def test_nc_simplify():
from sympy.simplify.simplify import nc_simplify
from sympy.matrices.expressions import (MatrixExpr, MatAdd, MatMul, MatPow,
Identity)
from sympy.core import Pow
from functools import reduce
a, b, c, d = symbols('a b c d', commutative=False)
x = Symbol('x')
A = MatrixSymbol("A", x, x)
B = MatrixSymbol("B", x, x)
C = MatrixSymbol("C", x, x)
D = MatrixSymbol("D", x, x)
subst = {a: A, b: B, c: C, d: D}
funcs = {Add: lambda x, y: x + y, Mul: lambda x, y: x * y}
def _to_matrix(expr):
if expr in subst:
return subst[expr]
if isinstance(expr, Pow):
return MatPow(_to_matrix(expr.args[0]), expr.args[1])
elif isinstance(expr, (Add, Mul)):
return reduce(funcs[expr.func], [_to_matrix(a) for a in expr.args])
else:
return expr * Identity(x)
def _check(expr, simplified, deep=True, matrix=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
if matrix:
m_simp = _to_matrix(simplified).doit(inv_expand=False)
assert nc_simplify(_to_matrix(expr), deep=deep) == m_simp
_check(a * b * a * b * a * b * c * (a * b)**3 * c, ((a * b)**3 * c)**2)
_check(a * b * (a * b)**-2 * a * b, 1)
_check(a**2 * b * a * b * a * b * (a * b)**-1,
a * (a * b)**2,
matrix=False)
_check(b * a * b**2 * a * b**2 * a * b**2, b * (a * b**2)**3)
_check(a * b * a**2 * b * a**2 * b * a**3, (a * b * a)**3 * a**2)
_check(a**2 * b * a**4 * b * a**4 * b * a**2, (a**2 * b * a**2)**3)
_check(a**3 * b * a**4 * b * a**4 * b * a, a**3 * (b * a**4)**3 * a**-3)
_check(a * b * a * b + a * b * c * x * a * b * c,
(a * b)**2 + x * (a * b * c)**2)
_check(a * b * a * b * c * a * b * a * b * c, ((a * b)**2 * c)**2)
_check(b**-1 * a**-1 * (a * b)**2, a * b)
_check(a**-1 * b * c**-1, (c * b**-1 * a)**-1)
expr = a**3 * b * a**4 * b * a**4 * b * a**2 * b * a**2 * (
b * a**2)**2 * b * a**2 * b * a**2
for i in range(10):
expr *= a * b
_check(expr, a**3 * (b * a**4)**2 * (b * a**2)**6 * (a * b)**10)
_check((a * b * a * b)**2, (a * b * a * b)**2, deep=False)
_check(a * b * (c * d)**2, a * b * (c * d)**2)
expr = b**-1 * (a**-1 * b**-1 - a**-1 * c * b**-1)**-1 * a**-1
assert nc_simplify(expr) == (1 - c)**-1
# commutative expressions should be returned without an error
assert nc_simplify(2 * x**2) == 2 * x**2
def test_nc_simplify():
from sympy.simplify.simplify import nc_simplify
from sympy.matrices.expressions import (MatrixExpr, MatAdd, MatMul,
MatPow, Identity)
from sympy.core import Pow
from functools import reduce
a, b, c, d = symbols('a b c d', commutative = False)
x = Symbol('x')
A = MatrixSymbol("A", x, x)
B = MatrixSymbol("B", x, x)
C = MatrixSymbol("C", x, x)
D = MatrixSymbol("D", x, x)
subst = {a: A, b: B, c: C, d:D}
funcs = {Add: lambda x,y: x+y, Mul: lambda x,y: x*y }
def _to_matrix(expr):
if expr in subst:
return subst[expr]
if isinstance(expr, Pow):
return MatPow(_to_matrix(expr.args[0]), expr.args[1])
elif isinstance(expr, (Add, Mul)):
return reduce(funcs[expr.func],[_to_matrix(a) for a in expr.args])
else:
return expr*Identity(x)
def _check(expr, simplified, deep=True, matrix=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
if matrix:
m_simp = _to_matrix(simplified).doit(inv_expand=False)
assert nc_simplify(_to_matrix(expr), deep=deep) == m_simp
_check(a*b*a*b*a*b*c*(a*b)**3*c, ((a*b)**3*c)**2)
_check(a*b*(a*b)**-2*a*b, 1)
_check(a**2*b*a*b*a*b*(a*b)**-1, a*(a*b)**2, matrix=False)
_check(b*a*b**2*a*b**2*a*b**2, b*(a*b**2)**3)
_check(a*b*a**2*b*a**2*b*a**3, (a*b*a)**3*a**2)
_check(a**2*b*a**4*b*a**4*b*a**2, (a**2*b*a**2)**3)
_check(a**3*b*a**4*b*a**4*b*a, a**3*(b*a**4)**3*a**-3)
_check(a*b*a*b + a*b*c*x*a*b*c, (a*b)**2 + x*(a*b*c)**2)
_check(a*b*a*b*c*a*b*a*b*c, ((a*b)**2*c)**2)
_check(b**-1*a**-1*(a*b)**2, a*b)
_check(a**-1*b*c**-1, (c*b**-1*a)**-1)
expr = a**3*b*a**4*b*a**4*b*a**2*b*a**2*(b*a**2)**2*b*a**2*b*a**2
for i in range(10):
expr *= a*b
_check(expr, a**3*(b*a**4)**2*(b*a**2)**6*(a*b)**10)
_check((a*b*a*b)**2, (a*b*a*b)**2, deep=False)
_check(a*b*(c*d)**2, a*b*(c*d)**2)
expr = b**-1*(a**-1*b**-1 - a**-1*c*b**-1)**-1*a**-1
assert nc_simplify(expr) == (1-c)**-1
# commutative expressions should be returned without an error
assert nc_simplify(2*x**2) == 2*x**2
def _check(expr, simplified, deep=True, matrix=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
if matrix:
m_simp = _to_matrix(simplified).doit(inv_expand=False)
assert nc_simplify(_to_matrix(expr), deep=deep) == m_simp
def _check(expr, simplified, deep=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
def _check(expr, simplified, deep=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
def _check(expr, simplified, deep=True, matrix=True):
assert nc_simplify(expr, deep=deep) == simplified
assert expand(expr) == expand(simplified)
if matrix:
m_simp = _to_matrix(simplified).doit(inv_expand=False)
assert nc_simplify(_to_matrix(expr), deep=deep) == m_simp
