"""Tests for dense recursive polynomials' basic tools. """ from sympy.polys.densebasic import ( dup_LC, dmp_LC, dup_TC, dmp_TC, dmp_ground_LC, dmp_ground_TC, dmp_true_LT, dup_degree, dmp_degree, dmp_degree_in, dmp_degree_list, dup_strip, dmp_strip, dmp_validate, dup_reverse, dup_copy, dmp_copy, dup_normal, dmp_normal, dup_convert, dmp_convert, dup_from_sympy, dmp_from_sympy, dup_nth, dmp_nth, dmp_ground_nth, dmp_zero_p, dmp_zero, dmp_one_p, dmp_one, dmp_ground_p, dmp_ground, dmp_negative_p, dmp_positive_p, dmp_zeros, dmp_grounds, dup_from_dict, dup_from_raw_dict, dup_to_dict, dup_to_raw_dict, dmp_from_dict, dmp_to_dict, dmp_swap, dmp_permute, dmp_nest, dmp_raise, dup_deflate, dmp_deflate, dup_multi_deflate, dmp_multi_deflate, dup_inflate, dmp_inflate, dmp_exclude, dmp_include, dmp_inject, dmp_eject, dup_terms_gcd, dmp_terms_gcd, dmp_list_terms, dmp_apply_pairs, dup_slice, dup_random, ) from sympy.polys.specialpolys import f_polys from sympy.polys.domains import ZZ, QQ from sympy.polys.rings import ring from sympy.core.singleton import S from sympy.testing.pytest import raises from sympy.core.numbers import oo 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_LC(): assert dup_LC([], ZZ) == 0 assert dup_LC([2, 3, 4, 5], ZZ) == 2 def test_dup_TC(): assert dup_TC([], ZZ) == 0 assert dup_TC([2, 3, 4, 5], ZZ) == 5 def test_dmp_LC(): assert dmp_LC([[]], ZZ) == [] assert dmp_LC([[2, 3, 4], [5]], ZZ) == [2, 3, 4] assert dmp_LC([[[]]], ZZ) == [[]] assert dmp_LC([[[2], [3, 4]], [[5]]], ZZ) == [[2], [3, 4]] def test_dmp_TC(): assert dmp_TC([[]], ZZ) == [] assert dmp_TC([[2, 3, 4], [5]], ZZ) == [5] assert dmp_TC([[[]]], ZZ) == [[]] assert dmp_TC([[[2], [3, 4]], [[5]]], ZZ) == [[5]] def test_dmp_ground_LC(): assert dmp_ground_LC([[]], 1, ZZ) == 0 assert dmp_ground_LC([[2, 3, 4], [5]], 1, ZZ) == 2 assert dmp_ground_LC([[[]]], 2, ZZ) == 0 assert dmp_ground_LC([[[2], [3, 4]], [[5]]], 2, ZZ) == 2 def test_dmp_ground_TC(): assert dmp_ground_TC([[]], 1, ZZ) == 0 assert dmp_ground_TC([[2, 3, 4], [5]], 1, ZZ) == 5 assert dmp_ground_TC([[[]]], 2, ZZ) == 0 assert dmp_ground_TC([[[2], [3, 4]], [[5]]], 2, ZZ) == 5 def test_dmp_true_LT(): assert dmp_true_LT([[]], 1, ZZ) == ((0, 0), 0) assert dmp_true_LT([[7]], 1, ZZ) == ((0, 0), 7) assert dmp_true_LT([[1, 0]], 1, ZZ) == ((0, 1), 1) assert dmp_true_LT([[1], []], 1, ZZ) == ((1, 0), 1) assert dmp_true_LT([[1, 0], []], 1, ZZ) == ((1, 1), 1) def test_dup_degree(): assert dup_degree([]) is -oo assert dup_degree([1]) == 0 assert dup_degree([1, 0]) == 1 assert dup_degree([1, 0, 0, 0, 1]) == 4 def test_dmp_degree(): assert dmp_degree([[]], 1) is -oo assert dmp_degree([[[]]], 2) is -oo assert dmp_degree([[1]], 1) == 0 assert dmp_degree([[2], [1]], 1) == 1 def test_dmp_degree_in(): assert dmp_degree_in([[[]]], 0, 2) is -oo assert dmp_degree_in([[[]]], 1, 2) is -oo assert dmp_degree_in([[[]]], 2, 2) is -oo assert dmp_degree_in([[[1]]], 0, 2) == 0 assert dmp_degree_in([[[1]]], 1, 2) == 0 assert dmp_degree_in([[[1]]], 2, 2) == 0 assert dmp_degree_in(f_4, 0, 2) == 9 assert dmp_degree_in(f_4, 1, 2) == 12 assert dmp_degree_in(f_4, 2, 2) == 8 assert dmp_degree_in(f_6, 0, 2) == 4 assert dmp_degree_in(f_6, 1, 2) == 4 assert dmp_degree_in(f_6, 2, 2) == 6 assert dmp_degree_in(f_6, 3, 3) == 3 raises(IndexError, lambda: dmp_degree_in([[1]], -5, 1)) def test_dmp_degree_list(): assert dmp_degree_list([[[[ ]]]], 3) == (-oo, -oo, -oo, -oo) assert dmp_degree_list([[[[1]]]], 3) == ( 0, 0, 0, 0) assert dmp_degree_list(f_0, 2) == (2, 2, 2) assert dmp_degree_list(f_1, 2) == (3, 3, 3) assert dmp_degree_list(f_2, 2) == (5, 3, 3) assert dmp_degree_list(f_3, 2) == (5, 4, 7) assert dmp_degree_list(f_4, 2) == (9, 12, 8) assert dmp_degree_list(f_5, 2) == (3, 3, 3) assert dmp_degree_list(f_6, 3) == (4, 4, 6, 3) def test_dup_strip(): assert dup_strip([]) == [] assert dup_strip([0]) == [] assert dup_strip([0, 0, 0]) == [] assert dup_strip([1]) == [1] assert dup_strip([0, 1]) == [1] assert dup_strip([0, 0, 0, 1]) == [1] assert dup_strip([1, 2, 0]) == [1, 2, 0] assert dup_strip([0, 1, 2, 0]) == [1, 2, 0] assert dup_strip([0, 0, 0, 1, 2, 0]) == [1, 2, 0] def test_dmp_strip(): assert dmp_strip([0, 1, 0], 0) == [1, 0] assert dmp_strip([[]], 1) == [[]] assert dmp_strip([[], []], 1) == [[]] assert dmp_strip([[], [], []], 1) == [[]] assert dmp_strip([[[]]], 2) == [[[]]] assert dmp_strip([[[]], [[]]], 2) == [[[]]] assert dmp_strip([[[]], [[]], [[]]], 2) == [[[]]] assert dmp_strip([[[1]]], 2) == [[[1]]] assert dmp_strip([[[]], [[1]]], 2) == [[[1]]] assert dmp_strip([[[]], [[1]], [[]]], 2) == [[[1]], [[]]] def test_dmp_validate(): assert dmp_validate([]) == ([], 0) assert dmp_validate([0, 0, 0, 1, 0]) == ([1, 0], 0) assert dmp_validate([[[]]]) == ([[[]]], 2) assert dmp_validate([[0], [], [0], [1], [0]]) == ([[1], []], 1) raises(ValueError, lambda: dmp_validate([[0], 0, [0], [1], [0]])) def test_dup_reverse(): assert dup_reverse([1, 2, 0, 3]) == [3, 0, 2, 1] assert dup_reverse([1, 2, 3, 0]) == [3, 2, 1] def test_dup_copy(): f = [ZZ(1), ZZ(0), ZZ(2)] g = dup_copy(f) g[0], g[2] = ZZ(7), ZZ(0) assert f != g def test_dmp_copy(): f = [[ZZ(1)], [ZZ(2), ZZ(0)]] g = dmp_copy(f, 1) g[0][0], g[1][1] = ZZ(7), ZZ(1) assert f != g def test_dup_normal(): assert dup_normal([0, 0, 2, 1, 0, 11, 0], ZZ) == \ [ZZ(2), ZZ(1), ZZ(0), ZZ(11), ZZ(0)] def test_dmp_normal(): assert dmp_normal([[0], [], [0, 2, 1], [0], [11], []], 1, ZZ) == \ [[ZZ(2), ZZ(1)], [], [ZZ(11)], []] def test_dup_convert(): K0, K1 = ZZ['x'], ZZ f = [K0(1), K0(2), K0(0), K0(3)] assert dup_convert(f, K0, K1) == \ [ZZ(1), ZZ(2), ZZ(0), ZZ(3)] def test_dmp_convert(): K0, K1 = ZZ['x'], ZZ f = [[K0(1)], [K0(2)], [], [K0(3)]] assert dmp_convert(f, 1, K0, K1) == \ [[ZZ(1)], [ZZ(2)], [], [ZZ(3)]] def test_dup_from_sympy(): assert dup_from_sympy([S.One, S(2)], ZZ) == \ [ZZ(1), ZZ(2)] assert dup_from_sympy([S.Half, S(3)], QQ) == \ [QQ(1, 2), QQ(3, 1)] def test_dmp_from_sympy(): assert dmp_from_sympy([[S.One, S(2)], [S.Zero]], 1, ZZ) == \ [[ZZ(1), ZZ(2)], []] assert dmp_from_sympy([[S.Half, S(2)]], 1, QQ) == \ [[QQ(1, 2), QQ(2, 1)]] def test_dup_nth(): assert dup_nth([1, 2, 3], 0, ZZ) == 3 assert dup_nth([1, 2, 3], 1, ZZ) == 2 assert dup_nth([1, 2, 3], 2, ZZ) == 1 assert dup_nth([1, 2, 3], 9, ZZ) == 0 raises(IndexError, lambda: dup_nth([3, 4, 5], -1, ZZ)) def test_dmp_nth(): assert dmp_nth([[1], [2], [3]], 0, 1, ZZ) == [3] assert dmp_nth([[1], [2], [3]], 1, 1, ZZ) == [2] assert dmp_nth([[1], [2], [3]], 2, 1, ZZ) == [1] assert dmp_nth([[1], [2], [3]], 9, 1, ZZ) == [] raises(IndexError, lambda: dmp_nth([[3], [4], [5]], -1, 1, ZZ)) def test_dmp_ground_nth(): assert dmp_ground_nth([[]], (0, 0), 1, ZZ) == 0 assert dmp_ground_nth([[1], [2], [3]], (0, 0), 1, ZZ) == 3 assert dmp_ground_nth([[1], [2], [3]], (1, 0), 1, ZZ) == 2 assert dmp_ground_nth([[1], [2], [3]], (2, 0), 1, ZZ) == 1 assert dmp_ground_nth([[1], [2], [3]], (2, 1), 1, ZZ) == 0 assert dmp_ground_nth([[1], [2], [3]], (3, 0), 1, ZZ) == 0 raises(IndexError, lambda: dmp_ground_nth([[3], [4], [5]], (2, -1), 1, ZZ)) def test_dmp_zero_p(): assert dmp_zero_p([], 0) is True assert dmp_zero_p([[]], 1) is True assert dmp_zero_p([[[]]], 2) is True assert dmp_zero_p([[[1]]], 2) is False def test_dmp_zero(): assert dmp_zero(0) == [] assert dmp_zero(2) == [[[]]] def test_dmp_one_p(): assert dmp_one_p([1], 0, ZZ) is True assert dmp_one_p([[1]], 1, ZZ) is True assert dmp_one_p([[[1]]], 2, ZZ) is True assert dmp_one_p([[[12]]], 2, ZZ) is False def test_dmp_one(): assert dmp_one(0, ZZ) == [ZZ(1)] assert dmp_one(2, ZZ) == [[[ZZ(1)]]] def test_dmp_ground_p(): assert dmp_ground_p([], 0, 0) is True assert dmp_ground_p([[]], 0, 1) is True assert dmp_ground_p([[]], 1, 1) is False assert dmp_ground_p([[ZZ(1)]], 1, 1) is True assert dmp_ground_p([[[ZZ(2)]]], 2, 2) is True assert dmp_ground_p([[[ZZ(2)]]], 3, 2) is False assert dmp_ground_p([[[ZZ(3)], []]], 3, 2) is False assert dmp_ground_p([], None, 0) is True assert dmp_ground_p([[]], None, 1) is True assert dmp_ground_p([ZZ(1)], None, 0) is True assert dmp_ground_p([[[ZZ(1)]]], None, 2) is True assert dmp_ground_p([[[ZZ(3)], []]], None, 2) is False def test_dmp_ground(): assert dmp_ground(ZZ(0), 2) == [[[]]] assert dmp_ground(ZZ(7), -1) == ZZ(7) assert dmp_ground(ZZ(7), 0) == [ZZ(7)] assert dmp_ground(ZZ(7), 2) == [[[ZZ(7)]]] def test_dmp_zeros(): assert dmp_zeros(4, 0, ZZ) == [[], [], [], []] assert dmp_zeros(0, 2, ZZ) == [] assert dmp_zeros(1, 2, ZZ) == [[[[]]]] assert dmp_zeros(2, 2, ZZ) == [[[[]]], [[[]]]] assert dmp_zeros(3, 2, ZZ) == [[[[]]], [[[]]], [[[]]]] assert dmp_zeros(3, -1, ZZ) == [0, 0, 0] def test_dmp_grounds(): assert dmp_grounds(ZZ(7), 0, 2) == [] assert dmp_grounds(ZZ(7), 1, 2) == [[[[7]]]] assert dmp_grounds(ZZ(7), 2, 2) == [[[[7]]], [[[7]]]] assert dmp_grounds(ZZ(7), 3, 2) == [[[[7]]], [[[7]]], [[[7]]]] assert dmp_grounds(ZZ(7), 3, -1) == [7, 7, 7] def test_dmp_negative_p(): assert dmp_negative_p([[[]]], 2, ZZ) is False assert dmp_negative_p([[[1], [2]]], 2, ZZ) is False assert dmp_negative_p([[[-1], [2]]], 2, ZZ) is True def test_dmp_positive_p(): assert dmp_positive_p([[[]]], 2, ZZ) is False assert dmp_positive_p([[[1], [2]]], 2, ZZ) is True assert dmp_positive_p([[[-1], [2]]], 2, ZZ) is False def test_dup_from_to_dict(): assert dup_from_raw_dict({}, ZZ) == [] assert dup_from_dict({}, ZZ) == [] assert dup_to_raw_dict([]) == {} assert dup_to_dict([]) == {} assert dup_to_raw_dict([], ZZ, zero=True) == {0: ZZ(0)} assert dup_to_dict([], ZZ, zero=True) == {(0,): ZZ(0)} f = [3, 0, 0, 2, 0, 0, 0, 0, 8] g = {8: 3, 5: 2, 0: 8} h = {(8,): 3, (5,): 2, (0,): 8} assert dup_from_raw_dict(g, ZZ) == f assert dup_from_dict(h, ZZ) == f assert dup_to_raw_dict(f) == g assert dup_to_dict(f) == h R, x,y = ring("x,y", ZZ) K = R.to_domain() f = [R(3), R(0), R(2), R(0), R(0), R(8)] g = {5: R(3), 3: R(2), 0: R(8)} h = {(5,): R(3), (3,): R(2), (0,): R(8)} assert dup_from_raw_dict(g, K) == f assert dup_from_dict(h, K) == f assert dup_to_raw_dict(f) == g assert dup_to_dict(f) == h def test_dmp_from_to_dict(): assert dmp_from_dict({}, 1, ZZ) == [[]] assert dmp_to_dict([[]], 1) == {} assert dmp_to_dict([], 0, ZZ, zero=True) == {(0,): ZZ(0)} assert dmp_to_dict([[]], 1, ZZ, zero=True) == {(0, 0): ZZ(0)} f = [[3], [], [], [2], [], [], [], [], [8]] g = {(8, 0): 3, (5, 0): 2, (0, 0): 8} assert dmp_from_dict(g, 1, ZZ) == f assert dmp_to_dict(f, 1) == g def test_dmp_swap(): f = dmp_normal([[1, 0, 0], [], [1, 0], [], [1]], 1, ZZ) g = dmp_normal([[1, 0, 0, 0, 0], [1, 0, 0], [1]], 1, ZZ) assert dmp_swap(f, 1, 1, 1, ZZ) == f assert dmp_swap(f, 0, 1, 1, ZZ) == g assert dmp_swap(g, 0, 1, 1, ZZ) == f raises(IndexError, lambda: dmp_swap(f, -1, -7, 1, ZZ)) def test_dmp_permute(): f = dmp_normal([[1, 0, 0], [], [1, 0], [], [1]], 1, ZZ) g = dmp_normal([[1, 0, 0, 0, 0], [1, 0, 0], [1]], 1, ZZ) assert dmp_permute(f, [0, 1], 1, ZZ) == f assert dmp_permute(g, [0, 1], 1, ZZ) == g assert dmp_permute(f, [1, 0], 1, ZZ) == g assert dmp_permute(g, [1, 0], 1, ZZ) == f def test_dmp_nest(): assert dmp_nest(ZZ(1), 2, ZZ) == [[[1]]] assert dmp_nest([[1]], 0, ZZ) == [[1]] assert dmp_nest([[1]], 1, ZZ) == [[[1]]] assert dmp_nest([[1]], 2, ZZ) == [[[[1]]]] def test_dmp_raise(): assert dmp_raise([], 2, 0, ZZ) == [[[]]] assert dmp_raise([[1]], 0, 1, ZZ) == [[1]] assert dmp_raise([[1, 2, 3], [], [2, 3]], 2, 1, ZZ) == \ [[[[1]], [[2]], [[3]]], [[[]]], [[[2]], [[3]]]] def test_dup_deflate(): assert dup_deflate([], ZZ) == (1, []) assert dup_deflate([2], ZZ) == (1, [2]) assert dup_deflate([1, 2, 3], ZZ) == (1, [1, 2, 3]) assert dup_deflate([1, 0, 2, 0, 3], ZZ) == (2, [1, 2, 3]) assert dup_deflate(dup_from_raw_dict({7: 1, 1: 1}, ZZ), ZZ) == \ (1, [1, 0, 0, 0, 0, 0, 1, 0]) assert dup_deflate(dup_from_raw_dict({7: 1, 0: 1}, ZZ), ZZ) == \ (7, [1, 1]) assert dup_deflate(dup_from_raw_dict({7: 1, 3: 1}, ZZ), ZZ) == \ (1, [1, 0, 0, 0, 1, 0, 0, 0]) assert dup_deflate(dup_from_raw_dict({7: 1, 4: 1}, ZZ), ZZ) == \ (1, [1, 0, 0, 1, 0, 0, 0, 0]) assert dup_deflate(dup_from_raw_dict({8: 1, 4: 1}, ZZ), ZZ) == \ (4, [1, 1, 0]) assert dup_deflate(dup_from_raw_dict({8: 1}, ZZ), ZZ) == \ (8, [1, 0]) assert dup_deflate(dup_from_raw_dict({7: 1}, ZZ), ZZ) == \ (7, [1, 0]) assert dup_deflate(dup_from_raw_dict({1: 1}, ZZ), ZZ) == \ (1, [1, 0]) def test_dmp_deflate(): assert dmp_deflate([[]], 1, ZZ) == ((1, 1), [[]]) assert dmp_deflate([[2]], 1, ZZ) == ((1, 1), [[2]]) f = [[1, 0, 0], [], [1, 0], [], [1]] assert dmp_deflate(f, 1, ZZ) == ((2, 1), [[1, 0, 0], [1, 0], [1]]) def test_dup_multi_deflate(): assert dup_multi_deflate(([2],), ZZ) == (1, ([2],)) assert dup_multi_deflate(([], []), ZZ) == (1, ([], [])) assert dup_multi_deflate(([1, 2, 3],), ZZ) == (1, ([1, 2, 3],)) assert dup_multi_deflate(([1, 0, 2, 0, 3],), ZZ) == (2, ([1, 2, 3],)) assert dup_multi_deflate(([1, 0, 2, 0, 3], [2, 0, 0]), ZZ) == \ (2, ([1, 2, 3], [2, 0])) assert dup_multi_deflate(([1, 0, 2, 0, 3], [2, 1, 0]), ZZ) == \ (1, ([1, 0, 2, 0, 3], [2, 1, 0])) def test_dmp_multi_deflate(): assert dmp_multi_deflate(([[]],), 1, ZZ) == \ ((1, 1), ([[]],)) assert dmp_multi_deflate(([[]], [[]]), 1, ZZ) == \ ((1, 1), ([[]], [[]])) assert dmp_multi_deflate(([[1]], [[]]), 1, ZZ) == \ ((1, 1), ([[1]], [[]])) assert dmp_multi_deflate(([[1]], [[2]]), 1, ZZ) == \ ((1, 1), ([[1]], [[2]])) assert dmp_multi_deflate(([[1]], [[2, 0]]), 1, ZZ) == \ ((1, 1), ([[1]], [[2, 0]])) assert dmp_multi_deflate(([[2, 0]], [[2, 0]]), 1, ZZ) == \ ((1, 1), ([[2, 0]], [[2, 0]])) assert dmp_multi_deflate( ([[2]], [[2, 0, 0]]), 1, ZZ) == ((1, 2), ([[2]], [[2, 0]])) assert dmp_multi_deflate( ([[2, 0, 0]], [[2, 0, 0]]), 1, ZZ) == ((1, 2), ([[2, 0]], [[2, 0]])) assert dmp_multi_deflate(([2, 0, 0], [1, 0, 4, 0, 1]), 0, ZZ) == \ ((2,), ([2, 0], [1, 4, 1])) f = [[1, 0, 0], [], [1, 0], [], [1]] g = [[1, 0, 1, 0], [], [1]] assert dmp_multi_deflate((f,), 1, ZZ) == \ ((2, 1), ([[1, 0, 0], [1, 0], [1]],)) assert dmp_multi_deflate((f, g), 1, ZZ) == \ ((2, 1), ([[1, 0, 0], [1, 0], [1]], [[1, 0, 1, 0], [1]])) def test_dup_inflate(): assert dup_inflate([], 17, ZZ) == [] assert dup_inflate([1, 2, 3], 1, ZZ) == [1, 2, 3] assert dup_inflate([1, 2, 3], 2, ZZ) == [1, 0, 2, 0, 3] assert dup_inflate([1, 2, 3], 3, ZZ) == [1, 0, 0, 2, 0, 0, 3] assert dup_inflate([1, 2, 3], 4, ZZ) == [1, 0, 0, 0, 2, 0, 0, 0, 3] raises(IndexError, lambda: dup_inflate([1, 2, 3], 0, ZZ)) def test_dmp_inflate(): assert dmp_inflate([1], (3,), 0, ZZ) == [1] assert dmp_inflate([[]], (3, 7), 1, ZZ) == [[]] assert dmp_inflate([[2]], (1, 2), 1, ZZ) == [[2]] assert dmp_inflate([[2, 0]], (1, 1), 1, ZZ) == [[2, 0]] assert dmp_inflate([[2, 0]], (1, 2), 1, ZZ) == [[2, 0, 0]] assert dmp_inflate([[2, 0]], (1, 3), 1, ZZ) == [[2, 0, 0, 0]] assert dmp_inflate([[1, 0, 0], [1], [1, 0]], (2, 1), 1, ZZ) == \ [[1, 0, 0], [], [1], [], [1, 0]] raises(IndexError, lambda: dmp_inflate([[]], (-3, 7), 1, ZZ)) def test_dmp_exclude(): assert dmp_exclude([[[]]], 2, ZZ) == ([], [[[]]], 2) assert dmp_exclude([[[7]]], 2, ZZ) == ([], [[[7]]], 2) assert dmp_exclude([1, 2, 3], 0, ZZ) == ([], [1, 2, 3], 0) assert dmp_exclude([[1], [2, 3]], 1, ZZ) == ([], [[1], [2, 3]], 1) assert dmp_exclude([[1, 2, 3]], 1, ZZ) == ([0], [1, 2, 3], 0) assert dmp_exclude([[1], [2], [3]], 1, ZZ) == ([1], [1, 2, 3], 0) assert dmp_exclude([[[1, 2, 3]]], 2, ZZ) == ([0, 1], [1, 2, 3], 0) assert dmp_exclude([[[1]], [[2]], [[3]]], 2, ZZ) == ([1, 2], [1, 2, 3], 0) def test_dmp_include(): assert dmp_include([1, 2, 3], [], 0, ZZ) == [1, 2, 3] assert dmp_include([1, 2, 3], [0], 0, ZZ) == [[1, 2, 3]] assert dmp_include([1, 2, 3], [1], 0, ZZ) == [[1], [2], [3]] assert dmp_include([1, 2, 3], [0, 1], 0, ZZ) == [[[1, 2, 3]]] assert dmp_include([1, 2, 3], [1, 2], 0, ZZ) == [[[1]], [[2]], [[3]]] def test_dmp_inject(): R, x,y = ring("x,y", ZZ) K = R.to_domain() assert dmp_inject([], 0, K) == ([[[]]], 2) assert dmp_inject([[]], 1, K) == ([[[[]]]], 3) assert dmp_inject([R(1)], 0, K) == ([[[1]]], 2) assert dmp_inject([[R(1)]], 1, K) == ([[[[1]]]], 3) assert dmp_inject([R(1), 2*x + 3*y + 4], 0, K) == ([[[1]], [[2], [3, 4]]], 2) f = [3*x**2 + 7*x*y + 5*y**2, 2*x, R(0), x*y**2 + 11] g = [[[3], [7, 0], [5, 0, 0]], [[2], []], [[]], [[1, 0, 0], [11]]] assert dmp_inject(f, 0, K) == (g, 2) def test_dmp_eject(): R, x,y = ring("x,y", ZZ) K = R.to_domain() assert dmp_eject([[[]]], 2, K) == [] assert dmp_eject([[[[]]]], 3, K) == [[]] assert dmp_eject([[[1]]], 2, K) == [R(1)] assert dmp_eject([[[[1]]]], 3, K) == [[R(1)]] assert dmp_eject([[[1]], [[2], [3, 4]]], 2, K) == [R(1), 2*x + 3*y + 4] f = [3*x**2 + 7*x*y + 5*y**2, 2*x, R(0), x*y**2 + 11] g = [[[3], [7, 0], [5, 0, 0]], [[2], []], [[]], [[1, 0, 0], [11]]] assert dmp_eject(g, 2, K) == f def test_dup_terms_gcd(): assert dup_terms_gcd([], ZZ) == (0, []) assert dup_terms_gcd([1, 0, 1], ZZ) == (0, [1, 0, 1]) assert dup_terms_gcd([1, 0, 1, 0], ZZ) == (1, [1, 0, 1]) def test_dmp_terms_gcd(): assert dmp_terms_gcd([[]], 1, ZZ) == ((0, 0), [[]]) assert dmp_terms_gcd([1, 0, 1, 0], 0, ZZ) == ((1,), [1, 0, 1]) assert dmp_terms_gcd([[1], [], [1], []], 1, ZZ) == ((1, 0), [[1], [], [1]]) assert dmp_terms_gcd( [[1, 0], [], [1]], 1, ZZ) == ((0, 0), [[1, 0], [], [1]]) assert dmp_terms_gcd( [[1, 0], [1, 0, 0], [], []], 1, ZZ) == ((2, 1), [[1], [1, 0]]) def test_dmp_list_terms(): assert dmp_list_terms([[[]]], 2, ZZ) == [((0, 0, 0), 0)] assert dmp_list_terms([[[1]]], 2, ZZ) == [((0, 0, 0), 1)] assert dmp_list_terms([1, 2, 4, 3, 5], 0, ZZ) == \ [((4,), 1), ((3,), 2), ((2,), 4), ((1,), 3), ((0,), 5)] assert dmp_list_terms([[1], [2, 4], [3, 5, 0]], 1, ZZ) == \ [((2, 0), 1), ((1, 1), 2), ((1, 0), 4), ((0, 2), 3), ((0, 1), 5)] f = [[2, 0, 0, 0], [1, 0, 0], []] assert dmp_list_terms(f, 1, ZZ, order='lex') == [((2, 3), 2), ((1, 2), 1)] assert dmp_list_terms( f, 1, ZZ, order='grlex') == [((2, 3), 2), ((1, 2), 1)] f = [[2, 0, 0, 0], [1, 0, 0, 0, 0, 0], []] assert dmp_list_terms(f, 1, ZZ, order='lex') == [((2, 3), 2), ((1, 5), 1)] assert dmp_list_terms( f, 1, ZZ, order='grlex') == [((1, 5), 1), ((2, 3), 2)] def test_dmp_apply_pairs(): h = lambda a, b: a*b assert dmp_apply_pairs([1, 2, 3], [4, 5, 6], h, [], 0, ZZ) == [4, 10, 18] assert dmp_apply_pairs([2, 3], [4, 5, 6], h, [], 0, ZZ) == [10, 18] assert dmp_apply_pairs([1, 2, 3], [5, 6], h, [], 0, ZZ) == [10, 18] assert dmp_apply_pairs( [[1, 2], [3]], [[4, 5], [6]], h, [], 1, ZZ) == [[4, 10], [18]] assert dmp_apply_pairs( [[1, 2], [3]], [[4], [5, 6]], h, [], 1, ZZ) == [[8], [18]] assert dmp_apply_pairs( [[1], [2, 3]], [[4, 5], [6]], h, [], 1, ZZ) == [[5], [18]] def test_dup_slice(): f = [1, 2, 3, 4] assert dup_slice(f, 0, 0, ZZ) == [] assert dup_slice(f, 0, 1, ZZ) == [4] assert dup_slice(f, 0, 2, ZZ) == [3, 4] assert dup_slice(f, 0, 3, ZZ) == [2, 3, 4] assert dup_slice(f, 0, 4, ZZ) == [1, 2, 3, 4] assert dup_slice(f, 0, 4, ZZ) == f assert dup_slice(f, 0, 9, ZZ) == f assert dup_slice(f, 1, 0, ZZ) == [] assert dup_slice(f, 1, 1, ZZ) == [] assert dup_slice(f, 1, 2, ZZ) == [3, 0] assert dup_slice(f, 1, 3, ZZ) == [2, 3, 0] assert dup_slice(f, 1, 4, ZZ) == [1, 2, 3, 0] assert dup_slice([1, 2], 0, 3, ZZ) == [1, 2] def test_dup_random(): f = dup_random(0, -10, 10, ZZ) assert dup_degree(f) == 0 assert all(-10 <= c <= 10 for c in f) f = dup_random(1, -20, 20, ZZ) assert dup_degree(f) == 1 assert all(-20 <= c <= 20 for c in f) f = dup_random(2, -30, 30, ZZ) assert dup_degree(f) == 2 assert all(-30 <= c <= 30 for c in f) f = dup_random(3, -40, 40, ZZ) assert dup_degree(f) == 3 assert all(-40 <= c <= 40 for c in f)