| """Tests of monomial orderings. """ | |
| from sympy.polys.orderings import ( | |
| monomial_key, lex, grlex, grevlex, ilex, igrlex, | |
| LexOrder, InverseOrder, ProductOrder, build_product_order, | |
| ) | |
| from sympy.abc import x, y, z, t | |
| from sympy.core import S | |
| from sympy.testing.pytest import raises | |
| def test_lex_order(): | |
| assert lex((1, 2, 3)) == (1, 2, 3) | |
| assert str(lex) == 'lex' | |
| assert lex((1, 2, 3)) == lex((1, 2, 3)) | |
| assert lex((2, 2, 3)) > lex((1, 2, 3)) | |
| assert lex((1, 3, 3)) > lex((1, 2, 3)) | |
| assert lex((1, 2, 4)) > lex((1, 2, 3)) | |
| assert lex((0, 2, 3)) < lex((1, 2, 3)) | |
| assert lex((1, 1, 3)) < lex((1, 2, 3)) | |
| assert lex((1, 2, 2)) < lex((1, 2, 3)) | |
| assert lex.is_global is True | |
| assert lex == LexOrder() | |
| assert lex != grlex | |
| def test_grlex_order(): | |
| assert grlex((1, 2, 3)) == (6, (1, 2, 3)) | |
| assert str(grlex) == 'grlex' | |
| assert grlex((1, 2, 3)) == grlex((1, 2, 3)) | |
| assert grlex((2, 2, 3)) > grlex((1, 2, 3)) | |
| assert grlex((1, 3, 3)) > grlex((1, 2, 3)) | |
| assert grlex((1, 2, 4)) > grlex((1, 2, 3)) | |
| assert grlex((0, 2, 3)) < grlex((1, 2, 3)) | |
| assert grlex((1, 1, 3)) < grlex((1, 2, 3)) | |
| assert grlex((1, 2, 2)) < grlex((1, 2, 3)) | |
| assert grlex((2, 2, 3)) > grlex((1, 2, 4)) | |
| assert grlex((1, 3, 3)) > grlex((1, 2, 4)) | |
| assert grlex((0, 2, 3)) < grlex((1, 2, 2)) | |
| assert grlex((1, 1, 3)) < grlex((1, 2, 2)) | |
| assert grlex((0, 1, 1)) > grlex((0, 0, 2)) | |
| assert grlex((0, 3, 1)) < grlex((2, 2, 1)) | |
| assert grlex.is_global is True | |
| def test_grevlex_order(): | |
| assert grevlex((1, 2, 3)) == (6, (-3, -2, -1)) | |
| assert str(grevlex) == 'grevlex' | |
| assert grevlex((1, 2, 3)) == grevlex((1, 2, 3)) | |
| assert grevlex((2, 2, 3)) > grevlex((1, 2, 3)) | |
| assert grevlex((1, 3, 3)) > grevlex((1, 2, 3)) | |
| assert grevlex((1, 2, 4)) > grevlex((1, 2, 3)) | |
| assert grevlex((0, 2, 3)) < grevlex((1, 2, 3)) | |
| assert grevlex((1, 1, 3)) < grevlex((1, 2, 3)) | |
| assert grevlex((1, 2, 2)) < grevlex((1, 2, 3)) | |
| assert grevlex((2, 2, 3)) > grevlex((1, 2, 4)) | |
| assert grevlex((1, 3, 3)) > grevlex((1, 2, 4)) | |
| assert grevlex((0, 2, 3)) < grevlex((1, 2, 2)) | |
| assert grevlex((1, 1, 3)) < grevlex((1, 2, 2)) | |
| assert grevlex((0, 1, 1)) > grevlex((0, 0, 2)) | |
| assert grevlex((0, 3, 1)) < grevlex((2, 2, 1)) | |
| assert grevlex.is_global is True | |
| def test_InverseOrder(): | |
| ilex = InverseOrder(lex) | |
| igrlex = InverseOrder(grlex) | |
| assert ilex((1, 2, 3)) > ilex((2, 0, 3)) | |
| assert igrlex((1, 2, 3)) < igrlex((0, 2, 3)) | |
| assert str(ilex) == "ilex" | |
| assert str(igrlex) == "igrlex" | |
| assert ilex.is_global is False | |
| assert igrlex.is_global is False | |
| assert ilex != igrlex | |
| assert ilex == InverseOrder(LexOrder()) | |
| def test_ProductOrder(): | |
| P = ProductOrder((grlex, lambda m: m[:2]), (grlex, lambda m: m[2:])) | |
| assert P((1, 3, 3, 4, 5)) > P((2, 1, 5, 5, 5)) | |
| assert str(P) == "ProductOrder(grlex, grlex)" | |
| assert P.is_global is True | |
| assert ProductOrder((grlex, None), (ilex, None)).is_global is None | |
| assert ProductOrder((igrlex, None), (ilex, None)).is_global is False | |
| def test_monomial_key(): | |
| assert monomial_key() == lex | |
| assert monomial_key('lex') == lex | |
| assert monomial_key('grlex') == grlex | |
| assert monomial_key('grevlex') == grevlex | |
| raises(ValueError, lambda: monomial_key('foo')) | |
| raises(ValueError, lambda: monomial_key(1)) | |
| M = [x, x**2*z**2, x*y, x**2, S.One, y**2, x**3, y, z, x*y**2*z, x**2*y**2] | |
| assert sorted(M, key=monomial_key('lex', [z, y, x])) == \ | |
| [S.One, x, x**2, x**3, y, x*y, y**2, x**2*y**2, z, x*y**2*z, x**2*z**2] | |
| assert sorted(M, key=monomial_key('grlex', [z, y, x])) == \ | |
| [S.One, x, y, z, x**2, x*y, y**2, x**3, x**2*y**2, x*y**2*z, x**2*z**2] | |
| assert sorted(M, key=monomial_key('grevlex', [z, y, x])) == \ | |
| [S.One, x, y, z, x**2, x*y, y**2, x**3, x**2*y**2, x**2*z**2, x*y**2*z] | |
| def test_build_product_order(): | |
| assert build_product_order((("grlex", x, y), ("grlex", z, t)), [x, y, z, t])((4, 5, 6, 7)) == \ | |
| ((9, (4, 5)), (13, (6, 7))) | |
| assert build_product_order((("grlex", x, y), ("grlex", z, t)), [x, y, z, t]) == \ | |
| build_product_order((("grlex", x, y), ("grlex", z, t)), [x, y, z, t]) | |