def test_mul_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = 1 + t * x + t * y
for i in range(2):
p = rs_mul(p, p, t, 3)
assert p == 6 * x**2 * t**2 + 12 * x * y * t**2 + 6 * y**2 * t**2 + 4 * x * t + 4 * y * t + 1
p = 1 + t * x + t * y + t**2 * x * y
p1 = rs_mul(p, p, t, 2)
assert p1 == 1 + 2 * t * x + 2 * t * y
R1, z = ring('z', QQ)
raises(ValueError, lambda: rs_mul(p, z, x, 2))
p1 = 2 + 2 * x + 3 * x**2
p2 = 3 + x**2
assert rs_mul(p1, p2, x, 4) == 2 * x**3 + 11 * x**2 + 6 * x + 6
def test_square_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = (1 + t * x + t * y) * 2
p1 = rs_mul(p, p, x, 3)
p2 = rs_square(p, x, 3)
assert p1 == p2
p = 1 + x + x**2 + x**3
assert rs_square(p, x, 4) == 4 * x**3 + 3 * x**2 + 2 * x + 1
def test_square_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = (1 + t*x + t*y)*2
p1 = rs_mul(p, p, x, 3)
p2 = rs_square(p, x, 3)
assert p1 == p2
p = 1 + x + x**2 + x**3
assert rs_square(p, x, 4) == 4*x**3 + 3*x**2 + 2*x + 1
def test_mul_trunc():
R, x, y, t = ring('x, y, t', QQ)
p = 1 + t*x + t*y
for i in range(2):
p = rs_mul(p, p, t, 3)
assert p == 6*x**2*t**2 + 12*x*y*t**2 + 6*y**2*t**2 + 4*x*t + 4*y*t + 1
p = 1 + t*x + t*y + t**2*x*y
p1 = rs_mul(p, p, t, 2)
assert p1 == 1 + 2*t*x + 2*t*y
R1, z = ring('z', QQ)
def test1(p):
p2 = rs_mul(p, z, x, 2)
raises(ValueError, lambda: test1(p))
p1 = 2 + 2*x + 3*x**2
p2 = 3 + x**2
assert rs_mul(p1, p2, x, 4) == 2*x**3 + 11*x**2 + 6*x + 6
def test1(p):
p2 = rs_mul(p, z, x, 2)
def test1(p):
p2 = rs_mul(p, z, x, 2)