MTtranslateService/Lib/site-packages/sympy/polys/tests/test_monomials.py

"""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))