"""Tests for dense recursive polynomials' arithmetics. """ from sympy.polys.densebasic import ( dup_normal, dmp_normal, ) from sympy.polys.densearith import ( dup_add_term, dmp_add_term, dup_sub_term, dmp_sub_term, dup_mul_term, dmp_mul_term, dup_add_ground, dmp_add_ground, dup_sub_ground, dmp_sub_ground, dup_mul_ground, dmp_mul_ground, dup_quo_ground, dmp_quo_ground, dup_exquo_ground, dmp_exquo_ground, dup_lshift, dup_rshift, dup_abs, dmp_abs, dup_neg, dmp_neg, dup_add, dmp_add, dup_sub, dmp_sub, dup_mul, dmp_mul, dup_sqr, dmp_sqr, dup_pow, dmp_pow, dup_add_mul, dmp_add_mul, dup_sub_mul, dmp_sub_mul, dup_pdiv, dup_prem, dup_pquo, dup_pexquo, dmp_pdiv, dmp_prem, dmp_pquo, dmp_pexquo, dup_rr_div, dmp_rr_div, dup_ff_div, dmp_ff_div, dup_div, dup_rem, dup_quo, dup_exquo, dmp_div, dmp_rem, dmp_quo, dmp_exquo, dup_max_norm, dmp_max_norm, dup_l1_norm, dmp_l1_norm, dup_l2_norm_squared, dmp_l2_norm_squared, dup_expand, dmp_expand, ) from sympy.polys.polyerrors import ( ExactQuotientFailed, ) from sympy.polys.specialpolys import f_polys from sympy.polys.domains import FF, ZZ, QQ from sympy.testing.pytest import raises f_0, f_1, f_2, f_3, f_4, f_5, f_6 = [ f.to_dense() for f in f_polys() ] F_0 = dmp_mul_ground(dmp_normal(f_0, 2, QQ), QQ(1, 7), 2, QQ) def test_dup_add_term(): f = dup_normal([], ZZ) assert dup_add_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ) assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1], ZZ) assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 0], ZZ) assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 0, 0], ZZ) f = dup_normal([1, 1, 1], ZZ) assert dup_add_term(f, ZZ(1), 0, ZZ) == dup_normal([1, 1, 2], ZZ) assert dup_add_term(f, ZZ(1), 1, ZZ) == dup_normal([1, 2, 1], ZZ) assert dup_add_term(f, ZZ(1), 2, ZZ) == dup_normal([2, 1, 1], ZZ) assert dup_add_term(f, ZZ(1), 3, ZZ) == dup_normal([1, 1, 1, 1], ZZ) assert dup_add_term(f, ZZ(1), 4, ZZ) == dup_normal([1, 0, 1, 1, 1], ZZ) assert dup_add_term(f, ZZ(1), 5, ZZ) == dup_normal([1, 0, 0, 1, 1, 1], ZZ) assert dup_add_term( f, ZZ(1), 6, ZZ) == dup_normal([1, 0, 0, 0, 1, 1, 1], ZZ) assert dup_add_term(f, ZZ(-1), 2, ZZ) == dup_normal([1, 1], ZZ) def test_dmp_add_term(): assert dmp_add_term([ZZ(1), ZZ(1), ZZ(1)], ZZ(1), 2, 0, ZZ) == \ dup_add_term([ZZ(1), ZZ(1), ZZ(1)], ZZ(1), 2, ZZ) assert dmp_add_term(f_0, [[]], 3, 2, ZZ) == f_0 assert dmp_add_term(F_0, [[]], 3, 2, QQ) == F_0 def test_dup_sub_term(): f = dup_normal([], ZZ) assert dup_sub_term(f, ZZ(0), 0, ZZ) == dup_normal([], ZZ) assert dup_sub_term(f, ZZ(1), 0, ZZ) == dup_normal([-1], ZZ) assert dup_sub_term(f, ZZ(1), 1, ZZ) == dup_normal([-1, 0], ZZ) assert dup_sub_term(f, ZZ(1), 2, ZZ) == dup_normal([-1, 0, 0], ZZ) f = dup_normal([1, 1, 1], ZZ) assert dup_sub_term(f, ZZ(2), 0, ZZ) == dup_normal([ 1, 1, -1], ZZ) assert dup_sub_term(f, ZZ(2), 1, ZZ) == dup_normal([ 1, -1, 1], ZZ) assert dup_sub_term(f, ZZ(2), 2, ZZ) == dup_normal([-1, 1, 1], ZZ) assert dup_sub_term(f, ZZ(1), 3, ZZ) == dup_normal([-1, 1, 1, 1], ZZ) assert dup_sub_term(f, ZZ(1), 4, ZZ) == dup_normal([-1, 0, 1, 1, 1], ZZ) assert dup_sub_term(f, ZZ(1), 5, ZZ) == dup_normal([-1, 0, 0, 1, 1, 1], ZZ) assert dup_sub_term( f, ZZ(1), 6, ZZ) == dup_normal([-1, 0, 0, 0, 1, 1, 1], ZZ) assert dup_sub_term(f, ZZ(1), 2, ZZ) == dup_normal([1, 1], ZZ) def test_dmp_sub_term(): assert dmp_sub_term([ZZ(1), ZZ(1), ZZ(1)], ZZ(1), 2, 0, ZZ) == \ dup_sub_term([ZZ(1), ZZ(1), ZZ(1)], ZZ(1), 2, ZZ) assert dmp_sub_term(f_0, [[]], 3, 2, ZZ) == f_0 assert dmp_sub_term(F_0, [[]], 3, 2, QQ) == F_0 def test_dup_mul_term(): f = dup_normal([], ZZ) assert dup_mul_term(f, ZZ(2), 3, ZZ) == dup_normal([], ZZ) f = dup_normal([1, 1], ZZ) assert dup_mul_term(f, ZZ(0), 3, ZZ) == dup_normal([], ZZ) f = dup_normal([1, 2, 3], ZZ) assert dup_mul_term(f, ZZ(2), 0, ZZ) == dup_normal([2, 4, 6], ZZ) assert dup_mul_term(f, ZZ(2), 1, ZZ) == dup_normal([2, 4, 6, 0], ZZ) assert dup_mul_term(f, ZZ(2), 2, ZZ) == dup_normal([2, 4, 6, 0, 0], ZZ) assert dup_mul_term(f, ZZ(2), 3, ZZ) == dup_normal([2, 4, 6, 0, 0, 0], ZZ) def test_dmp_mul_term(): assert dmp_mul_term([ZZ(1), ZZ(2), ZZ(3)], ZZ(2), 1, 0, ZZ) == \ dup_mul_term([ZZ(1), ZZ(2), ZZ(3)], ZZ(2), 1, ZZ) assert dmp_mul_term([[]], [ZZ(2)], 3, 1, ZZ) == [[]] assert dmp_mul_term([[ZZ(1)]], [], 3, 1, ZZ) == [[]] assert dmp_mul_term([[ZZ(1), ZZ(2)], [ZZ(3)]], [ZZ(2)], 2, 1, ZZ) == \ [[ZZ(2), ZZ(4)], [ZZ(6)], [], []] assert dmp_mul_term([[]], [QQ(2, 3)], 3, 1, QQ) == [[]] assert dmp_mul_term([[QQ(1, 2)]], [], 3, 1, QQ) == [[]] assert dmp_mul_term([[QQ(1, 5), QQ(2, 5)], [QQ(3, 5)]], [QQ(2, 3)], 2, 1, QQ) == \ [[QQ(2, 15), QQ(4, 15)], [QQ(6, 15)], [], []] def test_dup_add_ground(): f = ZZ.map([1, 2, 3, 4]) g = ZZ.map([1, 2, 3, 8]) assert dup_add_ground(f, ZZ(4), ZZ) == g def test_dmp_add_ground(): f = ZZ.map([[1], [2], [3], [4]]) g = ZZ.map([[1], [2], [3], [8]]) assert dmp_add_ground(f, ZZ(4), 1, ZZ) == g def test_dup_sub_ground(): f = ZZ.map([1, 2, 3, 4]) g = ZZ.map([1, 2, 3, 0]) assert dup_sub_ground(f, ZZ(4), ZZ) == g def test_dmp_sub_ground(): f = ZZ.map([[1], [2], [3], [4]]) g = ZZ.map([[1], [2], [3], []]) assert dmp_sub_ground(f, ZZ(4), 1, ZZ) == g def test_dup_mul_ground(): f = dup_normal([], ZZ) assert dup_mul_ground(f, ZZ(2), ZZ) == dup_normal([], ZZ) f = dup_normal([1, 2, 3], ZZ) assert dup_mul_ground(f, ZZ(0), ZZ) == dup_normal([], ZZ) assert dup_mul_ground(f, ZZ(2), ZZ) == dup_normal([2, 4, 6], ZZ) def test_dmp_mul_ground(): assert dmp_mul_ground(f_0, ZZ(2), 2, ZZ) == [ [[ZZ(2), ZZ(4), ZZ(6)], [ZZ(4)]], [[ZZ(6)]], [[ZZ(8), ZZ(10), ZZ(12)], [ZZ(2), ZZ(4), ZZ(2)], [ZZ(2)]] ] assert dmp_mul_ground(F_0, QQ(1, 2), 2, QQ) == [ [[QQ(1, 14), QQ(2, 14), QQ(3, 14)], [QQ(2, 14)]], [[QQ(3, 14)]], [[QQ(4, 14), QQ(5, 14), QQ(6, 14)], [QQ(1, 14), QQ(2, 14), QQ(1, 14)], [QQ(1, 14)]] ] def test_dup_quo_ground(): raises(ZeroDivisionError, lambda: dup_quo_ground(dup_normal([1, 2, 3], ZZ), ZZ(0), ZZ)) f = dup_normal([], ZZ) assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([], ZZ) f = dup_normal([6, 2, 8], ZZ) assert dup_quo_ground(f, ZZ(1), ZZ) == f assert dup_quo_ground(f, ZZ(2), ZZ) == dup_normal([3, 1, 4], ZZ) assert dup_quo_ground(f, ZZ(3), ZZ) == dup_normal([2, 0, 2], ZZ) f = dup_normal([6, 2, 8], QQ) assert dup_quo_ground(f, QQ(1), QQ) == f assert dup_quo_ground(f, QQ(2), QQ) == [QQ(3), QQ(1), QQ(4)] assert dup_quo_ground(f, QQ(7), QQ) == [QQ(6, 7), QQ(2, 7), QQ(8, 7)] def test_dup_exquo_ground(): raises(ZeroDivisionError, lambda: dup_exquo_ground(dup_normal([1, 2, 3], ZZ), ZZ(0), ZZ)) raises(ExactQuotientFailed, lambda: dup_exquo_ground(dup_normal([1, 2, 3], ZZ), ZZ(3), ZZ)) f = dup_normal([], ZZ) assert dup_exquo_ground(f, ZZ(3), ZZ) == dup_normal([], ZZ) f = dup_normal([6, 2, 8], ZZ) assert dup_exquo_ground(f, ZZ(1), ZZ) == f assert dup_exquo_ground(f, ZZ(2), ZZ) == dup_normal([3, 1, 4], ZZ) f = dup_normal([6, 2, 8], QQ) assert dup_exquo_ground(f, QQ(1), QQ) == f assert dup_exquo_ground(f, QQ(2), QQ) == [QQ(3), QQ(1), QQ(4)] assert dup_exquo_ground(f, QQ(7), QQ) == [QQ(6, 7), QQ(2, 7), QQ(8, 7)] def test_dmp_quo_ground(): f = dmp_normal([[6], [2], [8]], 1, ZZ) assert dmp_quo_ground(f, ZZ(1), 1, ZZ) == f assert dmp_quo_ground( f, ZZ(2), 1, ZZ) == dmp_normal([[3], [1], [4]], 1, ZZ) assert dmp_normal(dmp_quo_ground( f, ZZ(3), 1, ZZ), 1, ZZ) == dmp_normal([[2], [], [2]], 1, ZZ) def test_dmp_exquo_ground(): f = dmp_normal([[6], [2], [8]], 1, ZZ) assert dmp_exquo_ground(f, ZZ(1), 1, ZZ) == f assert dmp_exquo_ground( f, ZZ(2), 1, ZZ) == dmp_normal([[3], [1], [4]], 1, ZZ) def test_dup_lshift(): assert dup_lshift([], 3, ZZ) == [] assert dup_lshift([1], 3, ZZ) == [1, 0, 0, 0] def test_dup_rshift(): assert dup_rshift([], 3, ZZ) == [] assert dup_rshift([1, 0, 0, 0], 3, ZZ) == [1] def test_dup_abs(): assert dup_abs([], ZZ) == [] assert dup_abs([ZZ( 1)], ZZ) == [ZZ(1)] assert dup_abs([ZZ(-7)], ZZ) == [ZZ(7)] assert dup_abs([ZZ(-1), ZZ(2), ZZ(3)], ZZ) == [ZZ(1), ZZ(2), ZZ(3)] assert dup_abs([], QQ) == [] assert dup_abs([QQ( 1, 2)], QQ) == [QQ(1, 2)] assert dup_abs([QQ(-7, 3)], QQ) == [QQ(7, 3)] assert dup_abs( [QQ(-1, 7), QQ(2, 7), QQ(3, 7)], QQ) == [QQ(1, 7), QQ(2, 7), QQ(3, 7)] def test_dmp_abs(): assert dmp_abs([ZZ(-1)], 0, ZZ) == [ZZ(1)] assert dmp_abs([QQ(-1, 2)], 0, QQ) == [QQ(1, 2)] assert dmp_abs([[[]]], 2, ZZ) == [[[]]] assert dmp_abs([[[ZZ(1)]]], 2, ZZ) == [[[ZZ(1)]]] assert dmp_abs([[[ZZ(-7)]]], 2, ZZ) == [[[ZZ(7)]]] assert dmp_abs([[[]]], 2, QQ) == [[[]]] assert dmp_abs([[[QQ(1, 2)]]], 2, QQ) == [[[QQ(1, 2)]]] assert dmp_abs([[[QQ(-7, 9)]]], 2, QQ) == [[[QQ(7, 9)]]] def test_dup_neg(): assert dup_neg([], ZZ) == [] assert dup_neg([ZZ(1)], ZZ) == [ZZ(-1)] assert dup_neg([ZZ(-7)], ZZ) == [ZZ(7)] assert dup_neg([ZZ(-1), ZZ(2), ZZ(3)], ZZ) == [ZZ(1), ZZ(-2), ZZ(-3)] assert dup_neg([], QQ) == [] assert dup_neg([QQ(1, 2)], QQ) == [QQ(-1, 2)] assert dup_neg([QQ(-7, 9)], QQ) == [QQ(7, 9)] assert dup_neg([QQ( -1, 7), QQ(2, 7), QQ(3, 7)], QQ) == [QQ(1, 7), QQ(-2, 7), QQ(-3, 7)] def test_dmp_neg(): assert dmp_neg([ZZ(-1)], 0, ZZ) == [ZZ(1)] assert dmp_neg([QQ(-1, 2)], 0, QQ) == [QQ(1, 2)] assert dmp_neg([[[]]], 2, ZZ) == [[[]]] assert dmp_neg([[[ZZ(1)]]], 2, ZZ) == [[[ZZ(-1)]]] assert dmp_neg([[[ZZ(-7)]]], 2, ZZ) == [[[ZZ(7)]]] assert dmp_neg([[[]]], 2, QQ) == [[[]]] assert dmp_neg([[[QQ(1, 9)]]], 2, QQ) == [[[QQ(-1, 9)]]] assert dmp_neg([[[QQ(-7, 9)]]], 2, QQ) == [[[QQ(7, 9)]]] def test_dup_add(): assert dup_add([], [], ZZ) == [] assert dup_add([ZZ(1)], [], ZZ) == [ZZ(1)] assert dup_add([], [ZZ(1)], ZZ) == [ZZ(1)] assert dup_add([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(2)] assert dup_add([ZZ(1)], [ZZ(2)], ZZ) == [ZZ(3)] assert dup_add([ZZ(1), ZZ(2)], [ZZ(1)], ZZ) == [ZZ(1), ZZ(3)] assert dup_add([ZZ(1)], [ZZ(1), ZZ(2)], ZZ) == [ZZ(1), ZZ(3)] assert dup_add([ZZ(1), ZZ( 2), ZZ(3)], [ZZ(8), ZZ(9), ZZ(10)], ZZ) == [ZZ(9), ZZ(11), ZZ(13)] assert dup_add([], [], QQ) == [] assert dup_add([QQ(1, 2)], [], QQ) == [QQ(1, 2)] assert dup_add([], [QQ(1, 2)], QQ) == [QQ(1, 2)] assert dup_add([QQ(1, 4)], [QQ(1, 4)], QQ) == [QQ(1, 2)] assert dup_add([QQ(1, 4)], [QQ(1, 2)], QQ) == [QQ(3, 4)] assert dup_add([QQ(1, 2), QQ(2, 3)], [QQ(1)], QQ) == [QQ(1, 2), QQ(5, 3)] assert dup_add([QQ(1)], [QQ(1, 2), QQ(2, 3)], QQ) == [QQ(1, 2), QQ(5, 3)] assert dup_add([QQ(1, 7), QQ(2, 7), QQ(3, 7)], [QQ( 8, 7), QQ(9, 7), QQ(10, 7)], QQ) == [QQ(9, 7), QQ(11, 7), QQ(13, 7)] def test_dmp_add(): assert dmp_add([ZZ(1), ZZ(2)], [ZZ(1)], 0, ZZ) == \ dup_add([ZZ(1), ZZ(2)], [ZZ(1)], ZZ) assert dmp_add([QQ(1, 2), QQ(2, 3)], [QQ(1)], 0, QQ) == \ dup_add([QQ(1, 2), QQ(2, 3)], [QQ(1)], QQ) assert dmp_add([[[]]], [[[]]], 2, ZZ) == [[[]]] assert dmp_add([[[ZZ(1)]]], [[[]]], 2, ZZ) == [[[ZZ(1)]]] assert dmp_add([[[]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(1)]]] assert dmp_add([[[ZZ(2)]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(3)]]] assert dmp_add([[[ZZ(1)]]], [[[ZZ(2)]]], 2, ZZ) == [[[ZZ(3)]]] assert dmp_add([[[]]], [[[]]], 2, QQ) == [[[]]] assert dmp_add([[[QQ(1, 2)]]], [[[]]], 2, QQ) == [[[QQ(1, 2)]]] assert dmp_add([[[]]], [[[QQ(1, 2)]]], 2, QQ) == [[[QQ(1, 2)]]] assert dmp_add([[[QQ(2, 7)]]], [[[QQ(1, 7)]]], 2, QQ) == [[[QQ(3, 7)]]] assert dmp_add([[[QQ(1, 7)]]], [[[QQ(2, 7)]]], 2, QQ) == [[[QQ(3, 7)]]] def test_dup_sub(): assert dup_sub([], [], ZZ) == [] assert dup_sub([ZZ(1)], [], ZZ) == [ZZ(1)] assert dup_sub([], [ZZ(1)], ZZ) == [ZZ(-1)] assert dup_sub([ZZ(1)], [ZZ(1)], ZZ) == [] assert dup_sub([ZZ(1)], [ZZ(2)], ZZ) == [ZZ(-1)] assert dup_sub([ZZ(1), ZZ(2)], [ZZ(1)], ZZ) == [ZZ(1), ZZ(1)] assert dup_sub([ZZ(1)], [ZZ(1), ZZ(2)], ZZ) == [ZZ(-1), ZZ(-1)] assert dup_sub([ZZ(3), ZZ( 2), ZZ(1)], [ZZ(8), ZZ(9), ZZ(10)], ZZ) == [ZZ(-5), ZZ(-7), ZZ(-9)] assert dup_sub([], [], QQ) == [] assert dup_sub([QQ(1, 2)], [], QQ) == [QQ(1, 2)] assert dup_sub([], [QQ(1, 2)], QQ) == [QQ(-1, 2)] assert dup_sub([QQ(1, 3)], [QQ(1, 3)], QQ) == [] assert dup_sub([QQ(1, 3)], [QQ(2, 3)], QQ) == [QQ(-1, 3)] assert dup_sub([QQ(1, 7), QQ(2, 7)], [QQ(1)], QQ) == [QQ(1, 7), QQ(-5, 7)] assert dup_sub([QQ(1)], [QQ(1, 7), QQ(2, 7)], QQ) == [QQ(-1, 7), QQ(5, 7)] assert dup_sub([QQ(3, 7), QQ(2, 7), QQ(1, 7)], [QQ( 8, 7), QQ(9, 7), QQ(10, 7)], QQ) == [QQ(-5, 7), QQ(-7, 7), QQ(-9, 7)] def test_dmp_sub(): assert dmp_sub([ZZ(1), ZZ(2)], [ZZ(1)], 0, ZZ) == \ dup_sub([ZZ(1), ZZ(2)], [ZZ(1)], ZZ) assert dmp_sub([QQ(1, 2), QQ(2, 3)], [QQ(1)], 0, QQ) == \ dup_sub([QQ(1, 2), QQ(2, 3)], [QQ(1)], QQ) assert dmp_sub([[[]]], [[[]]], 2, ZZ) == [[[]]] assert dmp_sub([[[ZZ(1)]]], [[[]]], 2, ZZ) == [[[ZZ(1)]]] assert dmp_sub([[[]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(-1)]]] assert dmp_sub([[[ZZ(2)]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(1)]]] assert dmp_sub([[[ZZ(1)]]], [[[ZZ(2)]]], 2, ZZ) == [[[ZZ(-1)]]] assert dmp_sub([[[]]], [[[]]], 2, QQ) == [[[]]] assert dmp_sub([[[QQ(1, 2)]]], [[[]]], 2, QQ) == [[[QQ(1, 2)]]] assert dmp_sub([[[]]], [[[QQ(1, 2)]]], 2, QQ) == [[[QQ(-1, 2)]]] assert dmp_sub([[[QQ(2, 7)]]], [[[QQ(1, 7)]]], 2, QQ) == [[[QQ(1, 7)]]] assert dmp_sub([[[QQ(1, 7)]]], [[[QQ(2, 7)]]], 2, QQ) == [[[QQ(-1, 7)]]] def test_dup_add_mul(): assert dup_add_mul([ZZ(1), ZZ(2), ZZ(3)], [ZZ(3), ZZ(2), ZZ(1)], [ZZ(1), ZZ(2)], ZZ) == [ZZ(3), ZZ(9), ZZ(7), ZZ(5)] assert dmp_add_mul([[ZZ(1), ZZ(2)], [ZZ(3)]], [[ZZ(3)], [ZZ(2), ZZ(1)]], [[ZZ(1)], [ZZ(2)]], 1, ZZ) == [[ZZ(3)], [ZZ(3), ZZ(9)], [ZZ(4), ZZ(5)]] def test_dup_sub_mul(): assert dup_sub_mul([ZZ(1), ZZ(2), ZZ(3)], [ZZ(3), ZZ(2), ZZ(1)], [ZZ(1), ZZ(2)], ZZ) == [ZZ(-3), ZZ(-7), ZZ(-3), ZZ(1)] assert dmp_sub_mul([[ZZ(1), ZZ(2)], [ZZ(3)]], [[ZZ(3)], [ZZ(2), ZZ(1)]], [[ZZ(1)], [ZZ(2)]], 1, ZZ) == [[ZZ(-3)], [ZZ(-1), ZZ(-5)], [ZZ(-4), ZZ(1)]] def test_dup_mul(): assert dup_mul([], [], ZZ) == [] assert dup_mul([], [ZZ(1)], ZZ) == [] assert dup_mul([ZZ(1)], [], ZZ) == [] assert dup_mul([ZZ(1)], [ZZ(1)], ZZ) == [ZZ(1)] assert dup_mul([ZZ(5)], [ZZ(7)], ZZ) == [ZZ(35)] assert dup_mul([], [], QQ) == [] assert dup_mul([], [QQ(1, 2)], QQ) == [] assert dup_mul([QQ(1, 2)], [], QQ) == [] assert dup_mul([QQ(1, 2)], [QQ(4, 7)], QQ) == [QQ(2, 7)] assert dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) == [QQ(15, 49)] f = dup_normal([3, 0, 0, 6, 1, 2], ZZ) g = dup_normal([4, 0, 1, 0], ZZ) h = dup_normal([12, 0, 3, 24, 4, 14, 1, 2, 0], ZZ) assert dup_mul(f, g, ZZ) == h assert dup_mul(g, f, ZZ) == h f = dup_normal([2, 0, 0, 1, 7], ZZ) h = dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ) assert dup_mul(f, f, ZZ) == h K = FF(6) assert dup_mul([K(2), K(1)], [K(3), K(4)], K) == [K(5), K(4)] p1 = dup_normal([79, -1, 78, -94, -10, 11, 32, -19, 78, 2, -89, 30, 73, 42, 85, 77, 83, -30, -34, -2, 95, -81, 37, -49, -46, -58, -16, 37, 35, -11, -57, -15, -31, 67, -20, 27, 76, 2, 70, 67, -65, 65, -26, -93, -44, -12, -92, 57, -90, -57, -11, -67, -98, -69, 97, -41, 89, 33, 89, -50, 81, -31, 60, -27, 43, 29, -77, 44, 21, -91, 32, -57, 33, 3, 53, -51, -38, -99, -84, 23, -50, 66, -100, 1, -75, -25, 27, -60, 98, -51, -87, 6, 8, 78, -28, -95, -88, 12, -35, 26, -9, 16, -92, 55, -7, -86, 68, -39, -46, 84, 94, 45, 60, 92, 68, -75, -74, -19, 8, 75, 78, 91, 57, 34, 14, -3, -49, 65, 78, -18, 6, -29, -80, -98, 17, 13, 58, 21, 20, 9, 37, 7, -30, -53, -20, 34, 67, -42, 89, -22, 73, 43, -6, 5, 51, -8, -15, -52, -22, -58, -72, -3, 43, -92, 82, 83, -2, -13, -23, -60, 16, -94, -8, -28, -95, -72, 63, -90, 76, 6, -43, -100, -59, 76, 3, 3, 46, -85, 75, 62, -71, -76, 88, 97, -72, -1, 30, -64, 72, -48, 14, -78, 58, 63, -91, 24, -87, -27, -80, -100, -44, 98, 70, 100, -29, -38, 11, 77, 100, 52, 86, 65, -5, -42, -81, -38, -42, 43, -2, -70, -63, -52], ZZ) p2 = dup_normal([65, -19, -47, 1, 90, 81, -15, -34, 25, -75, 9, -83, 50, -5, -44, 31, 1, 70, -7, 78, 74, 80, 85, 65, 21, 41, 66, 19, -40, 63, -21, -27, 32, 69, 83, 34, -35, 14, 81, 57, -75, 32, -67, -89, -100, -61, 46, 84, -78, -29, -50, -94, -24, -32, -68, -16, 100, -7, -72, -89, 35, 82, 58, 81, -92, 62, 5, -47, -39, -58, -72, -13, 84, 44, 55, -25, 48, -54, -31, -56, -11, -50, -84, 10, 67, 17, 13, -14, 61, 76, -64, -44, -40, -96, 11, -11, -94, 2, 6, 27, -6, 68, -54, 66, -74, -14, -1, -24, -73, 96, 89, -11, -89, 56, -53, 72, -43, 96, 25, 63, -31, 29, 68, 83, 91, -93, -19, -38, -40, 40, -12, -19, -79, 44, 100, -66, -29, -77, 62, 39, -8, 11, -97, 14, 87, 64, 21, -18, 13, 15, -59, -75, -99, -88, 57, 54, 56, -67, 6, -63, -59, -14, 28, 87, -20, -39, 84, -91, -2, 49, -75, 11, -24, -95, 36, 66, 5, 25, -72, -40, 86, 90, 37, -33, 57, -35, 29, -18, 4, -79, 64, -17, -27, 21, 29, -5, -44, -87, -24, 52, 78, 11, -23, -53, 36, 42, 21, -68, 94, -91, -51, -21, 51, -76, 72, 31, 24, -48, -80, -9, 37, -47, -6, -8, -63, -91, 79, -79, -100, 38, -20, 38, 100, 83, -90, 87, 63, -36, 82, -19, 18, -98, -38, 26, 98, -70, 79, 92, 12, 12, 70, 74, 36, 48, -13, 31, 31, -47, -71, -12, -64, 36, -42, 32, -86, 60, 83, 70, 55, 0, 1, 29, -35, 8, -82, 8, -73, -46, -50, 43, 48, -5, -86, -72, 44, -90, 19, 19, 5, -20, 97, -13, -66, -5, 5, -69, 64, -30, 41, 51, 36, 13, -99, -61, 94, -12, 74, 98, 68, 24, 46, -97, -87, -6, -27, 82, 62, -11, -77, 86, 66, -47, -49, -50, 13, 18, 89, -89, 46, -80, 13, 98, -35, -36, -25, 12, 20, 26, -52, 79, 27, 79, 100, 8, 62, -58, -28, 37], ZZ) res = dup_normal([5135, -1566, 1376, -7466, 4579, 11710, 8001, -7183, -3737, -7439, 345, -10084, 24522, -1201, 1070, -10245, 9582, 9264, 1903, 23312, 18953, 10037, -15268, -5450, 6442, -6243, -3777, 5110, 10936, -16649, -6022, 16255, 31300, 24818, 31922, 32760, 7854, 27080, 15766, 29596, 7139, 31945, -19810, 465, -38026, -3971, 9641, 465, -19375, 5524, -30112, -11960, -12813, 13535, 30670, 5925, -43725, -14089, 11503, -22782, 6371, 43881, 37465, -33529, -33590, -39798, -37854, -18466, -7908, -35825, -26020, -36923, -11332, -5699, 25166, -3147, 19885, 12962, -20659, -1642, 27723, -56331, -24580, -11010, -20206, 20087, -23772, -16038, 38580, 20901, -50731, 32037, -4299, 26508, 18038, -28357, 31846, -7405, -20172, -15894, 2096, 25110, -45786, 45918, -55333, -31928, -49428, -29824, -58796, -24609, -15408, 69, -35415, -18439, 10123, -20360, -65949, 33356, -20333, 26476, -32073, 33621, 930, 28803, -42791, 44716, 38164, 12302, -1739, 11421, 73385, -7613, 14297, 38155, -414, 77587, 24338, -21415, 29367, 42639, 13901, -288, 51027, -11827, 91260, 43407, 88521, -15186, 70572, -12049, 5090, -12208, -56374, 15520, -623, -7742, 50825, 11199, -14894, 40892, 59591, -31356, -28696, -57842, -87751, -33744, -28436, -28945, -40287, 37957, -35638, 33401, -61534, 14870, 40292, 70366, -10803, 102290, -71719, -85251, 7902, -22409, 75009, 99927, 35298, -1175, -762, -34744, -10587, -47574, -62629, -19581, -43659, -54369, -32250, -39545, 15225, -24454, 11241, -67308, -30148, 39929, 37639, 14383, -73475, -77636, -81048, -35992, 41601, -90143, 76937, -8112, 56588, 9124, -40094, -32340, 13253, 10898, -51639, 36390, 12086, -1885, 100714, -28561, -23784, -18735, 18916, 16286, 10742, -87360, -13697, 10689, -19477, -29770, 5060, 20189, -8297, 112407, 47071, 47743, 45519, -4109, 17468, -68831, 78325, -6481, -21641, -19459, 30919, 96115, 8607, 53341, 32105, -16211, 23538, 57259, -76272, -40583, 62093, 38511, -34255, -40665, -40604, -37606, -15274, 33156, -13885, 103636, 118678, -14101, -92682, -100791, 2634, 63791, 98266, 19286, -34590, -21067, -71130, 25380, -40839, -27614, -26060, 52358, -15537, 27138, -6749, 36269, -33306, 13207, -91084, -5540, -57116, 69548, 44169, -57742, -41234, -103327, -62904, -8566, 41149, -12866, 71188, 23980, 1838, 58230, 73950, 5594, 43113, -8159, -15925, 6911, 85598, -75016, -16214, -62726, -39016, 8618, -63882, -4299, 23182, 49959, 49342, -3238, -24913, -37138, 78361, 32451, 6337, -11438, -36241, -37737, 8169, -3077, -24829, 57953, 53016, -31511, -91168, 12599, -41849, 41576, 55275, -62539, 47814, -62319, 12300, -32076, -55137, -84881, -27546, 4312, -3433, -54382, 113288, -30157, 74469, 18219, 79880, -2124, 98911, 17655, -33499, -32861, 47242, -37393, 99765, 14831, -44483, 10800, -31617, -52710, 37406, 22105, 29704, -20050, 13778, 43683, 36628, 8494, 60964, -22644, 31550, -17693, 33805, -124879, -12302, 19343, 20400, -30937, -21574, -34037, -33380, 56539, -24993, -75513, -1527, 53563, 65407, -101, 53577, 37991, 18717, -23795, -8090, -47987, -94717, 41967, 5170, -14815, -94311, 17896, -17734, -57718, -774, -38410, 24830, 29682, 76480, 58802, -46416, -20348, -61353, -68225, -68306, 23822, -31598, 42972, 36327, 28968, -65638, -21638, 24354, -8356, 26777, 52982, -11783, -44051, -26467, -44721, -28435, -53265, -25574, -2669, 44155, 22946, -18454, -30718, -11252, 58420, 8711, 67447, 4425, 41749, 67543, 43162, 11793, -41907, 20477, -13080, 6559, -6104, -13244, 42853, 42935, 29793, 36730, -28087, 28657, 17946, 7503, 7204, 21491, -27450, -24241, -98156, -18082, -42613, -24928, 10775, -14842, -44127, 55910, 14777, 31151, -2194, 39206, -2100, -4211, 11827, -8918, -19471, 72567, 36447, -65590, -34861, -17147, -45303, 9025, -7333, -35473, 11101, 11638, 3441, 6626, -41800, 9416, 13679, 33508, 40502, -60542, 16358, 8392, -43242, -35864, -34127, -48721, 35878, 30598, 28630, 20279, -19983, -14638, -24455, -1851, -11344, 45150, 42051, 26034, -28889, -32382, -3527, -14532, 22564, -22346, 477, 11706, 28338, -25972, -9185, -22867, -12522, 32120, -4424, 11339, -33913, -7184, 5101, -23552, -17115, -31401, -6104, 21906, 25708, 8406, 6317, -7525, 5014, 20750, 20179, 22724, 11692, 13297, 2493, -253, -16841, -17339, -6753, -4808, 2976, -10881, -10228, -13816, -12686, 1385, 2316, 2190, -875, -1924], ZZ) assert dup_mul(p1, p2, ZZ) == res p1 = dup_normal([83, -61, -86, -24, 12, 43, -88, -9, 42, 55, -66, 74, 95, -25, -12, 68, -99, 4, 45, 6, -15, -19, 78, 65, -55, 47, -13, 17, 86, 81, -58, -27, 50, -40, -24, 39, -41, -92, 75, 90, -1, 40, -15, -27, -35, 68, 70, -64, -40, 78, -88, -58, -39, 69, 46, 12, 28, -94, -37, -50, -80, -96, -61, 25, 1, 71, 4, 12, 48, 4, 34, -47, -75, 5, 48, 82, 88, 23, 98, 35, 17, -10, 48, -61, -95, 47, 65, -19, -66, -57, -6, -51, -42, -89, 66, -13, 18, 37, 90, -23, 72, 96, -53, 0, 40, -73, -52, -68, 32, -25, -53, 79, -52, 18, 44, 73, -81, 31, -90, 70, 3, 36, 48, 76, -24, -44, 23, 98, -4, 73, 69, 88, -70, 14, -68, 94, -78, -15, -64, -97, -70, -35, 65, 88, 49, -53, -7, 12, -45, -7, 59, -94, 99, -2, 67, -60, -71, 29, -62, -77, 1, 51, 17, 80, -20, -47, -19, 24, -9, 39, -23, 21, -84, 10, 84, 56, -17, -21, -66, 85, 70, 46, -51, -22, -95, 78, -60, -96, -97, -45, 72, 35, 30, -61, -92, -93, -60, -61, 4, -4, -81, -73, 46, 53, -11, 26, 94, 45, 14, -78, 55, 84, -68, 98, 60, 23, 100, -63, 68, 96, -16, 3, 56, 21, -58, 62, -67, 66, 85, 41, -79, -22, 97, -67, 82, 82, -96, -20, -7, 48, -67, 48, -9, -39, 78], ZZ) p2 = dup_normal([52, 88, 76, 66, 9, -64, 46, -20, -28, 69, 60, 96, -36, -92, -30, -11, -35, 35, 55, 63, -92, -7, 25, -58, 74, 55, -6, 4, 47, -92, -65, 67, -45, 74, -76, 59, -6, 69, 39, 24, -71, -7, 39, -45, 60, -68, 98, 97, -79, 17, 4, 94, -64, 68, -100, -96, -2, 3, 22, 96, 54, -77, -86, 67, 6, 57, 37, 40, 89, -78, 64, -94, -45, -92, 57, 87, -26, 36, 19, 97, 25, 77, -87, 24, 43, -5, 35, 57, 83, 71, 35, 63, 61, 96, -22, 8, -1, 96, 43, 45, 94, -93, 36, 71, -41, -99, 85, -48, 59, 52, -17, 5, 87, -16, -68, -54, 76, -18, 100, 91, -42, -70, -66, -88, -12, 1, 95, -82, 52, 43, -29, 3, 12, 72, -99, -43, -32, -93, -51, 16, -20, -12, -11, 5, 33, -38, 93, -5, -74, 25, 74, -58, 93, 59, -63, -86, 63, -20, -4, -74, -73, -95, 29, -28, 93, -91, -2, -38, -62, 77, -58, -85, -28, 95, 38, 19, -69, 86, 94, 25, -2, -4, 47, 34, -59, 35, -48, 29, -63, -53, 34, 29, 66, 73, 6, 92, -84, 89, 15, 81, 93, 97, 51, -72, -78, 25, 60, 90, -45, 39, 67, -84, -62, 57, 26, -32, -56, -14, -83, 76, 5, -2, 99, -100, 28, 46, 94, -7, 53, -25, 16, -23, -36, 89, -78, -63, 31, 1, 84, -99, -52, 76, 48, 90, -76, 44, -19, 54, -36, -9, -73, -100, -69, 31, 42, 25, -39, 76, -26, -8, -14, 51, 3, 37, 45, 2, -54, 13, -34, -92, 17, -25, -65, 53, -63, 30, 4, -70, -67, 90, 52, 51, 18, -3, 31, -45, -9, 59, 63, -87, 22, -32, 29, -38, 21, 36, -82, 27, -11], ZZ) res = dup_normal([4316, 4132, -3532, -7974, -11303, -10069, 5484, -3330, -5874, 7734, 4673, 11327, -9884, -8031, 17343, 21035, -10570, -9285, 15893, 3780, -14083, 8819, 17592, 10159, 7174, -11587, 8598, -16479, 3602, 25596, 9781, 12163, 150, 18749, -21782, -12307, 27578, -2757, -12573, 12565, 6345, -18956, 19503, -15617, 1443, -16778, 36851, 23588, -28474, 5749, 40695, -7521, -53669, -2497, -18530, 6770, 57038, 3926, -6927, -15399, 1848, -64649, -27728, 3644, 49608, 15187, -8902, -9480, -7398, -40425, 4824, 23767, -7594, -6905, 33089, 18786, 12192, 24670, 31114, 35334, -4501, -14676, 7107, -59018, -21352, 20777, 19661, 20653, 33754, -885, -43758, 6269, 51897, -28719, -97488, -9527, 13746, 11644, 17644, -21720, 23782, -10481, 47867, 20752, 33810, -1875, 39918, -7710, -40840, 19808, -47075, 23066, 46616, 25201, 9287, 35436, -1602, 9645, -11978, 13273, 15544, 33465, 20063, 44539, 11687, 27314, -6538, -37467, 14031, 32970, -27086, 41323, 29551, 65910, -39027, -37800, -22232, 8212, 46316, -28981, -55282, 50417, -44929, -44062, 73879, 37573, -2596, -10877, -21893, -133218, -33707, -25753, -9531, 17530, 61126, 2748, -56235, 43874, -10872, -90459, -30387, 115267, -7264, -44452, 122626, 14839, -599, 10337, 57166, -67467, -54957, 63669, 1202, 18488, 52594, 7205, -97822, 612, 78069, -5403, -63562, 47236, 36873, -154827, -26188, 82427, -39521, 5628, 7416, 5276, -53095, 47050, 26121, -42207, 79021, -13035, 2499, -66943, 29040, -72355, -23480, 23416, -12885, -44225, -42688, -4224, 19858, 55299, 15735, 11465, 101876, -39169, 51786, 14723, 43280, -68697, 16410, 92295, 56767, 7183, 111850, 4550, 115451, -38443, -19642, -35058, 10230, 93829, 8925, 63047, 3146, 29250, 8530, 5255, -98117, -115517, -76817, -8724, 41044, 1312, -35974, 79333, -28567, 7547, -10580, -24559, -16238, 10794, -3867, 24848, 57770, -51536, -35040, 71033, 29853, 62029, -7125, -125585, -32169, -47907, 156811, -65176, -58006, -15757, -57861, 11963, 30225, -41901, -41681, 31310, 27982, 18613, 61760, 60746, -59096, 33499, 30097, -17997, 24032, 56442, -83042, 23747, -20931, -21978, -158752, -9883, -73598, -7987, -7333, -125403, -116329, 30585, 53281, 51018, -29193, 88575, 8264, -40147, -16289, 113088, 12810, -6508, 101552, -13037, 34440, -41840, 101643, 24263, 80532, 61748, 65574, 6423, -20672, 6591, -10834, -71716, 86919, -92626, 39161, 28490, 81319, 46676, 106720, 43530, 26998, 57456, -8862, 60989, 13982, 3119, -2224, 14743, 55415, -49093, -29303, 28999, 1789, 55953, -84043, -7780, -65013, 57129, -47251, 61484, 61994, -78361, -82778, 22487, -26894, 9756, -74637, -15519, -4360, 30115, 42433, 35475, 15286, 69768, 21509, -20214, 78675, -21163, 13596, 11443, -10698, -53621, -53867, -24155, 64500, -42784, -33077, -16500, 873, -52788, 14546, -38011, 36974, -39849, -34029, -94311, 83068, -50437, -26169, -46746, 59185, 42259, -101379, -12943, 30089, -59086, 36271, 22723, -30253, -52472, -70826, -23289, 3331, -31687, 14183, -857, -28627, 35246, -51284, 5636, -6933, 66539, 36654, 50927, 24783, 3457, 33276, 45281, 45650, -4938, -9968, -22590, 47995, 69229, 5214, -58365, -17907, -14651, 18668, 18009, 12649, -11851, -13387, 20339, 52472, -1087, -21458, -68647, 52295, 15849, 40608, 15323, 25164, -29368, 10352, -7055, 7159, 21695, -5373, -54849, 101103, -24963, -10511, 33227, 7659, 41042, -69588, 26718, -20515, 6441, 38135, -63, 24088, -35364, -12785, -18709, 47843, 48533, -48575, 17251, -19394, 32878, -9010, -9050, 504, -12407, 28076, -3429, 25324, -4210, -26119, 752, -29203, 28251, -11324, -32140, -3366, -25135, 18702, -31588, -7047, -24267, 49987, -14975, -33169, 37744, -7720, -9035, 16964, -2807, -421, 14114, -17097, -13662, 40628, -12139, -9427, 5369, 17551, -13232, -16211, 9804, -7422, 2677, 28635, -8280, -4906, 2908, -22558, 5604, 12459, 8756, -3980, -4745, -18525, 7913, 5970, -16457, 20230, -6247, -13812, 2505, 11899, 1409, -15094, 22540, -18863, 137, 11123, -4516, 2290, -8594, 12150, -10380, 3005, 5235, -7350, 2535, -858], ZZ) assert dup_mul(p1, p2, ZZ) == res def test_dmp_mul(): assert dmp_mul([ZZ(5)], [ZZ(7)], 0, ZZ) == \ dup_mul([ZZ(5)], [ZZ(7)], ZZ) assert dmp_mul([QQ(5, 7)], [QQ(3, 7)], 0, QQ) == \ dup_mul([QQ(5, 7)], [QQ(3, 7)], QQ) assert dmp_mul([[[]]], [[[]]], 2, ZZ) == [[[]]] assert dmp_mul([[[ZZ(1)]]], [[[]]], 2, ZZ) == [[[]]] assert dmp_mul([[[]]], [[[ZZ(1)]]], 2, ZZ) == [[[]]] assert dmp_mul([[[ZZ(2)]]], [[[ZZ(1)]]], 2, ZZ) == [[[ZZ(2)]]] assert dmp_mul([[[ZZ(1)]]], [[[ZZ(2)]]], 2, ZZ) == [[[ZZ(2)]]] assert dmp_mul([[[]]], [[[]]], 2, QQ) == [[[]]] assert dmp_mul([[[QQ(1, 2)]]], [[[]]], 2, QQ) == [[[]]] assert dmp_mul([[[]]], [[[QQ(1, 2)]]], 2, QQ) == [[[]]] assert dmp_mul([[[QQ(2, 7)]]], [[[QQ(1, 3)]]], 2, QQ) == [[[QQ(2, 21)]]] assert dmp_mul([[[QQ(1, 7)]]], [[[QQ(2, 3)]]], 2, QQ) == [[[QQ(2, 21)]]] K = FF(6) assert dmp_mul( [[K(2)], [K(1)]], [[K(3)], [K(4)]], 1, K) == [[K(5)], [K(4)]] def test_dup_sqr(): assert dup_sqr([], ZZ) == [] assert dup_sqr([ZZ(2)], ZZ) == [ZZ(4)] assert dup_sqr([ZZ(1), ZZ(2)], ZZ) == [ZZ(1), ZZ(4), ZZ(4)] assert dup_sqr([], QQ) == [] assert dup_sqr([QQ(2, 3)], QQ) == [QQ(4, 9)] assert dup_sqr([QQ(1, 3), QQ(2, 3)], QQ) == [QQ(1, 9), QQ(4, 9), QQ(4, 9)] f = dup_normal([2, 0, 0, 1, 7], ZZ) assert dup_sqr(f, ZZ) == dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ) K = FF(9) assert dup_sqr([K(3), K(4)], K) == [K(6), K(7)] def test_dmp_sqr(): assert dmp_sqr([ZZ(1), ZZ(2)], 0, ZZ) == \ dup_sqr([ZZ(1), ZZ(2)], ZZ) assert dmp_sqr([[[]]], 2, ZZ) == [[[]]] assert dmp_sqr([[[ZZ(2)]]], 2, ZZ) == [[[ZZ(4)]]] assert dmp_sqr([[[]]], 2, QQ) == [[[]]] assert dmp_sqr([[[QQ(2, 3)]]], 2, QQ) == [[[QQ(4, 9)]]] K = FF(9) assert dmp_sqr([[K(3)], [K(4)]], 1, K) == [[K(6)], [K(7)]] def test_dup_pow(): assert dup_pow([], 0, ZZ) == [ZZ(1)] assert dup_pow([], 0, QQ) == [QQ(1)] assert dup_pow([], 1, ZZ) == [] assert dup_pow([], 7, ZZ) == [] assert dup_pow([ZZ(1)], 0, ZZ) == [ZZ(1)] assert dup_pow([ZZ(1)], 1, ZZ) == [ZZ(1)] assert dup_pow([ZZ(1)], 7, ZZ) == [ZZ(1)] assert dup_pow([ZZ(3)], 0, ZZ) == [ZZ(1)] assert dup_pow([ZZ(3)], 1, ZZ) == [ZZ(3)] assert dup_pow([ZZ(3)], 7, ZZ) == [ZZ(2187)] assert dup_pow([QQ(1, 1)], 0, QQ) == [QQ(1, 1)] assert dup_pow([QQ(1, 1)], 1, QQ) == [QQ(1, 1)] assert dup_pow([QQ(1, 1)], 7, QQ) == [QQ(1, 1)] assert dup_pow([QQ(3, 7)], 0, QQ) == [QQ(1, 1)] assert dup_pow([QQ(3, 7)], 1, QQ) == [QQ(3, 7)] assert dup_pow([QQ(3, 7)], 7, QQ) == [QQ(2187, 823543)] f = dup_normal([2, 0, 0, 1, 7], ZZ) assert dup_pow(f, 0, ZZ) == dup_normal([1], ZZ) assert dup_pow(f, 1, ZZ) == dup_normal([2, 0, 0, 1, 7], ZZ) assert dup_pow(f, 2, ZZ) == dup_normal([4, 0, 0, 4, 28, 0, 1, 14, 49], ZZ) assert dup_pow(f, 3, ZZ) == dup_normal( [8, 0, 0, 12, 84, 0, 6, 84, 294, 1, 21, 147, 343], ZZ) def test_dmp_pow(): assert dmp_pow([[]], 0, 1, ZZ) == [[ZZ(1)]] assert dmp_pow([[]], 0, 1, QQ) == [[QQ(1)]] assert dmp_pow([[]], 1, 1, ZZ) == [[]] assert dmp_pow([[]], 7, 1, ZZ) == [[]] assert dmp_pow([[ZZ(1)]], 0, 1, ZZ) == [[ZZ(1)]] assert dmp_pow([[ZZ(1)]], 1, 1, ZZ) == [[ZZ(1)]] assert dmp_pow([[ZZ(1)]], 7, 1, ZZ) == [[ZZ(1)]] assert dmp_pow([[QQ(3, 7)]], 0, 1, QQ) == [[QQ(1, 1)]] assert dmp_pow([[QQ(3, 7)]], 1, 1, QQ) == [[QQ(3, 7)]] assert dmp_pow([[QQ(3, 7)]], 7, 1, QQ) == [[QQ(2187, 823543)]] f = dup_normal([2, 0, 0, 1, 7], ZZ) assert dmp_pow(f, 2, 0, ZZ) == dup_pow(f, 2, ZZ) def test_dup_pdiv(): f = dup_normal([3, 1, 1, 5], ZZ) g = dup_normal([5, -3, 1], ZZ) q = dup_normal([15, 14], ZZ) r = dup_normal([52, 111], ZZ) assert dup_pdiv(f, g, ZZ) == (q, r) assert dup_pquo(f, g, ZZ) == q assert dup_prem(f, g, ZZ) == r raises(ExactQuotientFailed, lambda: dup_pexquo(f, g, ZZ)) f = dup_normal([3, 1, 1, 5], QQ) g = dup_normal([5, -3, 1], QQ) q = dup_normal([15, 14], QQ) r = dup_normal([52, 111], QQ) assert dup_pdiv(f, g, QQ) == (q, r) assert dup_pquo(f, g, QQ) == q assert dup_prem(f, g, QQ) == r raises(ExactQuotientFailed, lambda: dup_pexquo(f, g, QQ)) def test_dmp_pdiv(): f = dmp_normal([[1], [], [1, 0, 0]], 1, ZZ) g = dmp_normal([[1], [-1, 0]], 1, ZZ) q = dmp_normal([[1], [1, 0]], 1, ZZ) r = dmp_normal([[2, 0, 0]], 1, ZZ) assert dmp_pdiv(f, g, 1, ZZ) == (q, r) assert dmp_pquo(f, g, 1, ZZ) == q assert dmp_prem(f, g, 1, ZZ) == r raises(ExactQuotientFailed, lambda: dmp_pexquo(f, g, 1, ZZ)) f = dmp_normal([[1], [], [1, 0, 0]], 1, ZZ) g = dmp_normal([[2], [-2, 0]], 1, ZZ) q = dmp_normal([[2], [2, 0]], 1, ZZ) r = dmp_normal([[8, 0, 0]], 1, ZZ) assert dmp_pdiv(f, g, 1, ZZ) == (q, r) assert dmp_pquo(f, g, 1, ZZ) == q assert dmp_prem(f, g, 1, ZZ) == r raises(ExactQuotientFailed, lambda: dmp_pexquo(f, g, 1, ZZ)) def test_dup_rr_div(): raises(ZeroDivisionError, lambda: dup_rr_div([1, 2, 3], [], ZZ)) f = dup_normal([3, 1, 1, 5], ZZ) g = dup_normal([5, -3, 1], ZZ) q, r = [], f assert dup_rr_div(f, g, ZZ) == (q, r) def test_dmp_rr_div(): raises(ZeroDivisionError, lambda: dmp_rr_div([[1, 2], [3]], [[]], 1, ZZ)) f = dmp_normal([[1], [], [1, 0, 0]], 1, ZZ) g = dmp_normal([[1], [-1, 0]], 1, ZZ) q = dmp_normal([[1], [1, 0]], 1, ZZ) r = dmp_normal([[2, 0, 0]], 1, ZZ) assert dmp_rr_div(f, g, 1, ZZ) == (q, r) f = dmp_normal([[1], [], [1, 0, 0]], 1, ZZ) g = dmp_normal([[-1], [1, 0]], 1, ZZ) q = dmp_normal([[-1], [-1, 0]], 1, ZZ) r = dmp_normal([[2, 0, 0]], 1, ZZ) assert dmp_rr_div(f, g, 1, ZZ) == (q, r) f = dmp_normal([[1], [], [1, 0, 0]], 1, ZZ) g = dmp_normal([[2], [-2, 0]], 1, ZZ) q, r = [[]], f assert dmp_rr_div(f, g, 1, ZZ) == (q, r) def test_dup_ff_div(): raises(ZeroDivisionError, lambda: dup_ff_div([1, 2, 3], [], QQ)) f = dup_normal([3, 1, 1, 5], QQ) g = dup_normal([5, -3, 1], QQ) q = [QQ(3, 5), QQ(14, 25)] r = [QQ(52, 25), QQ(111, 25)] assert dup_ff_div(f, g, QQ) == (q, r) def test_dup_ff_div_gmpy2(): try: from gmpy2 import mpq except ImportError: return from sympy.polys.domains import GMPYRationalField K = GMPYRationalField() f = [mpq(1,3), mpq(3,2)] g = [mpq(2,1)] assert dmp_ff_div(f, g, 0, K) == ([mpq(1,6), mpq(3,4)], []) f = [mpq(1,2), mpq(1,3), mpq(1,4), mpq(1,5)] g = [mpq(-1,1), mpq(1,1), mpq(-1,1)] assert dmp_ff_div(f, g, 0, K) == ([mpq(-1,2), mpq(-5,6)], [mpq(7,12), mpq(-19,30)]) def test_dmp_ff_div(): raises(ZeroDivisionError, lambda: dmp_ff_div([[1, 2], [3]], [[]], 1, QQ)) f = dmp_normal([[1], [], [1, 0, 0]], 1, QQ) g = dmp_normal([[1], [-1, 0]], 1, QQ) q = [[QQ(1, 1)], [QQ(1, 1), QQ(0, 1)]] r = [[QQ(2, 1), QQ(0, 1), QQ(0, 1)]] assert dmp_ff_div(f, g, 1, QQ) == (q, r) f = dmp_normal([[1], [], [1, 0, 0]], 1, QQ) g = dmp_normal([[-1], [1, 0]], 1, QQ) q = [[QQ(-1, 1)], [QQ(-1, 1), QQ(0, 1)]] r = [[QQ(2, 1), QQ(0, 1), QQ(0, 1)]] assert dmp_ff_div(f, g, 1, QQ) == (q, r) f = dmp_normal([[1], [], [1, 0, 0]], 1, QQ) g = dmp_normal([[2], [-2, 0]], 1, QQ) q = [[QQ(1, 2)], [QQ(1, 2), QQ(0, 1)]] r = [[QQ(2, 1), QQ(0, 1), QQ(0, 1)]] assert dmp_ff_div(f, g, 1, QQ) == (q, r) def test_dup_div(): f, g, q, r = [5, 4, 3, 2, 1], [1, 2, 3], [5, -6, 0], [20, 1] assert dup_div(f, g, ZZ) == (q, r) assert dup_quo(f, g, ZZ) == q assert dup_rem(f, g, ZZ) == r raises(ExactQuotientFailed, lambda: dup_exquo(f, g, ZZ)) f, g, q, r = [5, 4, 3, 2, 1, 0], [1, 2, 0, 0, 9], [5, -6], [15, 2, -44, 54] assert dup_div(f, g, ZZ) == (q, r) assert dup_quo(f, g, ZZ) == q assert dup_rem(f, g, ZZ) == r raises(ExactQuotientFailed, lambda: dup_exquo(f, g, ZZ)) def test_dmp_div(): f, g, q, r = [5, 4, 3, 2, 1], [1, 2, 3], [5, -6, 0], [20, 1] assert dmp_div(f, g, 0, ZZ) == (q, r) assert dmp_quo(f, g, 0, ZZ) == q assert dmp_rem(f, g, 0, ZZ) == r raises(ExactQuotientFailed, lambda: dmp_exquo(f, g, 0, ZZ)) f, g, q, r = [[[1]]], [[[2]], [1]], [[[]]], [[[1]]] assert dmp_div(f, g, 2, ZZ) == (q, r) assert dmp_quo(f, g, 2, ZZ) == q assert dmp_rem(f, g, 2, ZZ) == r raises(ExactQuotientFailed, lambda: dmp_exquo(f, g, 2, ZZ)) def test_dup_max_norm(): assert dup_max_norm([], ZZ) == 0 assert dup_max_norm([1], ZZ) == 1 assert dup_max_norm([1, 4, 2, 3], ZZ) == 4 def test_dmp_max_norm(): assert dmp_max_norm([[[]]], 2, ZZ) == 0 assert dmp_max_norm([[[1]]], 2, ZZ) == 1 assert dmp_max_norm(f_0, 2, ZZ) == 6 def test_dup_l1_norm(): assert dup_l1_norm([], ZZ) == 0 assert dup_l1_norm([1], ZZ) == 1 assert dup_l1_norm([1, 4, 2, 3], ZZ) == 10 def test_dmp_l1_norm(): assert dmp_l1_norm([[[]]], 2, ZZ) == 0 assert dmp_l1_norm([[[1]]], 2, ZZ) == 1 assert dmp_l1_norm(f_0, 2, ZZ) == 31 def test_dup_l2_norm_squared(): assert dup_l2_norm_squared([], ZZ) == 0 assert dup_l2_norm_squared([1], ZZ) == 1 assert dup_l2_norm_squared([1, 4, 2, 3], ZZ) == 30 def test_dmp_l2_norm_squared(): assert dmp_l2_norm_squared([[[]]], 2, ZZ) == 0 assert dmp_l2_norm_squared([[[1]]], 2, ZZ) == 1 assert dmp_l2_norm_squared(f_0, 2, ZZ) == 111 def test_dup_expand(): assert dup_expand((), ZZ) == [1] assert dup_expand(([1, 2, 3], [1, 2], [7, 5, 4, 3]), ZZ) == \ dup_mul([1, 2, 3], dup_mul([1, 2], [7, 5, 4, 3], ZZ), ZZ) def test_dmp_expand(): assert dmp_expand((), 1, ZZ) == [[1]] assert dmp_expand(([[1], [2], [3]], [[1], [2]], [[7], [5], [4], [3]]), 1, ZZ) == \ dmp_mul([[1], [2], [3]], dmp_mul([[1], [2]], [[7], [5], [ 4], [3]], 1, ZZ), 1, ZZ)