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from sympy.core.numbers import (Rational, pi)
from sympy.functions.elementary.exponential import log
from sympy.functions.elementary.miscellaneous import sqrt
from sympy.functions.special.error_functions import erf
from sympy.polys.domains import GF
from sympy.simplify.ratsimp import (ratsimp, ratsimpmodprime)
from sympy.abc import x, y, z, t, a, b, c, d, e
def test_ratsimp():
f, g = 1/x + 1/y, (x + y)/(x*y)
assert f != g and ratsimp(f) == g
f, g = 1/(1 + 1/x), 1 - 1/(x + 1)
assert f != g and ratsimp(f) == g
f, g = x/(x + y) + y/(x + y), 1
assert f != g and ratsimp(f) == g
f, g = -x - y - y**2/(x + y) + x**2/(x + y), -2*y
assert f != g and ratsimp(f) == g
f = (a*c*x*y + a*c*z - b*d*x*y - b*d*z - b*t*x*y - b*t*x - b*t*z +
e*x)/(x*y + z)
G = [a*c - b*d - b*t + (-b*t*x + e*x)/(x*y + z),
a*c - b*d - b*t - ( b*t*x - e*x)/(x*y + z)]
assert f != g and ratsimp(f) in G
A = sqrt(pi)
B = log(erf(x) - 1)
C = log(erf(x) + 1)
D = 8 - 8*erf(x)
f = A*B/D - A*C/D + A*C*erf(x)/D - A*B*erf(x)/D + 2*A/D
assert ratsimp(f) == A*B/8 - A*C/8 - A/(4*erf(x) - 4)
def test_ratsimpmodprime():
a = y**5 + x + y
b = x - y
F = [x*y**5 - x - y]
assert ratsimpmodprime(a/b, F, x, y, order='lex') == \
(-x**2 - x*y - x - y) / (-x**2 + x*y)
a = x + y**2 - 2
b = x + y**2 - y - 1
F = [x*y - 1]
assert ratsimpmodprime(a/b, F, x, y, order='lex') == \
(1 + y - x)/(y - x)
a = 5*x**3 + 21*x**2 + 4*x*y + 23*x + 12*y + 15
b = 7*x**3 - y*x**2 + 31*x**2 + 2*x*y + 15*y + 37*x + 21
F = [x**2 + y**2 - 1]
assert ratsimpmodprime(a/b, F, x, y, order='lex') == \
(1 + 5*y - 5*x)/(8*y - 6*x)
a = x*y - x - 2*y + 4
b = x + y**2 - 2*y
F = [x - 2, y - 3]
assert ratsimpmodprime(a/b, F, x, y, order='lex') == \
Rational(2, 5)
# Test a bug where denominators would be dropped
assert ratsimpmodprime(x, [y - 2*x], order='lex') == \
y/2
a = (x**5 + 2*x**4 + 2*x**3 + 2*x**2 + x + 2/x + x**(-2))
assert ratsimpmodprime(a, [x + 1], domain=GF(2)) == 1
assert ratsimpmodprime(a, [x + 1], domain=GF(3)) == -1
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