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