def Add(expr, assumptions):
"""
Hermitian + Hermitian -> Hermitian
Hermitian + !Hermitian -> !Hermitian
"""
if expr.is_number:
return AskRealHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.hermitian)
def Add(expr, assumptions):
"""
Antihermitian + Antihermitian -> Antihermitian
Antihermitian + !Antihermitian -> !Antihermitian
"""
if expr.is_number:
return AskImaginaryHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.antihermitian)
def Add(expr, assumptions):
"""
Antihermitian + Antihermitian -> Antihermitian
Antihermitian + !Antihermitian -> !Antihermitian
"""
if expr.is_number:
return AskImaginaryHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.antihermitian)
def Add(expr, assumptions):
"""
Real + Real -> Real
Real + (Complex & !Real) -> !Real
"""
if expr.is_number:
return AskRealHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.real)
def Add(expr, assumptions):
"""
Real + Real -> Real
Real + (Complex & !Real) -> !Real
"""
if expr.is_number:
return AskRealHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.real)
def Add(expr, assumptions):
"""
Hermitian + Hermitian -> Hermitian
Hermitian + !Hermitian -> !Hermitian
"""
if expr.is_number:
return AskRealHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.hermitian)
def Add(expr, assumptions):
"""
Integer + Integer -> Integer
Integer + !Integer -> !Integer
!Integer + !Integer -> ?
"""
if expr.is_number:
return AskIntegerHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.integer)
def Add(expr, assumptions):
"""
Integer + Integer -> Integer
Integer + !Integer -> !Integer
!Integer + !Integer -> ?
"""
if expr.is_number:
return AskIntegerHandler._number(expr, assumptions)
return test_closed_group(expr, assumptions, Q.integer)
def Add(expr, assumptions):
"""
Rational + Rational -> Rational
Rational + !Rational -> !Rational
!Rational + !Rational -> ?
"""
if expr.is_number:
if expr.as_real_imag()[1]:
return False
return test_closed_group(expr, assumptions, Q.rational)
def Add(expr, assumptions):
"""
Rational + Rational -> Rational
Rational + !Rational -> !Rational
!Rational + !Rational -> ?
"""
if expr.is_number:
if expr.as_real_imag()[1]:
return False
return test_closed_group(expr, assumptions, Q.rational)
def MatAdd(expr, assumptions):
return test_closed_group(expr, assumptions, Q.complex_elements)
def MatAdd(expr, assumptions):
return test_closed_group(expr, assumptions, Q.integer_elements)
def Mul(expr, assumptions):
return test_closed_group(expr, assumptions, Q.algebraic)
def Add(expr, assumptions):
return test_closed_group(expr, assumptions, Q.complex)
def Add(expr, assumptions):
return test_closed_group(expr, assumptions, Q.extended_real)
def Mul(expr, assumptions):
return test_closed_group(expr, assumptions, Q.algebraic)
def _(expr, assumptions):
return test_closed_group(expr, assumptions, Q.real_elements)
def Add(expr, assumptions):
return test_closed_group(expr, assumptions, Q.complex)
def MatMul_elements(matrix_predicate, scalar_predicate, expr, assumptions):
d = sift(expr.args, lambda x: isinstance(x, MatrixExpr))
factors, matrices = d[False], d[True]
return fuzzy_and([
test_closed_group(Basic(*factors), assumptions, scalar_predicate),
test_closed_group(Basic(*matrices), assumptions, matrix_predicate)])
def MatMul_elements(matrix_predicate, scalar_predicate, expr, assumptions):
d = sift(expr.args, lambda x: isinstance(x, MatrixExpr))
factors, matrices = d[False], d[True]
return fuzzy_and(
test_closed_group(Basic(*factors), assumptions, scalar_predicate),
test_closed_group(Basic(*matrices), assumptions, matrix_predicate))
def Add(expr, assumptions):
return test_closed_group(expr, assumptions, Q.extended_real)