__init__.py

@@ -0,0 +1,66 @@
+from sympy.external import import_module
+from sympy.utilities.decorator import doctest_depends_on
+
+from sympy.parsing.latex.lark import LarkLaTeXParser, TransformToSymPyExpr, parse_latex_lark # noqa
+
+from .errors import LaTeXParsingError  # noqa
+
+
+__doctest_requires__ = {('parse_latex',): ['antlr4', 'lark']}
+
+
+@doctest_depends_on(modules=('antlr4', 'lark'))
+def parse_latex(s, strict=False, backend="antlr"):
+    r"""Converts the input LaTeX string ``s`` to a SymPy ``Expr``.
+
+    Parameters
+    ==========
+
+    s : str
+        The LaTeX string to parse. In Python source containing LaTeX,
+        *raw strings* (denoted with ``r"``, like this one) are preferred,
+        as LaTeX makes liberal use of the ``\`` character, which would
+        trigger escaping in normal Python strings.
+    backend : str, optional
+        Currently, there are two backends supported: ANTLR, and Lark.
+        The default setting is to use the ANTLR backend, which can be
+        changed to Lark if preferred.
+
+        Use ``backend="antlr"`` for the ANTLR-based parser, and
+        ``backend="lark"`` for the Lark-based parser.
+
+        The ``backend`` option is case-sensitive, and must be in
+        all lowercase.
+    strict : bool, optional
+        This option is only available with the ANTLR backend.
+
+        If True, raise an exception if the string cannot be parsed as
+        valid LaTeX. If False, try to recover gracefully from common
+        mistakes.
+
+    Examples
+    ========
+
+    >>> from sympy.parsing.latex import parse_latex
+    >>> expr = parse_latex(r"\frac {1 + \sqrt {\a}} {\b}")
+    >>> expr
+    (sqrt(a) + 1)/b
+    >>> expr.evalf(4, subs=dict(a=5, b=2))
+    1.618
+    >>> func = parse_latex(r"\int_1^\alpha \dfrac{\mathrm{d}t}{t}", backend="lark")
+    >>> func.evalf(subs={"alpha": 2})
+    0.693147180559945
+    """
+
+    if backend == "antlr":
+        _latex = import_module(
+            'sympy.parsing.latex._parse_latex_antlr',
+            import_kwargs={'fromlist': ['X']})
+
+        if _latex is not None:
+            return _latex.parse_latex(s, strict)
+    elif backend == "lark":
+        return parse_latex_lark(s)
+    else:
+        raise NotImplementedError(f"Using the '{backend}' backend in the LaTeX" \
+                                   " parser is not supported.")

lib/python3.12/site-packages/sympy/parsing/latex/_antlr/__init__.py

@@ -0,0 +1,9 @@
+# *** GENERATED BY `setup.py antlr`, DO NOT EDIT BY HAND ***
+#
+# Generated from ../LaTeX.g4, derived from latex2sympy
+#     latex2sympy is licensed under the MIT license
+#     https://github.com/augustt198/latex2sympy/blob/master/LICENSE.txt
+#
+# Generated with antlr4
+#    antlr4 is licensed under the BSD-3-Clause License
+#    https://github.com/antlr/antlr4/blob/master/LICENSE.txt