示例#1
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文件: matrices.py 项目: Lenqth/sympy
 def MatPow(expr, assumptions):
     # only for integer powers
     base, exp = expr.args
     int_exp = ask(Q.integer(exp), assumptions)
     if int_exp:
         return ask(Q.orthogonal(base), assumptions)
     return None
示例#2
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文件: matrices.py 项目: Maihj/sympy
 def MatMul(expr, assumptions):
     factor, mmul = expr.as_coeff_mmul()
     if (all(ask(Q.orthogonal(arg), assumptions) for arg in mmul.args) and
             factor == 1):
         return True
     if any(ask(Q.invertible(arg), assumptions) is False
             for arg in mmul.args):
         return False
示例#3
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 def MatMul(expr, assumptions):
     factor, mmul = expr.as_coeff_mmul()
     if (all(ask(Q.orthogonal(arg), assumptions) for arg in mmul.args)
             and factor == 1):
         return True
     if any(
             ask(Q.invertible(arg), assumptions) is False
             for arg in mmul.args):
         return False
示例#4
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 def MatrixSlice(expr, assumptions):
     if ask(Q.orthogonal(expr.parent), assumptions):
         return True
示例#5
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 def MatrixSlice(expr, assumptions):
     if not expr.on_diag:
         return None
     else:
         return ask(Q.orthogonal(expr.parent), assumptions)
示例#6
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 def Transpose(expr, assumptions):
     return ask(Q.orthogonal(expr.arg), assumptions)
示例#7
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 def MatrixSymbol(expr, assumptions):
     if not expr.is_square:
         return False
     if Q.orthogonal(expr) in conjuncts(assumptions):
         return True
示例#8
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 def MatAdd(expr, assumptions):
     if (len(expr.args) == 1 and
             ask(Q.orthogonal(expr.args[0]), assumptions)):
         return True
示例#9
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 def MatrixSymbol(expr, assumptions):
     if (not expr.is_square
             or ask(Q.invertible(expr), assumptions) is False):
         return False
     if Q.orthogonal(expr) in conjuncts(assumptions):
         return True
示例#10
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文件: matrices.py 项目: Lenqth/sympy
 def MatrixSymbol(expr, assumptions):
     if (not expr.is_square or
                     ask(Q.invertible(expr), assumptions) is False):
         return False
     if Q.orthogonal(expr) in conjuncts(assumptions):
         return True
示例#11
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def _(expr, assumptions):
    if ask(Q.orthogonal(expr.parent), assumptions):
        return True
示例#12
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def _(expr, assumptions):
    return ask(Q.orthogonal(expr.arg), assumptions)
示例#13
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def get_known_facts(x=None):
    """
    Facts between unary predicates.

    Parameters
    ==========

    x : Symbol, optional
        Placeholder symbol for unary facts. Default is ``Symbol('x')``.

    Returns
    =======

    fact : Known facts in conjugated normal form.

    """
    if x is None:
        x = Symbol('x')

    fact = And(
        # primitive predicates for extended real exclude each other.
        Exclusive(Q.negative_infinite(x), Q.negative(x), Q.zero(x),
                  Q.positive(x), Q.positive_infinite(x)),

        # build complex plane
        Exclusive(Q.real(x), Q.imaginary(x)),
        Implies(Q.real(x) | Q.imaginary(x), Q.complex(x)),

        # other subsets of complex
        Exclusive(Q.transcendental(x), Q.algebraic(x)),
        Equivalent(Q.real(x),
                   Q.rational(x) | Q.irrational(x)),
        Exclusive(Q.irrational(x), Q.rational(x)),
        Implies(Q.rational(x), Q.algebraic(x)),

        # integers
        Exclusive(Q.even(x), Q.odd(x)),
        Implies(Q.integer(x), Q.rational(x)),
        Implies(Q.zero(x), Q.even(x)),
        Exclusive(Q.composite(x), Q.prime(x)),
        Implies(Q.composite(x) | Q.prime(x),
                Q.integer(x) & Q.positive(x)),
        Implies(Q.even(x) & Q.positive(x) & ~Q.prime(x), Q.composite(x)),

        # hermitian and antihermitian
        Implies(Q.real(x), Q.hermitian(x)),
        Implies(Q.imaginary(x), Q.antihermitian(x)),
        Implies(Q.zero(x),
                Q.hermitian(x) | Q.antihermitian(x)),

        # define finity and infinity, and build extended real line
        Exclusive(Q.infinite(x), Q.finite(x)),
        Implies(Q.complex(x), Q.finite(x)),
        Implies(
            Q.negative_infinite(x) | Q.positive_infinite(x), Q.infinite(x)),

        # commutativity
        Implies(Q.finite(x) | Q.infinite(x), Q.commutative(x)),

        # matrices
        Implies(Q.orthogonal(x), Q.positive_definite(x)),
        Implies(Q.orthogonal(x), Q.unitary(x)),
        Implies(Q.unitary(x) & Q.real_elements(x), Q.orthogonal(x)),
        Implies(Q.unitary(x), Q.normal(x)),
        Implies(Q.unitary(x), Q.invertible(x)),
        Implies(Q.normal(x), Q.square(x)),
        Implies(Q.diagonal(x), Q.normal(x)),
        Implies(Q.positive_definite(x), Q.invertible(x)),
        Implies(Q.diagonal(x), Q.upper_triangular(x)),
        Implies(Q.diagonal(x), Q.lower_triangular(x)),
        Implies(Q.lower_triangular(x), Q.triangular(x)),
        Implies(Q.upper_triangular(x), Q.triangular(x)),
        Implies(Q.triangular(x),
                Q.upper_triangular(x) | Q.lower_triangular(x)),
        Implies(Q.upper_triangular(x) & Q.lower_triangular(x), Q.diagonal(x)),
        Implies(Q.diagonal(x), Q.symmetric(x)),
        Implies(Q.unit_triangular(x), Q.triangular(x)),
        Implies(Q.invertible(x), Q.fullrank(x)),
        Implies(Q.invertible(x), Q.square(x)),
        Implies(Q.symmetric(x), Q.square(x)),
        Implies(Q.fullrank(x) & Q.square(x), Q.invertible(x)),
        Equivalent(Q.invertible(x), ~Q.singular(x)),
        Implies(Q.integer_elements(x), Q.real_elements(x)),
        Implies(Q.real_elements(x), Q.complex_elements(x)),
    )
    return fact