"""Tests for tools and arithmetics for monomials of distributed polynomials. """ from sympy.polys.monomials import ( itermonomials, monomial_count, monomial_mul, monomial_div, monomial_gcd, monomial_lcm, monomial_max, monomial_min, monomial_divides, monomial_pow, Monomial, ) from sympy.polys.polyerrors import ExactQuotientFailed from sympy.abc import a, b, c, x, y, z from sympy.core import S, symbols from sympy.testing.pytest import raises def test_monomials(): # total_degree tests assert set(itermonomials([], 0)) == {S.One} assert set(itermonomials([], 1)) == {S.One} assert set(itermonomials([], 2)) == {S.One} assert set(itermonomials([], 0, 0)) == {S.One} assert set(itermonomials([], 1, 0)) == {S.One} assert set(itermonomials([], 2, 0)) == {S.One} raises(StopIteration, lambda: next(itermonomials([], 0, 1))) raises(StopIteration, lambda: next(itermonomials([], 0, 2))) raises(StopIteration, lambda: next(itermonomials([], 0, 3))) assert set(itermonomials([], 0, 1)) == set() assert set(itermonomials([], 0, 2)) == set() assert set(itermonomials([], 0, 3)) == set() raises(ValueError, lambda: set(itermonomials([], -1))) raises(ValueError, lambda: set(itermonomials([x], -1))) raises(ValueError, lambda: set(itermonomials([x, y], -1))) assert set(itermonomials([x], 0)) == {S.One} assert set(itermonomials([x], 1)) == {S.One, x} assert set(itermonomials([x], 2)) == {S.One, x, x**2} assert set(itermonomials([x], 3)) == {S.One, x, x**2, x**3} assert set(itermonomials([x, y], 0)) == {S.One} assert set(itermonomials([x, y], 1)) == {S.One, x, y} assert set(itermonomials([x, y], 2)) == {S.One, x, y, x**2, y**2, x*y} assert set(itermonomials([x, y], 3)) == \ {S.One, x, y, x**2, x**3, y**2, y**3, x*y, x*y**2, y*x**2} i, j, k = symbols('i j k', commutative=False) assert set(itermonomials([i, j, k], 0)) == {S.One} assert set(itermonomials([i, j, k], 1)) == {S.One, i, j, k} assert set(itermonomials([i, j, k], 2)) == \ {S.One, i, j, k, i**2, j**2, k**2, i*j, i*k, j*i, j*k, k*i, k*j} assert set(itermonomials([i, j, k], 3)) == \ {S.One, i, j, k, i**2, j**2, k**2, i*j, i*k, j*i, j*k, k*i, k*j, i**3, j**3, k**3, i**2 * j, i**2 * k, j * i**2, k * i**2, j**2 * i, j**2 * k, i * j**2, k * j**2, k**2 * i, k**2 * j, i * k**2, j * k**2, i*j*i, i*k*i, j*i*j, j*k*j, k*i*k, k*j*k, i*j*k, i*k*j, j*i*k, j*k*i, k*i*j, k*j*i, } assert set(itermonomials([x, i, j], 0)) == {S.One} assert set(itermonomials([x, i, j], 1)) == {S.One, x, i, j} assert set(itermonomials([x, i, j], 2)) == {S.One, x, i, j, x*i, x*j, i*j, j*i, x**2, i**2, j**2} assert set(itermonomials([x, i, j], 3)) == \ {S.One, x, i, j, x*i, x*j, i*j, j*i, x**2, i**2, j**2, x**3, i**3, j**3, x**2 * i, x**2 * j, x * i**2, j * i**2, i**2 * j, i*j*i, x * j**2, i * j**2, j**2 * i, j*i*j, x * i * j, x * j * i } # degree_list tests assert set(itermonomials([], [])) == {S.One} raises(ValueError, lambda: set(itermonomials([], [0]))) raises(ValueError, lambda: set(itermonomials([], [1]))) raises(ValueError, lambda: set(itermonomials([], [2]))) raises(ValueError, lambda: set(itermonomials([x], [1], []))) raises(ValueError, lambda: set(itermonomials([x], [1, 2], []))) raises(ValueError, lambda: set(itermonomials([x], [1, 2, 3], []))) raises(ValueError, lambda: set(itermonomials([x], [], [1]))) raises(ValueError, lambda: set(itermonomials([x], [], [1, 2]))) raises(ValueError, lambda: set(itermonomials([x], [], [1, 2, 3]))) raises(ValueError, lambda: set(itermonomials([x, y], [1, 2], [1, 2, 3]))) raises(ValueError, lambda: set(itermonomials([x, y, z], [1, 2, 3], [0, 1]))) raises(ValueError, lambda: set(itermonomials([x], [1], [-1]))) raises(ValueError, lambda: set(itermonomials([x, y], [1, 2], [1, -1]))) raises(ValueError, lambda: set(itermonomials([], [], 1))) raises(ValueError, lambda: set(itermonomials([], [], 2))) raises(ValueError, lambda: set(itermonomials([], [], 3))) raises(ValueError, lambda: set(itermonomials([x, y], [0, 1], [1, 2]))) raises(ValueError, lambda: set(itermonomials([x, y, z], [0, 0, 3], [0, 1, 2]))) assert set(itermonomials([x], [0])) == {S.One} assert set(itermonomials([x], [1])) == {S.One, x} assert set(itermonomials([x], [2])) == {S.One, x, x**2} assert set(itermonomials([x], [3])) == {S.One, x, x**2, x**3} assert set(itermonomials([x], [3], [1])) == {x, x**3, x**2} assert set(itermonomials([x], [3], [2])) == {x**3, x**2} assert set(itermonomials([x, y], 3, 3)) == {x**3, x**2*y, x*y**2, y**3} assert set(itermonomials([x, y], 3, 2)) == {x**2, x*y, y**2, x**3, x**2*y, x*y**2, y**3} assert set(itermonomials([x, y], [0, 0])) == {S.One} assert set(itermonomials([x, y], [0, 1])) == {S.One, y} assert set(itermonomials([x, y], [0, 2])) == {S.One, y, y**2} assert set(itermonomials([x, y], [0, 2], [0, 1])) == {y, y**2} assert set(itermonomials([x, y], [0, 2], [0, 2])) == {y**2} assert set(itermonomials([x, y], [1, 0])) == {S.One, x} assert set(itermonomials([x, y], [1, 1])) == {S.One, x, y, x*y} assert set(itermonomials([x, y], [1, 2])) == {S.One, x, y, x*y, y**2, x*y**2} assert set(itermonomials([x, y], [1, 2], [1, 1])) == {x*y, x*y**2} assert set(itermonomials([x, y], [1, 2], [1, 2])) == {x*y**2} assert set(itermonomials([x, y], [2, 0])) == {S.One, x, x**2} assert set(itermonomials([x, y], [2, 1])) == {S.One, x, y, x*y, x**2, x**2*y} assert set(itermonomials([x, y], [2, 2])) == \ {S.One, y**2, x*y**2, x, x*y, x**2, x**2*y**2, y, x**2*y} i, j, k = symbols('i j k', commutative=False) assert set(itermonomials([i, j, k], 2, 2)) == \ {k*i, i**2, i*j, j*k, j*i, k**2, j**2, k*j, i*k} assert set(itermonomials([i, j, k], 3, 2)) == \ {j*k**2, i*k**2, k*i*j, k*i**2, k**2, j*k*j, k*j**2, i*k*i, i*j, j**2*k, i**2*j, j*i*k, j**3, i**3, k*j*i, j*k*i, j*i, k**2*j, j*i**2, k*j, k*j*k, i*j*i, j*i*j, i*j**2, j**2, k*i*k, i**2, j*k, i*k, i*k*j, k**3, i**2*k, j**2*i, k**2*i, i*j*k, k*i } assert set(itermonomials([i, j, k], [0, 0, 0])) == {S.One} assert set(itermonomials([i, j, k], [0, 0, 1])) == {1, k} assert set(itermonomials([i, j, k], [0, 1, 0])) == {1, j} assert set(itermonomials([i, j, k], [1, 0, 0])) == {i, 1} assert set(itermonomials([i, j, k], [0, 0, 2])) == {k**2, 1, k} assert set(itermonomials([i, j, k], [0, 2, 0])) == {1, j, j**2} assert set(itermonomials([i, j, k], [2, 0, 0])) == {i, 1, i**2} assert set(itermonomials([i, j, k], [1, 1, 1])) == {1, k, j, j*k, i*k, i, i*j, i*j*k} assert set(itermonomials([i, j, k], [2, 2, 2])) == \ {1, k, i**2*k**2, j*k, j**2, i, i*k, j*k**2, i*j**2*k**2, i**2*j, i**2*j**2, k**2, j**2*k, i*j**2*k, j**2*k**2, i*j, i**2*k, i**2*j**2*k, j, i**2*j*k, i*j**2, i*k**2, i*j*k, i**2*j**2*k**2, i*j*k**2, i**2, i**2*j*k**2 } assert set(itermonomials([x, j, k], [0, 0, 0])) == {S.One} assert set(itermonomials([x, j, k], [0, 0, 1])) == {1, k} assert set(itermonomials([x, j, k], [0, 1, 0])) == {1, j} assert set(itermonomials([x, j, k], [1, 0, 0])) == {x, 1} assert set(itermonomials([x, j, k], [0, 0, 2])) == {k**2, 1, k} assert set(itermonomials([x, j, k], [0, 2, 0])) == {1, j, j**2} assert set(itermonomials([x, j, k], [2, 0, 0])) == {x, 1, x**2} assert set(itermonomials([x, j, k], [1, 1, 1])) == {1, k, j, j*k, x*k, x, x*j, x*j*k} assert set(itermonomials([x, j, k], [2, 2, 2])) == \ {1, k, x**2*k**2, j*k, j**2, x, x*k, j*k**2, x*j**2*k**2, x**2*j, x**2*j**2, k**2, j**2*k, x*j**2*k, j**2*k**2, x*j, x**2*k, x**2*j**2*k, j, x**2*j*k, x*j**2, x*k**2, x*j*k, x**2*j**2*k**2, x*j*k**2, x**2, x**2*j*k**2 } def test_monomial_count(): assert monomial_count(2, 2) == 6 assert monomial_count(2, 3) == 10 def test_monomial_mul(): assert monomial_mul((3, 4, 1), (1, 2, 0)) == (4, 6, 1) def test_monomial_div(): assert monomial_div((3, 4, 1), (1, 2, 0)) == (2, 2, 1) def test_monomial_gcd(): assert monomial_gcd((3, 4, 1), (1, 2, 0)) == (1, 2, 0) def test_monomial_lcm(): assert monomial_lcm((3, 4, 1), (1, 2, 0)) == (3, 4, 1) def test_monomial_max(): assert monomial_max((3, 4, 5), (0, 5, 1), (6, 3, 9)) == (6, 5, 9) def test_monomial_pow(): assert monomial_pow((1, 2, 3), 3) == (3, 6, 9) def test_monomial_min(): assert monomial_min((3, 4, 5), (0, 5, 1), (6, 3, 9)) == (0, 3, 1) def test_monomial_divides(): assert monomial_divides((1, 2, 3), (4, 5, 6)) is True assert monomial_divides((1, 2, 3), (0, 5, 6)) is False def test_Monomial(): m = Monomial((3, 4, 1), (x, y, z)) n = Monomial((1, 2, 0), (x, y, z)) assert m.as_expr() == x**3*y**4*z assert n.as_expr() == x**1*y**2 assert m.as_expr(a, b, c) == a**3*b**4*c assert n.as_expr(a, b, c) == a**1*b**2 assert m.exponents == (3, 4, 1) assert m.gens == (x, y, z) assert n.exponents == (1, 2, 0) assert n.gens == (x, y, z) assert m == (3, 4, 1) assert n != (3, 4, 1) assert m != (1, 2, 0) assert n == (1, 2, 0) assert (m == 1) is False assert m[0] == m[-3] == 3 assert m[1] == m[-2] == 4 assert m[2] == m[-1] == 1 assert n[0] == n[-3] == 1 assert n[1] == n[-2] == 2 assert n[2] == n[-1] == 0 assert m[:2] == (3, 4) assert n[:2] == (1, 2) assert m*n == Monomial((4, 6, 1)) assert m/n == Monomial((2, 2, 1)) assert m*(1, 2, 0) == Monomial((4, 6, 1)) assert m/(1, 2, 0) == Monomial((2, 2, 1)) assert m.gcd(n) == Monomial((1, 2, 0)) assert m.lcm(n) == Monomial((3, 4, 1)) assert m.gcd((1, 2, 0)) == Monomial((1, 2, 0)) assert m.lcm((1, 2, 0)) == Monomial((3, 4, 1)) assert m**0 == Monomial((0, 0, 0)) assert m**1 == m assert m**2 == Monomial((6, 8, 2)) assert m**3 == Monomial((9, 12, 3)) raises(ExactQuotientFailed, lambda: m/Monomial((5, 2, 0))) mm = Monomial((1, 2, 3)) raises(ValueError, lambda: mm.as_expr()) assert str(mm) == 'Monomial((1, 2, 3))' assert str(m) == 'x**3*y**4*z**1' raises(NotImplementedError, lambda: m*1) raises(NotImplementedError, lambda: m/1) raises(ValueError, lambda: m**-1) raises(TypeError, lambda: m.gcd(3)) raises(TypeError, lambda: m.lcm(3))