Vehicle-cpp/hkpc/software/sympy/printing/tests/test_conventions.py

# -*- coding: utf-8 -*-

from sympy.core.function import (Derivative, Function)
from sympy.core.numbers import oo
from sympy.core.symbol import symbols
from sympy.functions.elementary.exponential import exp
from sympy.functions.elementary.trigonometric import cos
from sympy.integrals.integrals import Integral
from sympy.functions.special.bessel import besselj
from sympy.functions.special.polynomials import legendre
from sympy.functions.combinatorial.numbers import bell
from sympy.printing.conventions import split_super_sub, requires_partial
from sympy.testing.pytest import XFAIL

def test_super_sub():
    assert split_super_sub("beta_13_2") == ("beta", [], ["13", "2"])
    assert split_super_sub("beta_132_20") == ("beta", [], ["132", "20"])
    assert split_super_sub("beta_13") == ("beta", [], ["13"])
    assert split_super_sub("x_a_b") == ("x", [], ["a", "b"])
    assert split_super_sub("x_1_2_3") == ("x", [], ["1", "2", "3"])
    assert split_super_sub("x_a_b1") == ("x", [], ["a", "b1"])
    assert split_super_sub("x_a_1") == ("x", [], ["a", "1"])
    assert split_super_sub("x_1_a") == ("x", [], ["1", "a"])
    assert split_super_sub("x_1^aa") == ("x", ["aa"], ["1"])
    assert split_super_sub("x_1__aa") == ("x", ["aa"], ["1"])
    assert split_super_sub("x_11^a") == ("x", ["a"], ["11"])
    assert split_super_sub("x_11__a") == ("x", ["a"], ["11"])
    assert split_super_sub("x_a_b_c_d") == ("x", [], ["a", "b", "c", "d"])
    assert split_super_sub("x_a_b^c^d") == ("x", ["c", "d"], ["a", "b"])
    assert split_super_sub("x_a_b__c__d") == ("x", ["c", "d"], ["a", "b"])
    assert split_super_sub("x_a^b_c^d") == ("x", ["b", "d"], ["a", "c"])
    assert split_super_sub("x_a__b_c__d") == ("x", ["b", "d"], ["a", "c"])
    assert split_super_sub("x^a^b_c_d") == ("x", ["a", "b"], ["c", "d"])
    assert split_super_sub("x__a__b_c_d") == ("x", ["a", "b"], ["c", "d"])
    assert split_super_sub("x^a^b^c^d") == ("x", ["a", "b", "c", "d"], [])
    assert split_super_sub("x__a__b__c__d") == ("x", ["a", "b", "c", "d"], [])
    assert split_super_sub("alpha_11") == ("alpha", [], ["11"])
    assert split_super_sub("alpha_11_11") == ("alpha", [], ["11", "11"])
    assert split_super_sub("w1") == ("w", [], ["1"])
    assert split_super_sub("w𝟙") == ("w", [], ["𝟙"])
    assert split_super_sub("w11") == ("w", [], ["11"])
    assert split_super_sub("w𝟙𝟙") == ("w", [], ["𝟙𝟙"])
    assert split_super_sub("w𝟙2𝟙") == ("w", [], ["𝟙2𝟙"])
    assert split_super_sub("w1^a") == ("w", ["a"], ["1"])
    assert split_super_sub("ω1") == ("ω", [], ["1"])
    assert split_super_sub("ω11") == ("ω", [], ["11"])
    assert split_super_sub("ω1^a") == ("ω", ["a"], ["1"])
    assert split_super_sub("ω𝟙^α") == ("ω", ["α"], ["𝟙"])
    assert split_super_sub("ω𝟙2^3α") == ("ω", ["3α"], ["𝟙2"])
    assert split_super_sub("") == ("", [], [])


def test_requires_partial():
    x, y, z, t, nu = symbols('x y z t nu')
    n = symbols('n', integer=True)

    f = x * y
    assert requires_partial(Derivative(f, x)) is True
    assert requires_partial(Derivative(f, y)) is True

    ## integrating out one of the variables
    assert requires_partial(Derivative(Integral(exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False

    ## bessel function with smooth parameter
    f = besselj(nu, x)
    assert requires_partial(Derivative(f, x)) is True
    assert requires_partial(Derivative(f, nu)) is True

    ## bessel function with integer parameter
    f = besselj(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # this is not really valid (differentiating with respect to an integer)
    # but there's no reason to use the partial derivative symbol there. make
    # sure we don't throw an exception here, though
    assert requires_partial(Derivative(f, n)) is False

    ## bell polynomial
    f = bell(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # again, invalid
    assert requires_partial(Derivative(f, n)) is False

    ## legendre polynomial
    f = legendre(0, x)
    assert requires_partial(Derivative(f, x)) is False

    f = legendre(n, x)
    assert requires_partial(Derivative(f, x)) is False
    # again, invalid
    assert requires_partial(Derivative(f, n)) is False

    f = x ** n
    assert requires_partial(Derivative(f, x)) is False

    assert requires_partial(Derivative(Integral((x*y) ** n * exp(-x * y), (x, 0, oo)), y, evaluate=False)) is False

    # parametric equation
    f = (exp(t), cos(t))
    g = sum(f)
    assert requires_partial(Derivative(g, t)) is False

    f = symbols('f', cls=Function)
    assert requires_partial(Derivative(f(x), x)) is False
    assert requires_partial(Derivative(f(x), y)) is False
    assert requires_partial(Derivative(f(x, y), x)) is True
    assert requires_partial(Derivative(f(x, y), y)) is True
    assert requires_partial(Derivative(f(x, y), z)) is True
    assert requires_partial(Derivative(f(x, y), x, y)) is True

@XFAIL
def test_requires_partial_unspecified_variables():
    x, y = symbols('x y')
    # function of unspecified variables
    f = symbols('f', cls=Function)
    assert requires_partial(Derivative(f, x)) is False
    assert requires_partial(Derivative(f, x, y)) is True