def get_rubi_object():
"""
Returns rubi ManyToOneReplacer by adding all rules from different modules.
Uncomment the lines to add integration capabilities of that module.
Currently, there are parsing issues with special_function,
derivative and miscellaneous_integration. Hence they are commented.
"""
from sympy.integrals.rubi.rules.integrand_simplification import (
integrand_simplification, )
from sympy.integrals.rubi.rules.linear_products import linear_products
from sympy.integrals.rubi.rules.quadratic_products import quadratic_products
from sympy.integrals.rubi.rules.binomial_products import binomial_products
from sympy.integrals.rubi.rules.trinomial_products import trinomial_products
from sympy.integrals.rubi.rules.miscellaneous_algebraic import (
miscellaneous_algebraic, )
from sympy.integrals.rubi.rules.exponential import exponential
from sympy.integrals.rubi.rules.logarithms import logarithms
from sympy.integrals.rubi.rules.sine import sine
from sympy.integrals.rubi.rules.tangent import tangent
from sympy.integrals.rubi.rules.secant import secant
from sympy.integrals.rubi.rules.miscellaneous_trig import miscellaneous_trig
from sympy.integrals.rubi.rules.inverse_trig import inverse_trig
from sympy.integrals.rubi.rules.hyperbolic import hyperbolic
from sympy.integrals.rubi.rules.inverse_hyperbolic import inverse_hyperbolic
from sympy.integrals.rubi.rules.special_functions import special_functions
# from sympy.integrals.rubi.rules.derivative import derivative
# from sympy.integrals.rubi.rules.piecewise_linear import piecewise_linear
from sympy.integrals.rubi.rules.miscellaneous_integration import (
miscellaneous_integration, )
rules = []
rules += integrand_simplification()
rules += linear_products()
rules += quadratic_products()
rules += binomial_products()
rules += trinomial_products()
rules += miscellaneous_algebraic()
rules += exponential()
rules += logarithms()
rules += special_functions()
rules += sine()
rules += tangent()
rules += secant()
rules += miscellaneous_trig()
rules += inverse_trig()
rules += hyperbolic()
rules += inverse_hyperbolic()
# rubi = piecewise_linear(rubi)
rules += miscellaneous_integration()
rubi = ManyToOneReplacer(*rules)
return rubi, rules
def rubi_object():
'''
Returns rubi ManyToOneReplacer by adding all rules form different modules.
Uncomment the lines to add integration capabilities of that module.
Currently, there are parsing issues with special_function,
derivative nad miscellaneous_integration. Hence they are commented.
'''
from sympy.integrals.rubi.rules.integrand_simplification import integrand_simplification
from sympy.integrals.rubi.rules.linear_products import linear_products
from sympy.integrals.rubi.rules.quadratic_products import quadratic_products
from sympy.integrals.rubi.rules.binomial_products import binomial_products
from sympy.integrals.rubi.rules.trinomial_products import trinomial_products
from sympy.integrals.rubi.rules.miscellaneous_algebraic import miscellaneous_algebraic
from sympy.integrals.rubi.rules.exponential import exponential
from sympy.integrals.rubi.rules.logarithms import logarithms
from sympy.integrals.rubi.rules.sine import sine
from sympy.integrals.rubi.rules.tangent import tangent
from sympy.integrals.rubi.rules.secant import secant
from sympy.integrals.rubi.rules.miscellaneous_trig import miscellaneous_trig
from sympy.integrals.rubi.rules.inverse_trig import inverse_trig
from sympy.integrals.rubi.rules.hyperbolic import hyperbolic
from sympy.integrals.rubi.rules.inverse_hyperbolic import inverse_hyperbolic
#from sympy.integrals.rubi.rules.special_function import special_function
#from sympy.integrals.rubi.rules.derivative import derivative
from sympy.integrals.rubi.rules.piecewise_linear import piecewise_linear
#from sympy.integrals.rubi.rules.miscellaneous_integration import miscellaneous_integration
rubi = ManyToOneReplacer()
#rubi = integrand_simplification(rubi)
rubi = linear_products(rubi)
rubi = quadratic_products(rubi)
rubi = binomial_products(rubi)
#rubi = trinomial_products(rubi)
#rubi = miscellaneous_algebraic(rubi)
#rubi = exponential(rubi)
#rubi = logarithms(rubi)
#rubi = sine(rubi)
#rubi = tangent(rubi)
#rubi = secant(rubi)
#rubi = miscellaneous_trig(rubi)
#rubi = inverse_trig(rubi)
#rubi = hyperbolic(rubi)
#rubi = inverse_hyperbolic(rubi)
#rubi = piecewise_linear(rubi)
#rubi = miscellaneous_integration(rubi)
return rubi
def test_matchpy_optional():
if matchpy is None:
skip("matchpy not installed")
from matchpy import Pattern, Substitution
from matchpy import ManyToOneReplacer, ReplacementRule
p = WildDot("p", optional=1)
q = WildDot("q", optional=0)
pattern = p*x + q
expr1 = 2*x
pa, subst = _get_first_match(expr1, pattern)
assert pa == Pattern(pattern)
assert subst == Substitution({'p': 2, 'q': 0})
expr2 = x + 3
pa, subst = _get_first_match(expr2, pattern)
assert pa == Pattern(pattern)
assert subst == Substitution({'p': 1, 'q': 3})
expr3 = x
pa, subst = _get_first_match(expr3, pattern)
assert pa == Pattern(pattern)
assert subst == Substitution({'p': 1, 'q': 0})
expr4 = x*y + z
pa, subst = _get_first_match(expr4, pattern)
assert pa == Pattern(pattern)
assert subst == Substitution({'p': y, 'q': z})
replacer = ManyToOneReplacer()
replacer.add(ReplacementRule(Pattern(pattern), lambda p, q: sin(p)*cos(q)))
assert replacer.replace(expr1) == sin(2)*cos(0)
assert replacer.replace(expr2) == sin(1)*cos(3)
assert replacer.replace(expr3) == sin(1)*cos(0)
assert replacer.replace(expr4) == sin(y)*cos(z)
a, b, c, d, e, f, g, h, x = map(VariableSymbol, 'abcdefghx')
n, m = map(VariableSymbol, 'nm')
a_, b_, c_, d_, e_, f_, g_, h_ = map(Wildcard.dot, 'abcdefgh')
n_, m_ = map(Wildcard.dot, 'nm')
x_ = Wildcard.symbol('x')
u_ = Wildcard.symbol('u')
one = ConstantSymbol(1)
m_one = ConstantSymbol(-1)
pattern1 = Pattern(Int(Mul(a_, Pow(x_, -1)), x), FreeQ((a, ), x))
rule1 = ReplacementRule(pattern1, lambda a, x: Mul(a, Log(x)))
pattern2 = Pattern(Int(Pow(x_, m_), x), FreeQ((m, ), x),
NonzeroQ(Add(m_, one), (m, )))
rule2 = ReplacementRule(
pattern2, lambda m, x: Mul(Pow(x, Add(m, one)), Pow(Add(m, one), m_one)))
rubi = ManyToOneReplacer(rule1)
rubi.add(rule2)
test = [[
Int(Pow(x, one), x),
Mul(Pow(Add(one, one), m_one), Pow(x, Add(one, one)))
], [Int(Mul(a, Pow(x, -1)), x), Mul(Log(x), a)]]
for i in test:
assert rubi.replace(i[0]) == i[1]