def test_dmp_ground_trunc():
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_trunc(f, ZZ(3)) == (x**2*y*z**2 - x**2*y*z - x**2 +
y**2*z**2 - y**2*z + y*z**2 - y*z + y + 1)
def test_dmp_add_term():
R, x = ring('x', ZZ)
f = 0
assert R.dmp_add_term(f, 0, 0) == 0
assert R.dmp_add_term(f, 1, 0) == 1
assert R.dmp_add_term(f, 1, 1) == x
assert R.dmp_add_term(f, 1, 2) == x**2
f = x**2 + x + 1
assert R.dmp_add_term(f, 1, 0) == x**2 + x + 2
assert R.dmp_add_term(f, 1, 1) == x**2 + 2*x + 1
assert R.dmp_add_term(f, 1, 2) == 2*x**2 + x + 1
assert R.dmp_add_term(f, 1, 3) == x**3 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 4) == x**4 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 5) == x**5 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 6) == x**6 + x**2 + x + 1
assert R.dmp_add_term(f, -1, 2) == x + 1
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_add_term(f, 0, 3) == f
R, x, y, z = ring('x y z', QQ)
f = f.set_ring(R)/7
assert R.dmp_add_term(f, 0, 3) == f
def test_dmp_add_term():
R, x = ring('x', ZZ)
f = 0
assert R.dmp_add_term(f, 0, 0) == 0
assert R.dmp_add_term(f, 1, 0) == 1
assert R.dmp_add_term(f, 1, 1) == x
assert R.dmp_add_term(f, 1, 2) == x**2
f = x**2 + x + 1
assert R.dmp_add_term(f, 1, 0) == x**2 + x + 2
assert R.dmp_add_term(f, 1, 1) == x**2 + 2 * x + 1
assert R.dmp_add_term(f, 1, 2) == 2 * x**2 + x + 1
assert R.dmp_add_term(f, 1, 3) == x**3 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 4) == x**4 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 5) == x**5 + x**2 + x + 1
assert R.dmp_add_term(f, 1, 6) == x**6 + x**2 + x + 1
assert R.dmp_add_term(f, -1, 2) == x + 1
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_add_term(f, 0, 3) == f
R, x, y, z = ring('x y z', QQ)
f = f.set_ring(R) / 7
assert R.dmp_add_term(f, 0, 3) == f
def test_dmp_mul_ground():
R, x = ring('x', ZZ)
f = 0
assert R.dmp_mul_ground(f, ZZ(2)) == 0
f = x**2 + 2 * x - 1
assert R.dmp_mul_ground(f, ZZ(3)) == 3 * x**2 + 6 * x - 3
f = x**2 + 2 * x + 3
assert R.dmp_mul_ground(f, ZZ(0)) == 0
assert R.dmp_mul_ground(f, ZZ(2)) == 2 * x**2 + 4 * x + 6
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert (R.dmp_mul_ground(f,
ZZ(2)) == 2 * x**2 * y * z**2 + 4 * x**2 * y * z +
6 * x**2 * y + 4 * x**2 + 6 * x + 8 * y**2 * z**2 + 10 * y**2 * z +
12 * y**2 + 2 * y * z**2 + 4 * y * z + 2 * y + 2)
R, x, y, z = ring('x y z', QQ)
f = f.set_ring(R) / 7
assert (R.dmp_mul_ground(f, QQ(
1, 2)) == x**2 * y * z**2 / 14 + x**2 * y * z / 7 + 3 * x**2 * y / 14 +
x**2 / 7 + 3 * x / 14 + 2 * y**2 * z**2 / 7 + 5 * y**2 * z / 14 +
3 * y**2 / 7 + y * z**2 / 14 + y * z / 7 + y / 14 + QQ(1, 14))
def test_dmp_mul_ground():
R, x = ring('x', ZZ)
f = 0
assert R.dmp_mul_ground(f, ZZ(2)) == 0
f = x**2 + 2*x - 1
assert R.dmp_mul_ground(f, ZZ(3)) == 3*x**2 + 6*x - 3
f = x**2 + 2*x + 3
assert R.dmp_mul_ground(f, ZZ(0)) == 0
assert R.dmp_mul_ground(f, ZZ(2)) == 2*x**2 + 4*x + 6
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert (R.dmp_mul_ground(f, ZZ(2)) ==
2*x**2*y*z**2 + 4*x**2*y*z + 6*x**2*y + 4*x**2 + 6*x +
8*y**2*z**2 + 10*y**2*z + 12*y**2 + 2*y*z**2 + 4*y*z + 2*y + 2)
R, x, y, z = ring('x y z', QQ)
f = f.set_ring(R)/7
assert (R.dmp_mul_ground(f, QQ(1, 2)) ==
x**2*y*z**2/14 + x**2*y*z/7 + 3*x**2*y/14 + x**2/7 + 3*x/14 +
2*y**2*z**2/7 + 5*y**2*z/14 + 3*y**2/7 + y*z**2/14 + y*z/7 +
y/14 + QQ(1, 14))
def test_dmp_eval_in():
R, x = ring('x', ZZ)
assert R.dmp_eval_in(0, ZZ(7), 0) == 0
assert R.dmp_eval_in(x + 2, ZZ(0), 0) == 2
assert R.dmp_eval_in(x**2 + 2 * x + 3, ZZ(7), 0) == 66
assert R.dmp_eval_in(x**2 + 2 * x + 3, ZZ(2), 0) == 11
assert R.dmp_eval_in(0, ZZ(3), 0) == 0
R, x, y = ring('x y', ZZ)
R1 = R.drop(x)
assert R.dmp_eval_in(0, 3, 0) == 0
assert R.dmp_eval_in(y + 2, 0, 0) == R1.y + 2
assert R.dmp_eval_in(3 * x * y + 2 * x + y + 2, 3, 0) == 10 * R1.y + 8
assert R.dmp_eval_in(2 * x * y + 3 * x + y + 2, 2, 0) == 5 * R1.y + 8
R, x, y, z = ring('x y z', ZZ)
R1 = R.drop(x)
R3 = R.drop(z)
assert R.dmp_eval_in(0, 3, 0) == 0
assert R.dmp_eval_in(1, 3, 0) == 1
assert R.dmp_eval_in(z + 2, 3, 0) == R1.z + 2
assert R.dmp_eval_in(3 * x * z + 2 * x + z + 2, 3, 0) == 10 * R1.z + 8
f = 45 * x**3 - 9 * y**3 - y**2 + 3 * z**3 + 10 * z
assert R.dmp_eval_in(f, -2, 2) == 45 * R3.x**3 - 9 * R3.y**3 - R3.y**2 - 44
pytest.raises(IndexError, lambda: R.dmp_eval_in(f, -2, -1))
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
R2 = R.drop(y)
R3 = R.drop(z)
x, z, t = R2.gens
assert (R.dmp_eval_in(f, -2, 1) == -4230 * x**4 + 45 * x**3 * z**3 * t**2 -
45 * x**3 * t**2 - 282 * x * z**3 - 188 * x * z * t - 6392 * x +
3 * z**6 * t**2 + 2 * z**4 * t**3 + 65 * z**3 * t**2 -
2 * z * t**3 - 68 * t**2)
assert (R.dmp_eval_in(
f, 7, 1) == 14805 * x**4 + 45 * x**3 * z**3 * t**2 - 45 * x**3 * t**2 +
987 * x * z**3 + 658 * x * z * t - 1031744 * x + 3 * z**6 * t**2 +
2 * z**4 * t**3 - 3139 * z**3 * t**2 - 2 * z * t**3 + 3136 * t**2)
x, y, t = R3.gens
assert (R.dmp_eval_in(f, -2, 2) == 2115 * x**4 * y - 405 * x**3 * t**2 -
423 * x * y**4 - 47 * x * y**3 - 188 * x * y * t - 1128 * x * y +
81 * y**3 * t**2 + 9 * y**2 * t**2 + 36 * t**3 + 216 * t**2)
assert (R.dmp_eval_in(f, 7, 2) == 2115 * x**4 * y + 15390 * x**3 * t**2 -
423 * x * y**4 - 47 * x * y**3 + 658 * x * y * t + 48363 * x * y -
3078 * y**3 * t**2 - 342 * y**2 * t**2 + 4788 * t**3 +
351918 * t**2)
def test_dmp_eval_in():
R, x = ring('x', ZZ)
assert R.dmp_eval_in(0, ZZ(7), 0) == 0
assert R.dmp_eval_in(x + 2, ZZ(0), 0) == 2
assert R.dmp_eval_in(x**2 + 2*x + 3, ZZ(7), 0) == 66
assert R.dmp_eval_in(x**2 + 2*x + 3, ZZ(2), 0) == 11
assert R.dmp_eval_in(0, ZZ(3), 0) == 0
R, x, y = ring('x y', ZZ)
R1 = R.drop(x)
assert R.dmp_eval_in(0, 3, 0) == 0
assert R.dmp_eval_in(y + 2, 0, 0) == R1.y + 2
assert R.dmp_eval_in(3*x*y + 2*x + y + 2, 3, 0) == 10*R1.y + 8
assert R.dmp_eval_in(2*x*y + 3*x + y + 2, 2, 0) == 5*R1.y + 8
R, x, y, z = ring('x y z', ZZ)
R1 = R.drop(x)
R3 = R.drop(z)
assert R.dmp_eval_in(0, 3, 0) == 0
assert R.dmp_eval_in(1, 3, 0) == 1
assert R.dmp_eval_in(z + 2, 3, 0) == R1.z + 2
assert R.dmp_eval_in(3*x*z + 2*x + z + 2, 3, 0) == 10*R1.z + 8
f = 45*x**3 - 9*y**3 - y**2 + 3*z**3 + 10*z
assert R.dmp_eval_in(f, -2, 2) == 45*R3.x**3 - 9*R3.y**3 - R3.y**2 - 44
pytest.raises(IndexError, lambda: R.dmp_eval_in(f, -2, -1))
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
R2 = R.drop(y)
R3 = R.drop(z)
x, z, t = R2.gens
assert (R.dmp_eval_in(f, -2, 1) ==
-4230*x**4 + 45*x**3*z**3*t**2 - 45*x**3*t**2 - 282*x*z**3 -
188*x*z*t - 6392*x + 3*z**6*t**2 + 2*z**4*t**3 + 65*z**3*t**2 -
2*z*t**3 - 68*t**2)
assert (R.dmp_eval_in(f, 7, 1) ==
14805*x**4 + 45*x**3*z**3*t**2 - 45*x**3*t**2 + 987*x*z**3 +
658*x*z*t - 1031744*x + 3*z**6*t**2 + 2*z**4*t**3 -
3139*z**3*t**2 - 2*z*t**3 + 3136*t**2)
x, y, t = R3.gens
assert (R.dmp_eval_in(f, -2, 2) ==
2115*x**4*y - 405*x**3*t**2 - 423*x*y**4 - 47*x*y**3 - 188*x*y*t -
1128*x*y + 81*y**3*t**2 + 9*y**2*t**2 + 36*t**3 + 216*t**2)
assert (R.dmp_eval_in(f, 7, 2) ==
2115*x**4*y + 15390*x**3*t**2 - 423*x*y**4 - 47*x*y**3 + 658*x*y*t +
48363*x*y - 3078*y**3*t**2 - 342*y**2*t**2 + 4788*t**3 + 351918*t**2)
def test_dmp_l1_norm():
R, x = ring('x', ZZ)
assert R.dmp_l1_norm(0) == 0
assert R.dmp_l1_norm(1) == 1
assert R.dmp_l1_norm(2*x**3 - 3*x**2 + 1) == 6
assert R.dmp_l1_norm(x**3 + 4*x**2 + 2*x + 3) == 10
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_l1_norm(0) == 0
assert R.dmp_l1_norm(1) == 1
assert R.dmp_l1_norm(f_polys()[0]) == 31
def test_dmp_l1_norm():
R, x = ring('x', ZZ)
assert R.dmp_l1_norm(0) == 0
assert R.dmp_l1_norm(1) == 1
assert R.dmp_l1_norm(2 * x**3 - 3 * x**2 + 1) == 6
assert R.dmp_l1_norm(x**3 + 4 * x**2 + 2 * x + 3) == 10
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_l1_norm(0) == 0
assert R.dmp_l1_norm(1) == 1
assert R.dmp_l1_norm(f_polys()[0]) == 31
def test_dmp_max_norm():
R, x = ring('x', ZZ)
assert R.dmp_max_norm(0) == 0
assert R.dmp_max_norm(1) == 1
assert R.dmp_max_norm(-x**2 + 2*x - 3) == 3
assert R.dmp_max_norm(x**3 + 4*x**2 + 2*x + 3) == 4
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_max_norm(0) == 0
assert R.dmp_max_norm(1) == 1
assert R.dmp_max_norm(f_polys()[0]) == 6
def test_dmp_max_norm():
R, x = ring('x', ZZ)
assert R.dmp_max_norm(0) == 0
assert R.dmp_max_norm(1) == 1
assert R.dmp_max_norm(-x**2 + 2 * x - 3) == 3
assert R.dmp_max_norm(x**3 + 4 * x**2 + 2 * x + 3) == 4
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_max_norm(0) == 0
assert R.dmp_max_norm(1) == 1
assert R.dmp_max_norm(f_polys()[0]) == 6
def test_dmp_sub_term():
R, x = ring('x', ZZ)
f = 0
assert R.dmp_sub_term(f, 0, 0) == 0
assert R.dmp_sub_term(f, 1, 0) == -1
assert R.dmp_sub_term(f, 1, 1) == -x
assert R.dmp_sub_term(f, 1, 2) == -x**2
f = x**2 + x + 1
assert R.dmp_sub_term(f, 2, 0) == x**2 + x - 1
assert R.dmp_sub_term(f, 2, 1) == x**2 - x + 1
assert R.dmp_sub_term(f, 2, 2) == -x**2 + x + 1
assert R.dmp_sub_term(f, 1, 3) == -x**3 + x**2 + x + 1
assert R.dmp_sub_term(f, 1, 4) == -x**4 + x**2 + x + 1
assert R.dmp_sub_term(f, 1, 5) == -x**5 + x**2 + x + 1
assert R.dmp_sub_term(f, 1, 6) == -x**6 + x**2 + x + 1
assert R.dmp_sub_term(f, 1, 2) == x + 1
assert R.dmp_sub_term(2*x**4 + x**2 - 1, ZZ(2), 4) == x**2 - 1
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_sub_term(f, 0, 3) == f
R, x, y, z = ring('x y z', QQ)
f = f.set_ring(R)/7
assert R.dmp_sub_term(f, 0, 3) == f
R, x, y = ring('x y', ZZ)
f = 2*x**2 + x*y + 1
assert R.dmp_sub_term(f, 2, 3) == -2*x**3 + 2*x**2 + x*y + 1
assert R.dmp_sub_term(f, 2, 1) == 2*x**2 + x*y - 2*x + 1
assert R.dmp_sub_term(f, 2, 2) == x*y + 1
def test_dmp_diff_eval_in():
R, x = ring('x', ZZ)
assert R.dmp_diff_eval_in(x**2 + x + 1, 1, 1, 0) == 3
R, x, y = ring('x y', ZZ)
R0 = R.drop(x)
f = x * y**2 + 2 * x * y + 3 * x + 2 * y**2 + 3 * y + 1
assert R.dmp_diff_eval_in(f, 1, 2, 0) == R0.y**2 + 2 * R0.y + 3
R, x, y, z, t = ring('x y z t', ZZ)
R1 = R.drop(y)
f = f_polys()[6]
assert (R.dmp_diff_eval_in(f, 2, 7, 1) == -250698 * R1.x -
380 * R1.z**3 * R1.t**2 + 380 * R1.t**2)
pytest.raises(IndexError, lambda: R.dmp_diff_eval_in(f, 2, 7, 4))
def test_dmp_diff_eval_in():
R, x = ring('x', ZZ)
assert R.dmp_diff_eval_in(x**2 + x + 1, 1, 1, 0) == 3
R, x, y = ring('x y', ZZ)
R0 = R.drop(x)
f = x*y**2 + 2*x*y + 3*x + 2*y**2 + 3*y + 1
assert R.dmp_diff_eval_in(f, 1, 2, 0) == R0.y**2 + 2*R0.y + 3
R, x, y, z, t = ring('x y z t', ZZ)
R1 = R.drop(y)
f = f_polys()[6]
assert (R.dmp_diff_eval_in(f, 2, 7, 1) ==
-250698*R1.x - 380*R1.z**3*R1.t**2 + 380*R1.t**2)
pytest.raises(IndexError, lambda: R.dmp_diff_eval_in(f, 2, 7, 4))
def test_dmp_ground_trunc():
R, x = ring('x', ZZ)
assert R.dmp_ground_trunc(
x**5 + 2 * x**4 + 3 * x**3 + 4 * x**2 + 5 * x + 6,
ZZ(3)) == x**5 - x**4 + x**2 - x
assert R.dmp_ground_trunc(
6 * x**5 + 5 * x**4 + 4 * x**3 + 3 * x**2 + 2 * x + 1,
ZZ(3)) == -x**4 + x**3 - x + 1
R, x = ring('x', QQ)
assert R.dmp_ground_trunc(
x**5 + 2 * x**4 + 3 * x**3 + 4 * x**2 + 5 * x + 6,
ZZ(3)) == x**5 + 2 * x**4 + x**2 + 2 * x
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_trunc(
f, ZZ(3)) == (x**2 * y * z**2 - x**2 * y * z - x**2 + y**2 * z**2 -
y**2 * z + y * z**2 - y * z + y + 1)
import pytest
from diofant.domains import CC, QQ, RR, ZZ
from diofant.functions import sqrt
from diofant.polys.polyconfig import using
from diofant.polys.polyerrors import HeuristicGCDFailed, NotInvertible
from diofant.polys.rings import ring
from diofant.polys.specialpolys import (dmp_fateman_poly_F_1,
dmp_fateman_poly_F_2,
dmp_fateman_poly_F_3, f_polys)
__all__ = ()
f_0, f_1, f_2, f_3, f_4, f_5, f_6 = f_polys()
def test_dup_gcdex():
R, x = ring("x", QQ)
f = x**4 - 2*x**3 - 6*x**2 + 12*x + 15
g = x**3 + x**2 - 4*x - 4
s = -x/5 + QQ(3, 5)
t = x**2/5 - 6*x/5 + 2
h = x + 1
assert R.dup_half_gcdex(f, g) == (s, h)
assert R.dup_gcdex(f, g) == (s, t, h)
def test_dmp_eval_tail():
R, x, y = ring("x y", ZZ)
assert R.dmp_eval_tail(0, [ZZ(1)]) == 0
f = 2*x*y + 3*x + y + 2
R0 = R.drop(y)
assert R.dmp_eval_tail(f, [ZZ(2)]) == 7*R0.x + 4
assert R.dmp_eval_tail(f, [ZZ(2), ZZ(2)]) == 18
R, x, y, z = ring('x y z', ZZ)
R12 = R.drop(y, z)
R2 = R.drop(z)
assert R.dmp_eval_tail(0, [ZZ(1)]) == 0
assert R.dmp_eval_tail(0, [ZZ(1), ZZ(2)]) == 0
f = f_polys()[0]
assert R.dmp_eval_tail(f, []) == f
assert R.dmp_eval_tail(f, [ZZ(1), ZZ(-17), ZZ(8)]) == 84496
assert R.dmp_eval_tail(f, [ZZ(-17), ZZ(8)]) == -1409*R12.x**2 + 3*R12.x + 85902
assert (R.dmp_eval_tail(f, [ZZ(8)]) ==
83*R2.x**2*R2.y + 2*R2.x**2 + 3*R2.x + 302*R2.y**2 + 81*R2.y + 1)
f = f_polys()[1]
assert (R.dmp_eval_tail(f, [ZZ(-17), ZZ(8)]) ==
-136*R12.x**3 + 15699*R12.x**2 + 9166*R12.x - 27144)
f = f_polys()[2]
assert (R.dmp_eval_tail(f, [ZZ(-12), ZZ(3)]) ==
-1377*R12.x**5 - 702*R12.x**3 - 1224*R12.x**2 - 624)
f = f_polys()[3]
assert (R.dmp_eval_tail(f, [ZZ(-12), ZZ(3)]) ==
144*R12.x**5 + 82*R12.x**4 - 5181*R12.x**3 - 28872*R12.x**2 -
14868*R12.x - 540)
f = f_polys()[4]
assert (R.dmp_eval_tail(f, [ZZ(25), ZZ(-1)]) ==
152587890625*R12.x**9 + 9765625*R12.x**8 - 59605407714843750*R12.x**7 -
3839159765625*R12.x**6 - 1562475*R12.x**5 + 9536712644531250*R12.x**4 +
610349546750*R12.x**3 - 4*R12.x**2 + 24414375000*R12.x + 1562520)
f = f_polys()[5]
assert (R.dmp_eval_tail(f, [ZZ(25), ZZ(-1)]) ==
-R12.x**3 - 78*R12.x**2 - 2028*R12.x - 17576)
R, x, y, z, t = ring('x y z t', ZZ)
R123 = R.drop(y, z, t)
f = f_polys()[6]
assert R.dmp_eval_tail(f, [ZZ(0), ZZ(2), ZZ(4)]) == 5040*R123.x**3 + 4480
dmp_integrate_in, dmp_lift, dmp_trunc,
dup_clear_denoms, dup_decompose,
dup_diff, dup_eval, dup_integrate,
dup_mirror, dup_real_imag, dup_revert,
dup_scale, dup_shift,
dup_sign_variations, dup_transform,
dup_trunc)
from diofant.polys.polyerrors import (DomainError, ExactQuotientFailed,
NotReversible)
from diofant.polys.rings import ring
from diofant.polys.specialpolys import f_polys
__all__ = ()
f_0, f_1, f_2, f_3, f_4, f_5, f_6 = [ f.to_dense() for f in f_polys() ]
def test_dup_integrate():
assert dup_integrate([], 1, QQ) == []
assert dup_integrate([], 2, QQ) == []
assert dup_integrate([QQ(1)], 1, QQ) == [QQ(1), QQ(0)]
assert dup_integrate([QQ(1)], 2, QQ) == [QQ(1, 2), QQ(0), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 0, QQ) == \
[QQ(1), QQ(2), QQ(3)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 1, QQ) == \
[QQ(1, 3), QQ(1), QQ(3), QQ(0)]
assert dup_integrate([QQ(1), QQ(2), QQ(3)], 2, QQ) == \
[QQ(1, 12), QQ(1, 3), QQ(3, 2), QQ(0), QQ(0)]
def test_dmp_diff_in():
R, x = ring('x', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
assert R.dmp_diff_in(7, 1, 0) == 0
assert R.dmp_diff_in(2 * x + 7, 1, 0) == 2
assert R.dmp_diff_in(x**2 + 2 * x + 1, 1, 0) == 2 * x + 2
assert R.dmp_diff_in(x**3 + 2 * x**2 + 3 * x + 4, 1,
0) == 3 * x**2 + 4 * x + 3
assert R.dmp_diff_in(x**4 - x**3 + 2, 1, 0) == 4 * x**3 - 3 * x**2
assert R.dmp_diff_in(x**3 + 2 * x**2 + 3 * x + 4, 2, 0) == 6 * x + 4
f = 17 * x**10 + 34 * x**9 + 56 * x**8 - 345 * x**7 + 23 * x**6 + 76 * x**5 + 12 * x**2 + 3 * x + 7
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1,
0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(
R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0), 1, 0)
R, x = ring('x', FF(3))
f = 2 * x**10 + x**9 + 2 * x**8 + 2 * x**6 + x**5 + 1
assert R.dmp_diff_in(f, 1, 0) == 2 * x**9 + x**7 + 2 * x**4
assert R.dmp_diff_in(f, 2, 0) == x**6 + 2 * x**3
assert R.dmp_diff_in(f, 3, 0) == 0
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1,
0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(
R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0), 1, 0)
R, x, y = ring('x y', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
f = x * y**2 + 2 * x * y + 3 * x + 2 * y**2 + 3 * y + 1
assert R.dmp_diff_in(f, 1, 0) == y**2 + 2 * y + 3
assert R.dmp_diff_in(f, 2, 0) == 0
assert R.dmp_diff_in(f, 1, 1) == 2 * x * y + 2 * x + 4 * y + 3
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
assert R.dmp_diff_in(y + 2, 1, 0) == 0
assert R.dmp_diff_in(x, 1, 0) == 1
assert R.dmp_diff_in(3 * x**2 + x, 1, 0) == 6 * x + 1
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1,
0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(
R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0), 1, 0)
assert (R.dmp_diff_in(f, 2, 1) == -5076 * x * y**2 - 282 * x * y -
54 * y * z**3 * t**2 + 54 * y * t**2 - 2 * z**3 * t**2 + 2 * t**2)
assert R.dmp_diff_in(
f, 3, 1) == -10152 * x * y - 282 * x - 54 * z**3 * t**2 + 54 * t**2
assert (R.dmp_diff_in(f, 2, 2) == 270 * x**3 * z * t**2 + 846 * x * y * z -
54 * y**3 * z * t**2 - 6 * y**2 * z * t**2 + 90 * z**4 * t**2 +
24 * z**2 * t**3 - 18 * z * t**2)
assert (R.dmp_diff_in(
f, 3, 2) == 270 * x**3 * t**2 + 846 * x * y - 54 * y**3 * t**2 -
6 * y**2 * t**2 + 360 * z**3 * t**2 + 48 * z * t**3 - 18 * t**2)
pytest.raises(IndexError, lambda: R.dmp_diff_in(f, 2, -1))
R, x, y, z, t = ring('x y z t', FF(23))
f = R.from_dense(f_polys()[6].to_dense())
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1,
0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(
R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0), 1, 0)
def test_dmp_ground_primitive():
R, x = ring('x', ZZ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(1) == (1, 1)
assert R.dmp_ground_primitive(x + 1) == (1, x + 1)
assert R.dmp_ground_primitive(2 * x + 2) == (2, x + 1)
assert R.dmp_ground_primitive(x**2 + 2 * x + 1) == (1, x**2 + 2 * x + 1)
assert R.dmp_ground_primitive(2 * x**2 + 4 * x + 2) == (2,
x**2 + 2 * x + 1)
assert R.dmp_ground_primitive(6 * x**2 + 8 * x + 12) == (2, 3 * x**2 +
4 * x + 6)
R, x = ring('x', QQ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(1) == (1, 1)
assert R.dmp_ground_primitive(x + 1) == (1, x + 1)
assert R.dmp_ground_primitive(2 * x + 2) == (2, x + 1)
assert R.dmp_ground_primitive(x**2 + 2 * x + 1) == (1, x**2 + 2 * x + 1)
assert R.dmp_ground_primitive(2 * x**2 + 4 * x + 2) == (2,
x**2 + 2 * x + 1)
assert R.dmp_ground_primitive(6 * x**2 + 8 * x + 12) == (2, 3 * x**2 +
4 * x + 6)
assert R.dmp_ground_primitive(2 * x / 3 + QQ(4, 9)) == (QQ(2,
9), 3 * x + 2)
assert R.dmp_ground_primitive(2 * x / 3 + QQ(4, 5)) == (QQ(2,
15), 5 * x + 6)
R, x, y = ring('x y', ZZ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(2) == (2, 1)
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(2 * f) == (2, f)
f = f_polys()[1]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(3 * f) == (3, f)
f = f_polys()[2]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(4 * f) == (4, f)
f = f_polys()[3]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(5 * f) == (5, f)
f = f_polys()[4]
assert R.dmp_ground_primitive(f) == (-1, -f)
assert R.dmp_ground_primitive(6 * f) == (-6, -f)
f = f_polys()[5]
assert R.dmp_ground_primitive(f) == (-1, -f)
assert R.dmp_ground_primitive(7 * f) == (-7, -f)
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(8 * f) == (8, f)
R, x, y = ring('x y', QQ)
assert R.dmp_ground_primitive(2) == (2, 1)
assert R.dmp_ground_primitive(2 * x / 3 + QQ(4, 9)) == (QQ(2,
9), 3 * x + 2)
assert R.dmp_ground_primitive(2 * x / 3 + QQ(4, 5)) == (QQ(2,
15), 5 * x + 6)
def test_dmp_ground_content():
R, x = ring('x', ZZ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(+1) == 1
assert R.dmp_ground_content(-1) == -1
assert R.dmp_ground_content(x + 1) == 1
assert R.dmp_ground_content(2 * x + 2) == 2
assert R.dmp_ground_content(x**2 + 2 * x + 1) == 1
assert R.dmp_ground_content(2 * x**2 + 4 * x + 2) == 2
assert R.dmp_ground_content(6 * x**2 + 8 * x + 12) == 2
R, x = ring('x', QQ)
assert R.dmp_ground_content(6 * x**2 + 8 * x + 12) == 2
assert R.dmp_ground_content(2 * x / 3 + QQ(4, 9)) == QQ(2, 9)
assert R.dmp_ground_content(2 * x / 3 + QQ(4, 5)) == QQ(2, 15)
R, x, y = ring('x y', ZZ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(+1) == 1
assert R.dmp_ground_content(-1) == -1
assert R.dmp_ground_content(x + 1) == 1
assert R.dmp_ground_content(2 * x + 2) == 2
assert R.dmp_ground_content(x**2 + 2 * x + 1) == 1
assert R.dmp_ground_content(2 * x**2 + 4 * x + 2) == 2
R, x, y = ring('x y', QQ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(2 * x / 3 + QQ(4, 9)) == QQ(2, 9)
assert R.dmp_ground_content(2 * x / 3 + QQ(4, 5)) == QQ(2, 15)
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(2 * f) == 2
f = f_polys()[1]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(3 * f) == 3
f = f_polys()[2]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(4 * f) == 4
f = f_polys()[3]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(5 * f) == 5
f = f_polys()[4]
assert R.dmp_ground_content(f) == -1
assert R.dmp_ground_content(6 * f) == -6
f = f_polys()[5]
assert R.dmp_ground_content(f) == -1
assert R.dmp_ground_content(7 * f) == -7
R, x, y, z, t = ring('x y, z t', ZZ)
f = f_polys()[6]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(8 * f) == 8
def test_dmp_eval_tail():
R, x, y = ring("x y", ZZ)
assert R.dmp_eval_tail(0, [ZZ(1)]) == 0
f = 2 * x * y + 3 * x + y + 2
R0 = R.drop(y)
assert R.dmp_eval_tail(f, [ZZ(2)]) == 7 * R0.x + 4
assert R.dmp_eval_tail(f, [ZZ(2), ZZ(2)]) == 18
R, x, y, z = ring('x y z', ZZ)
R12 = R.drop(y, z)
R2 = R.drop(z)
assert R.dmp_eval_tail(0, [ZZ(1)]) == 0
assert R.dmp_eval_tail(0, [ZZ(1), ZZ(2)]) == 0
f = f_polys()[0]
assert R.dmp_eval_tail(f, []) == f
assert R.dmp_eval_tail(f, [ZZ(1), ZZ(-17), ZZ(8)]) == 84496
assert R.dmp_eval_tail(
f, [ZZ(-17), ZZ(8)]) == -1409 * R12.x**2 + 3 * R12.x + 85902
assert (R.dmp_eval_tail(f, [ZZ(8)]) == 83 * R2.x**2 * R2.y + 2 * R2.x**2 +
3 * R2.x + 302 * R2.y**2 + 81 * R2.y + 1)
f = f_polys()[1]
assert (R.dmp_eval_tail(f, [ZZ(-17), ZZ(8)]) == -136 * R12.x**3 +
15699 * R12.x**2 + 9166 * R12.x - 27144)
f = f_polys()[2]
assert (R.dmp_eval_tail(f, [ZZ(-12), ZZ(3)]) == -1377 * R12.x**5 -
702 * R12.x**3 - 1224 * R12.x**2 - 624)
f = f_polys()[3]
assert (R.dmp_eval_tail(
f, [ZZ(-12), ZZ(3)]) == 144 * R12.x**5 + 82 * R12.x**4 -
5181 * R12.x**3 - 28872 * R12.x**2 - 14868 * R12.x - 540)
f = f_polys()[4]
assert (R.dmp_eval_tail(f, [ZZ(25), ZZ(-1)]) == 152587890625 * R12.x**9 +
9765625 * R12.x**8 - 59605407714843750 * R12.x**7 -
3839159765625 * R12.x**6 - 1562475 * R12.x**5 +
9536712644531250 * R12.x**4 + 610349546750 * R12.x**3 -
4 * R12.x**2 + 24414375000 * R12.x + 1562520)
f = f_polys()[5]
assert (R.dmp_eval_tail(f, [ZZ(25), ZZ(-1)]) == -R12.x**3 - 78 * R12.x**2 -
2028 * R12.x - 17576)
R, x, y, z, t = ring('x y z t', ZZ)
R123 = R.drop(y, z, t)
f = f_polys()[6]
assert R.dmp_eval_tail(f, [ZZ(0), ZZ(2), ZZ(4)]) == 5040 * R123.x**3 + 4480
def test_dmp_ground_content():
R, x = ring('x', ZZ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(+1) == 1
assert R.dmp_ground_content(-1) == 1
assert R.dmp_ground_content(x + 1) == 1
assert R.dmp_ground_content(2*x + 2) == 2
assert R.dmp_ground_content(x**2 + 2*x + 1) == 1
assert R.dmp_ground_content(2*x**2 + 4*x + 2) == 2
assert R.dmp_ground_content(6*x**2 + 8*x + 12) == 2
R, x = ring('x', QQ)
assert R.dmp_ground_content(6*x**2 + 8*x + 12) == 2
assert R.dmp_ground_content(2*x/3 + QQ(4, 9)) == QQ(2, 9)
assert R.dmp_ground_content(2*x/3 + QQ(4, 5)) == QQ(2, 15)
R, x, y = ring('x y', ZZ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(+1) == 1
assert R.dmp_ground_content(-1) == 1
assert R.dmp_ground_content(x + 1) == 1
assert R.dmp_ground_content(2*x + 2) == 2
assert R.dmp_ground_content(x**2 + 2*x + 1) == 1
assert R.dmp_ground_content(2*x**2 + 4*x + 2) == 2
R, x, y = ring('x y', QQ)
assert R.dmp_ground_content(0) == 0
assert R.dmp_ground_content(2*x/3 + QQ(4, 9)) == QQ(2, 9)
assert R.dmp_ground_content(2*x/3 + QQ(4, 5)) == QQ(2, 15)
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(2*f) == 2
f = f_polys()[1]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(3*f) == 3
f = f_polys()[2]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(4*f) == 4
f = f_polys()[3]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(5*f) == 5
f = f_polys()[4]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(6*f) == 6
f = f_polys()[5]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(7*f) == 7
R, x, y, z, t = ring('x y, z t', ZZ)
f = f_polys()[6]
assert R.dmp_ground_content(f) == 1
assert R.dmp_ground_content(8*f) == 8
def test_PolyElement_integrate():
R, x = ring('x', QQ)
assert R(0).integrate() == 0
assert R(0).integrate(m=2) == 0
assert R(1).integrate() == x
assert R(1).integrate(m=2) == x**2 / 2
assert (x**2 + 2 * x + 3).integrate(m=0) == x**2 + 2 * x + 3
assert (x**2 + 2 * x + 3).integrate() == x**3 / 3 + x**2 + 3 * x
assert (x**2 + 2 * x +
3).integrate(m=2) == x**4 / 12 + x**3 / 3 + 3 * x**2 / 2
assert (x**2 + 2 * x +
3).integrate(m=3) == x**5 / 60 + x**4 / 12 + x**3 / 2
assert (x**2 + 2 * x).integrate() == x**3 / 3 + x**2
assert (x**2 + 2 * x).integrate(m=2) == x**4 / 12 + x**3 / 3
assert (17 * x**29).integrate(m=3) == 17 * x**32 / 29760
assert (17 * x**29 +
x**5 / 2).integrate(m=3) == 17 * x**32 / 29760 + x**8 / 672
R, x, y, z = ring('x y z', QQ)
assert R(0).integrate() == 0
assert R(0).integrate(m=2) == 0
assert R(1).integrate() == x
assert R(1).integrate(m=2) == x**2 / 2
R, x, y = ring('x y', QQ)
assert (x**2 + 2 * x + 3).integrate(m=0) == x**2 + 2 * x + 3
assert (x**2 + 2 * x + 3).integrate(m=1) == x**3 / 3 + x**2 + 3 * x
assert (x**2 + 2 * x +
3).integrate(m=2) == x**4 / 12 + x**3 / 3 + 3 * x**2 / 2
assert (x**2 + 2 * x +
3).integrate(m=3) == x**5 / 60 + x**4 / 12 + x**3 / 2
assert (x + 2 * y).integrate() == x**2 / 2 + 2 * x * y
assert (x + 2 * y).integrate(x=y) == x * y + y**2
assert (x + 2 * y).integrate(m=2) == x**3 / 6 + x**2 * y
R, x, y, z, t = ring('x y z t', QQ)
f = R.from_dense(f_polys()[6].to_dense())
assert (f.integrate(
x=y,
m=2) == 705 * x**4 * y**3 / 2 + 45 * x**3 * y**2 * z**3 * t**2 / 2 -
45 * x**3 * y**2 * t**2 / 2 - 141 * x * y**6 / 10 -
47 * x * y**5 / 20 + 47 * x * y**3 * z**3 / 2 +
47 * x * y**3 * z * t / 3 - 9 * y**5 * z**3 * t**2 / 20 +
9 * y**5 * t**2 / 20 - y**4 * z**3 * t**2 / 12 + y**4 * t**2 / 12 +
3 * y**2 * z**6 * t**2 / 2 + y**2 * z**4 * t**3 -
3 * y**2 * z**3 * t**2 / 2 - y**2 * z * t**3)
assert (f.integrate(
x=y,
m=3) == 705 * x**4 * y**4 / 8 + 15 * x**3 * y**3 * z**3 * t**2 / 2 -
15 * x**3 * y**3 * t**2 / 2 - 141 * x * y**7 / 70 -
47 * x * y**6 / 120 + 47 * x * y**4 * z**3 / 8 +
47 * x * y**4 * z * t / 12 - 3 * y**6 * z**3 * t**2 / 40 +
3 * y**6 * t**2 / 40 - y**5 * z**3 * t**2 / 60 + y**5 * t**2 / 60 +
y**3 * z**6 * t**2 / 2 + y**3 * z**4 * t**3 / 3 -
y**3 * z**3 * t**2 / 2 - y**3 * z * t**3 / 3)
assert (f.integrate(
x=z, m=2) == 2115 * x**4 * y * z**2 / 2 + 9 * x**3 * z**5 * t**2 / 4 -
45 * x**3 * z**2 * t**2 / 2 - 423 * x * y**4 * z**2 / 2 -
47 * x * y**3 * z**2 / 2 + 141 * x * y * z**5 / 20 +
47 * x * y * z**3 * t / 3 - 9 * y**3 * z**5 * t**2 / 20 +
9 * y**3 * z**2 * t**2 / 2 - y**2 * z**5 * t**2 / 20 +
y**2 * z**2 * t**2 / 2 + 3 * z**8 * t**2 / 56 + z**6 * t**3 / 15 -
3 * z**5 * t**2 / 20 - z**3 * t**3 / 3)
assert (f.integrate(
x=z, m=3) == 705 * x**4 * y * z**3 / 2 + 3 * x**3 * z**6 * t**2 / 8 -
15 * x**3 * z**3 * t**2 / 2 - 141 * x * y**4 * z**3 / 2 -
47 * x * y**3 * z**3 / 6 + 47 * x * y * z**6 / 40 +
47 * x * y * z**4 * t / 12 - 3 * y**3 * z**6 * t**2 / 40 +
3 * y**3 * z**3 * t**2 / 2 - y**2 * z**6 * t**2 / 120 +
y**2 * z**3 * t**2 / 6 + z**9 * t**2 / 168 + z**7 * t**3 / 105 -
z**6 * t**2 / 40 - z**4 * t**3 / 12)
def test_dmp_integrate_in():
R, x = ring('x', QQ)
assert R.dmp_integrate_in(0, 1, 0) == 0
assert R.dmp_integrate_in(0, 2, 0) == 0
assert R.dmp_integrate_in(1, 1, 0) == x
assert R.dmp_integrate_in(1, 2, 0) == x**2/2
assert R.dmp_integrate_in(x**2 + 2*x + 3, 0, 0) == x**2 + 2*x + 3
assert R.dmp_integrate_in(x**2 + 2*x + 3, 1, 0) == x**3/3 + x**2 + 3*x
assert R.dmp_integrate_in(x**2 + 2*x + 3, 2, 0) == x**4/12 + x**3/3 + 3*x**2/2
assert R.dmp_integrate_in(x**2 + 2*x + 3, 3, 0) == x**5/60 + x**4/12 + x**3/2
assert R.dmp_integrate_in(x**2 + 2*x, 1, 0) == x**3/3 + x**2
assert R.dmp_integrate_in(x**2 + 2*x, 2, 0) == x**4/12 + x**3/3
assert R.dmp_integrate_in(17*x**29, 3, 0) == 17*x**32/29760
assert R.dmp_integrate_in(17*x**29 + x**5/2, 3, 0) == 17*x**32/29760 + x**8/672
R, x, y, z = ring('x y z', QQ)
assert R.dmp_integrate_in(0, 1, 0) == 0
assert R.dmp_integrate_in(0, 2, 0) == 0
assert R.dmp_integrate_in(1, 1, 0) == x
assert R.dmp_integrate_in(1, 2, 0) == x**2/2
R, x, y = ring('x y', QQ)
assert R.dmp_integrate_in(x**2 + 2*x + 3, 0, 0) == x**2 + 2*x + 3
assert R.dmp_integrate_in(x**2 + 2*x + 3, 1, 0) == x**3/3 + x**2 + 3*x
assert R.dmp_integrate_in(x**2 + 2*x + 3, 2, 0) == x**4/12 + x**3/3 + 3*x**2/2
assert R.dmp_integrate_in(x**2 + 2*x + 3, 3, 0) == x**5/60 + x**4/12 + x**3/2
assert R.dmp_integrate_in(x + 2*y, 1, 0) == x**2/2 + 2*x*y
assert R.dmp_integrate_in(x + 2*y, 2, 0) == x**3/6 + x**2*y
R, x, y, z, t = ring('x y, z, t', QQ)
f = R.from_dense(f_polys()[6].to_dense())
assert (R.dmp_integrate_in(f, 2, 1) ==
705*x**4*y**3/2 + 45*x**3*y**2*z**3*t**2/2 - 45*x**3*y**2*t**2/2 -
141*x*y**6/10 - 47*x*y**5/20 + 47*x*y**3*z**3/2 + 47*x*y**3*z*t/3 -
9*y**5*z**3*t**2/20 + 9*y**5*t**2/20 - y**4*z**3*t**2/12 + y**4*t**2/12 +
3*y**2*z**6*t**2/2 + y**2*z**4*t**3 - 3*y**2*z**3*t**2/2 - y**2*z*t**3)
assert (R.dmp_integrate_in(f, 3, 1) ==
705*x**4*y**4/8 + 15*x**3*y**3*z**3*t**2/2 - 15*x**3*y**3*t**2/2 -
141*x*y**7/70 - 47*x*y**6/120 + 47*x*y**4*z**3/8 + 47*x*y**4*z*t/12 -
3*y**6*z**3*t**2/40 + 3*y**6*t**2/40 - y**5*z**3*t**2/60 + y**5*t**2/60 +
y**3*z**6*t**2/2 + y**3*z**4*t**3/3 - y**3*z**3*t**2/2 - y**3*z*t**3/3)
assert (R.dmp_integrate_in(f, 2, 2) ==
2115*x**4*y*z**2/2 + 9*x**3*z**5*t**2/4 - 45*x**3*z**2*t**2/2 -
423*x*y**4*z**2/2 - 47*x*y**3*z**2/2 + 141*x*y*z**5/20 + 47*x*y*z**3*t/3 -
9*y**3*z**5*t**2/20 + 9*y**3*z**2*t**2/2 - y**2*z**5*t**2/20 +
y**2*z**2*t**2/2 + 3*z**8*t**2/56 + z**6*t**3/15 - 3*z**5*t**2/20 -
z**3*t**3/3)
assert (R.dmp_integrate_in(f, 3, 2) ==
705*x**4*y*z**3/2 + 3*x**3*z**6*t**2/8 - 15*x**3*z**3*t**2/2 -
141*x*y**4*z**3/2 - 47*x*y**3*z**3/6 + 47*x*y*z**6/40 + 47*x*y*z**4*t/12 -
3*y**3*z**6*t**2/40 + 3*y**3*z**3*t**2/2 - y**2*z**6*t**2/120 +
y**2*z**3*t**2/6 + z**9*t**2/168 + z**7*t**3/105 - z**6*t**2/40 -
z**4*t**3/12)
pytest.raises(IndexError, lambda: R.dmp_integrate_in(f, 2, -1))
def test_dmp_ground_primitive():
R, x = ring('x', ZZ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(1) == (1, 1)
assert R.dmp_ground_primitive(x + 1) == (1, x + 1)
assert R.dmp_ground_primitive(2*x + 2) == (2, x + 1)
assert R.dmp_ground_primitive(x**2 + 2*x + 1) == (1, x**2 + 2*x + 1)
assert R.dmp_ground_primitive(2*x**2 + 4*x + 2) == (2, x**2 + 2*x + 1)
assert R.dmp_ground_primitive(6*x**2 + 8*x + 12) == (2, 3*x**2 + 4*x + 6)
R, x = ring('x', QQ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(1) == (1, 1)
assert R.dmp_ground_primitive(x + 1) == (1, x + 1)
assert R.dmp_ground_primitive(2*x + 2) == (2, x + 1)
assert R.dmp_ground_primitive(x**2 + 2*x + 1) == (1, x**2 + 2*x + 1)
assert R.dmp_ground_primitive(2*x**2 + 4*x + 2) == (2, x**2 + 2*x + 1)
assert R.dmp_ground_primitive(6*x**2 + 8*x + 12) == (2, 3*x**2 + 4*x + 6)
assert R.dmp_ground_primitive(2*x/3 + QQ(4, 9)) == (QQ(2, 9), 3*x + 2)
assert R.dmp_ground_primitive(2*x/3 + QQ(4, 5)) == (QQ(2, 15), 5*x + 6)
R, x, y = ring('x y', ZZ)
assert R.dmp_ground_primitive(0) == (0, 0)
assert R.dmp_ground_primitive(2) == (2, 1)
R, x, y, z = ring('x y z', ZZ)
f = f_polys()[0]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(2*f) == (2, f)
f = f_polys()[1]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(3*f) == (3, f)
f = f_polys()[2]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(4*f) == (4, f)
f = f_polys()[3]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(5*f) == (5, f)
f = f_polys()[4]
assert R.dmp_ground_primitive(f) == (-1, -f)
assert R.dmp_ground_primitive(6*f) == (-6, -f)
f = f_polys()[5]
assert R.dmp_ground_primitive(f) == (-1, -f)
assert R.dmp_ground_primitive(7*f) == (-7, -f)
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
assert R.dmp_ground_primitive(f) == (1, f)
assert R.dmp_ground_primitive(8*f) == (8, f)
R, x, y = ring('x y', QQ)
assert R.dmp_ground_primitive(2) == (2, 1)
assert R.dmp_ground_primitive(2*x/3 + QQ(4, 9)) == (QQ(2, 9), 3*x + 2)
assert R.dmp_ground_primitive(2*x/3 + QQ(4, 5)) == (QQ(2, 15), 5*x + 6)
def test_dmp_diff_in():
R, x = ring('x', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
assert R.dmp_diff_in(7, 1, 0) == 0
assert R.dmp_diff_in(2*x + 7, 1, 0) == 2
assert R.dmp_diff_in(x**2 + 2*x + 1, 1, 0) == 2*x + 2
assert R.dmp_diff_in(x**3 + 2*x**2 + 3*x + 4, 1, 0) == 3*x**2 + 4*x + 3
assert R.dmp_diff_in(x**4 - x**3 + 2, 1, 0) == 4*x**3 - 3*x**2
assert R.dmp_diff_in(x**3 + 2*x**2 + 3*x + 4, 2, 0) == 6*x + 4
f = 17*x**10 + 34*x**9 + 56*x**8 - 345*x**7 + 23*x**6 + 76*x**5 + 12*x**2 + 3*x + 7
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(R.dmp_diff_in(R.dmp_diff_in(f, 1, 0),
1, 0), 1, 0)
R, x = ring('x', FF(3))
f = 2*x**10 + x**9 + 2*x**8 + 2*x**6 + x**5 + 1
assert R.dmp_diff_in(f, 1, 0) == 2*x**9 + x**7 + 2*x**4
assert R.dmp_diff_in(f, 2, 0) == x**6 + 2*x**3
assert R.dmp_diff_in(f, 3, 0) == 0
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(R.dmp_diff_in(R.dmp_diff_in(f, 1, 0),
1, 0), 1, 0)
R, x, y = ring('x y', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
f = x*y**2 + 2*x*y + 3*x + 2*y**2 + 3*y + 1
assert R.dmp_diff_in(f, 1, 0) == y**2 + 2*y + 3
assert R.dmp_diff_in(f, 2, 0) == 0
assert R.dmp_diff_in(f, 1, 1) == 2*x*y + 2*x + 4*y + 3
R, x, y, z = ring('x y z', ZZ)
assert R.dmp_diff_in(0, 1, 0) == 0
assert R.dmp_diff_in(y + 2, 1, 0) == 0
assert R.dmp_diff_in(x, 1, 0) == 1
assert R.dmp_diff_in(3*x**2 + x, 1, 0) == 6*x + 1
R, x, y, z, t = ring('x y z t', ZZ)
f = f_polys()[6]
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(R.dmp_diff_in(R.dmp_diff_in(f, 1, 0),
1, 0), 1, 0)
assert (R.dmp_diff_in(f, 2, 1) ==
-5076*x*y**2 - 282*x*y - 54*y*z**3*t**2 + 54*y*t**2 - 2*z**3*t**2 + 2*t**2)
assert R.dmp_diff_in(f, 3, 1) == -10152*x*y - 282*x - 54*z**3*t**2 + 54*t**2
assert (R.dmp_diff_in(f, 2, 2) ==
270*x**3*z*t**2 + 846*x*y*z - 54*y**3*z*t**2 - 6*y**2*z*t**2 +
90*z**4*t**2 + 24*z**2*t**3 - 18*z*t**2)
assert (R.dmp_diff_in(f, 3, 2) ==
270*x**3*t**2 + 846*x*y - 54*y**3*t**2 - 6*y**2*t**2 +
360*z**3*t**2 + 48*z*t**3 - 18*t**2)
pytest.raises(IndexError, lambda: R.dmp_diff_in(f, 2, -1))
R, x, y, z, t = ring('x y z t', FF(23))
f = R.from_dense(f_polys()[6].to_dense())
assert R.dmp_diff_in(f, 0, 0) == f
assert R.dmp_diff_in(f, 2, 0) == R.dmp_diff_in(R.dmp_diff_in(f, 1, 0), 1, 0)
assert R.dmp_diff_in(f, 3, 0) == R.dmp_diff_in(R.dmp_diff_in(R.dmp_diff_in(f, 1, 0),
1, 0), 1, 0)
"""Tools for polynomial factorization routines in characteristic zero."""
import functools
import operator
import pytest
from diofant import (EX, FF, QQ, RR, ZZ, DomainError, ExtraneousFactors, I,
nextprime, pi, ring, sin, sqrt)
from diofant.polys.polyconfig import using
from diofant.polys.specialpolys import f_polys, w_polys
__all__ = ()
f_0, f_1, f_2, f_3, f_4, f_5, f_6 = f_polys()
w_1, w_2 = w_polys()
def test__trial_division():
R, x = ring('x', ZZ)
assert R._trial_division(
x**5 + 8 * x**4 + 25 * x**3 + 38 * x**2 + 28 * x + 8,
(x + 1, x + 2)) == [(x + 1, 2), (x + 2, 3)]
R, x, y = ring('x y', ZZ)
assert R._trial_division(
x**5 + 8 * x**4 + 25 * x**3 + 38 * x**2 + 28 * x + 8,
(x + 1, x + 2)) == [(x + 1, 2), (x + 2, 3)]
"""Tests for OO layer of several polynomial representations. """
import pytest
from diofant.domains import QQ, ZZ
from diofant.polys.polyclasses import DMP
from diofant.polys.polyerrors import ExactQuotientFailed, PolynomialError
from diofant.polys.specialpolys import f_polys
__all__ = ()
f_0, f_1, f_2, f_3, f_4, f_5, f_6 = [f.to_dense() for f in f_polys()]
def test_DMP___init__():
f = DMP([[0], [], [0, 1, 2], [3]], ZZ)
assert f.rep == [[1, 2], [3]]
assert f.domain == ZZ
assert f.lev == 1
f = DMP([[1, 2], [3]], ZZ, 1)
assert f.rep == [[1, 2], [3]]
assert f.domain == ZZ
assert f.lev == 1
f = DMP({(1, 1): 1, (0, 0): 2}, ZZ, 1)
assert f.rep == [[1, 0], [2]]
