test_poly_poly_poly.py

from commutative_ring import verify_ring_properties
from lib.test_helpers import assert_equal, assert_str, run_test
from poly_integer import IntegerPoly
from math_helper import MathHelper
from poly import SingleVarPoly
from poly_poly import PolyPoly
from poly_poly_poly import PolyPolyPoly

IP = IntegerPoly.from_list
PP = PolyPoly.from_list
PPP = PolyPolyPoly.from_list

ip_a = IP([1, 2])
ip_b = IP([3, 4])
ip_c = ip_a * ip_b

assert_str(ip_a, "(2)*x+1")
assert_str(ip_b, "(4)*x+3")
assert_str(ip_c, "(8)*x**2+(10)*x+3")

pp_a = PP([ip_a, ip_c])
pp_b = PP([ip_b, ip_a])
pp_c = pp_a * pp_b

assert_str(
    pp_c,
    "((16)*x**3+(28)*x**2+(16)*x+3)*p**2+((32)*x**3+(68)*x**2+(46)*x+10)*p+(8)*x**2+(10)*x+3",
)

ppp_a = PPP([pp_a, pp_c])
assert_equal(ppp_a.type_string, "SingleVarPoly.SingleVarPoly.SingleVarPoly.int")

assert_str(
    ppp_a,
    "(((16)*x**3+(28)*x**2+(16)*x+3)*p**2+((32)*x**3+(68)*x**2+(46)*x+10)*p+(8)*x**2+(10)*x+3)*q+((8)*x**2+(10)*x+3)*p+(2)*x+1",
)

# Now start evaluating.
pp_d = ppp_a.eval(pp_c)
assert_str(
    pp_d,
    "((256)*x**6+(896)*x**5+(1296)*x**4+(992)*x**3+(424)*x**2+(96)*x+9)*p**4+((1024)*x**6+(3968)*x**5+(6304)*x**4+(5264)*x**3+(2440)*x**2+(596)*x+60)*p**3+((1024)*x**6+(4608)*x**5+(8336)*x**4+(7808)*x**3+(4012)*x**2+(1076)*x+118)*p**2+((512)*x**5+(1728)*x**4+(2288)*x**3+(1496)*x**2+(486)*x+63)*p+(64)*x**4+(160)*x**3+(148)*x**2+(62)*x+10",
)

ip_d = pp_d.eval(ip_a)
assert_str(
    ip_d,
    "(4096)*x**10+(30720)*x**9+(103680)*x**8+(207616)*x**7+(273472)*x**6+(247808)*x**5+(156544)*x**4+(68112)*x**3+(19548)*x**2+(3346)*x+260",
)

big_int = ip_d.eval(1000000000)
assert (
    big_int
    == 4096000030720000103680000207616000273472000247808000156544000068112000019548000003346000000260
)


@run_test
def verify_ring_axioms():
    samples = [
        PPP([pp_a, pp_d, pp_c]),
        PPP([pp_c, pp_a]),
        PPP([pp_a, pp_d]),
        PPP([pp_b]),
    ]

    math = MathHelper(
        value_type=SingleVarPoly,
        zero=PolyPolyPoly.zero,
        one=PolyPolyPoly.one,
    )

    verify_ring_properties(math, samples)