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"""Tests for functions for generating interesting polynomials. """ |
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from sympy.core.add import Add |
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from sympy.core.symbol import symbols |
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from sympy.functions.elementary.miscellaneous import sqrt |
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from sympy.ntheory.generate import prime |
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from sympy.polys.domains.integerring import ZZ |
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from sympy.polys.polytools import Poly |
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from sympy.utilities.iterables import permute_signs |
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from sympy.testing.pytest import raises |
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from sympy.polys.specialpolys import ( |
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swinnerton_dyer_poly, |
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cyclotomic_poly, |
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symmetric_poly, |
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random_poly, |
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interpolating_poly, |
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fateman_poly_F_1, |
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dmp_fateman_poly_F_1, |
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fateman_poly_F_2, |
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dmp_fateman_poly_F_2, |
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fateman_poly_F_3, |
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dmp_fateman_poly_F_3, |
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) |
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from sympy.abc import x, y, z |
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def test_swinnerton_dyer_poly(): |
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raises(ValueError, lambda: swinnerton_dyer_poly(0, x)) |
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assert swinnerton_dyer_poly(1, x, polys=True) == Poly(x**2 - 2) |
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assert swinnerton_dyer_poly(1, x) == x**2 - 2 |
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assert swinnerton_dyer_poly(2, x) == x**4 - 10*x**2 + 1 |
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assert swinnerton_dyer_poly( |
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3, x) == x**8 - 40*x**6 + 352*x**4 - 960*x**2 + 576 |
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p = [sqrt(prime(i)) for i in range(1, 5)] |
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assert str([i.n(3) for i in |
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swinnerton_dyer_poly(4, polys=True).all_roots()] |
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) == str(sorted([Add(*i).n(3) for i in permute_signs(p)])) |
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def test_cyclotomic_poly(): |
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raises(ValueError, lambda: cyclotomic_poly(0, x)) |
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assert cyclotomic_poly(1, x, polys=True) == Poly(x - 1) |
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assert cyclotomic_poly(1, x) == x - 1 |
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assert cyclotomic_poly(2, x) == x + 1 |
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assert cyclotomic_poly(3, x) == x**2 + x + 1 |
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assert cyclotomic_poly(4, x) == x**2 + 1 |
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assert cyclotomic_poly(5, x) == x**4 + x**3 + x**2 + x + 1 |
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assert cyclotomic_poly(6, x) == x**2 - x + 1 |
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def test_symmetric_poly(): |
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raises(ValueError, lambda: symmetric_poly(-1, x, y, z)) |
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raises(ValueError, lambda: symmetric_poly(5, x, y, z)) |
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assert symmetric_poly(1, x, y, z, polys=True) == Poly(x + y + z) |
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assert symmetric_poly(1, (x, y, z), polys=True) == Poly(x + y + z) |
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assert symmetric_poly(0, x, y, z) == 1 |
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assert symmetric_poly(1, x, y, z) == x + y + z |
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assert symmetric_poly(2, x, y, z) == x*y + x*z + y*z |
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assert symmetric_poly(3, x, y, z) == x*y*z |
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def test_random_poly(): |
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poly = random_poly(x, 10, -100, 100, polys=False) |
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assert Poly(poly).degree() == 10 |
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assert all(-100 <= coeff <= 100 for coeff in Poly(poly).coeffs()) is True |
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poly = random_poly(x, 10, -100, 100, polys=True) |
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assert poly.degree() == 10 |
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assert all(-100 <= coeff <= 100 for coeff in poly.coeffs()) is True |
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def test_interpolating_poly(): |
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x0, x1, x2, x3, y0, y1, y2, y3 = symbols('x:4, y:4') |
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assert interpolating_poly(0, x) == 0 |
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assert interpolating_poly(1, x) == y0 |
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assert interpolating_poly(2, x) == \ |
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y0*(x - x1)/(x0 - x1) + y1*(x - x0)/(x1 - x0) |
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assert interpolating_poly(3, x) == \ |
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y0*(x - x1)*(x - x2)/((x0 - x1)*(x0 - x2)) + \ |
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y1*(x - x0)*(x - x2)/((x1 - x0)*(x1 - x2)) + \ |
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y2*(x - x0)*(x - x1)/((x2 - x0)*(x2 - x1)) |
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assert interpolating_poly(4, x) == \ |
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y0*(x - x1)*(x - x2)*(x - x3)/((x0 - x1)*(x0 - x2)*(x0 - x3)) + \ |
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y1*(x - x0)*(x - x2)*(x - x3)/((x1 - x0)*(x1 - x2)*(x1 - x3)) + \ |
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y2*(x - x0)*(x - x1)*(x - x3)/((x2 - x0)*(x2 - x1)*(x2 - x3)) + \ |
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y3*(x - x0)*(x - x1)*(x - x2)/((x3 - x0)*(x3 - x1)*(x3 - x2)) |
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raises(ValueError, lambda: |
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interpolating_poly(2, x, (x, 2), (1, 3))) |
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raises(ValueError, lambda: |
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interpolating_poly(2, x, (x + y, 2), (1, 3))) |
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raises(ValueError, lambda: |
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interpolating_poly(2, x + y, (x, 2), (1, 3))) |
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raises(ValueError, lambda: |
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interpolating_poly(2, 3, (4, 5), (6, 7))) |
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raises(ValueError, lambda: |
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interpolating_poly(2, 3, (4, 5), (6, 7, 8))) |
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assert interpolating_poly(0, x, (1, 2), (3, 4)) == 0 |
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assert interpolating_poly(1, x, (1, 2), (3, 4)) == 3 |
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assert interpolating_poly(2, x, (1, 2), (3, 4)) == x + 2 |
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def test_fateman_poly_F_1(): |
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f, g, h = fateman_poly_F_1(1) |
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F, G, H = dmp_fateman_poly_F_1(1, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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f, g, h = fateman_poly_F_1(3) |
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F, G, H = dmp_fateman_poly_F_1(3, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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def test_fateman_poly_F_2(): |
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f, g, h = fateman_poly_F_2(1) |
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F, G, H = dmp_fateman_poly_F_2(1, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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f, g, h = fateman_poly_F_2(3) |
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F, G, H = dmp_fateman_poly_F_2(3, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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def test_fateman_poly_F_3(): |
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f, g, h = fateman_poly_F_3(1) |
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F, G, H = dmp_fateman_poly_F_3(1, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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f, g, h = fateman_poly_F_3(3) |
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F, G, H = dmp_fateman_poly_F_3(3, ZZ) |
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assert [ t.rep.to_list() for t in [f, g, h] ] == [F, G, H] |
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