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# sympy.integrals.prde.prde_linear_constraints

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"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, Matrix, S, symbols, I
from sympy.integrals.risch import DifferentialExtension
from sympy.integrals.prde import (prde_normal_denom, prde_special_denom,
prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large,
def test_prde_linear_constraints():
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
G = [(Poly(2*x**3 + 3*x + 1, x), Poly(x**2 - 1, x)), (Poly(1, x), Poly(x - 1, x)),
(Poly(1, x), Poly(x + 1, x))]
assert prde_linear_constraints(Poly(1, x), Poly(0, x), G, DE) == \
((Poly(2*x, x), Poly(0, x), Poly(0, x)), Matrix([[1, 1, -1], [5, 1, 1]]))
G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert prde_linear_constraints(Poly(t + 1, t), Poly(t**2, t), G, DE) == \
G = [(Poly(2*x, t), Poly(t, t)), (Poly(-x, t), Poly(t, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
prde_linear_constraints(Poly(1, t), Poly(0, t), G, DE) == \
((Poly(0, t), Poly(0, t)), Matrix([[2*x, -x]]))

"""Most of these tests come from the examples in Bronstein's book."""
from sympy import Poly, Matrix, S, symbols, I
from sympy.integrals.risch import DifferentialExtension
from sympy.integrals.prde import (prde_normal_denom, prde_special_denom,
prde_linear_constraints, constant_system, prde_spde, prde_no_cancel_b_large,
def test_prde_linear_constraints():
DE = DifferentialExtension(extension={'D': [Poly(1, x)]})
G = [(Poly(2*x**3 + 3*x + 1, x), Poly(x**2 - 1, x)), (Poly(1, x), Poly(x - 1, x)),
(Poly(1, x), Poly(x + 1, x))]
assert prde_linear_constraints(Poly(1, x), Poly(0, x), G, DE) == \
((Poly(2*x, x), Poly(0, x), Poly(0, x)), Matrix([[1, 1, -1], [5, 1, 1]]))
G = [(Poly(t, t), Poly(1, t)), (Poly(t**2, t), Poly(1, t)), (Poly(t**3, t), Poly(1, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(t, t)]})
assert prde_linear_constraints(Poly(t + 1, t), Poly(t**2, t), G, DE) == \
G = [(Poly(2*x, t), Poly(t, t)), (Poly(-x, t), Poly(t, t))]
DE = DifferentialExtension(extension={'D': [Poly(1, x), Poly(1/x, t)]})
prde_linear_constraints(Poly(1, t), Poly(0, t), G, DE) == \
((Poly(0, t), Poly(0, t)), Matrix([[2*x, -x]]))