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
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
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
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') == \
(x - y - 1)/(x - y)
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') == \
(3*x + 4*y + 5)/(5*x + 5*y + 7)
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)
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') == \
(x - y - 1)/(x - y)
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') == \
(3*x + 4*y + 5)/(5*x + 5*y + 7)
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)