precedence.py

"""A module providing information about the necessity of brackets"""

from __future__ import print_function, division

from sympy.core.function import _coeff_isneg

# Default precedence values for some basic types
PRECEDENCE = {
    "Lambda": 1,
    "Xor": 10,
    "Or": 20,
    "And": 30,
    "Relational": 35,
    "Add": 40,
    "Mul": 50,
    "Pow": 60,
    "Not": 100,
    "Atom": 1000
}

# A dictionary assigning precedence values to certain classes. These values are
# treated like they were inherited, so not every single class has to be named
# here.
PRECEDENCE_VALUES = {
    "Equivalent": PRECEDENCE["Xor"],
    "Xor": PRECEDENCE["Xor"],
    "Implies": PRECEDENCE["Xor"],
    "Or": PRECEDENCE["Or"],
    "And": PRECEDENCE["And"],
    "Add": PRECEDENCE["Add"],
    "Pow": PRECEDENCE["Pow"],
    "Relational": PRECEDENCE["Relational"],
    "Sub": PRECEDENCE["Add"],
    "Not": PRECEDENCE["Not"],
    "factorial": PRECEDENCE["Pow"],
    "factorial2": PRECEDENCE["Pow"],
    "NegativeInfinity": PRECEDENCE["Add"],
    "MatAdd": PRECEDENCE["Add"],
    "MatMul": PRECEDENCE["Mul"],
    "HadamardProduct": PRECEDENCE["Mul"]
}

# Sometimes it's not enough to assign a fixed precedence value to a
# class. Then a function can be inserted in this dictionary that takes
# an instance of this class as argument and returns the appropriate
# precedence value.

# Precedence functions


def precedence_Mul(item):
    if _coeff_isneg(item):
        return PRECEDENCE["Add"]
    return PRECEDENCE["Mul"]


def precedence_Rational(item):
    if item.p < 0:
        return PRECEDENCE["Add"]
    return PRECEDENCE["Mul"]


def precedence_Integer(item):
    if item.p < 0:
        return PRECEDENCE["Add"]
    return PRECEDENCE["Atom"]


def precedence_Float(item):
    if item < 0:
        return PRECEDENCE["Add"]
    return PRECEDENCE["Atom"]


def precedence_PolyElement(item):
    if item.is_generator:
        return PRECEDENCE["Atom"]
    elif item.is_ground:
        return precedence(item.coeff(1))
    elif item.is_term:
        return PRECEDENCE["Mul"]
    else:
        return PRECEDENCE["Add"]


def precedence_FracElement(item):
    if item.denom == 1:
        return precedence_PolyElement(item.numer)
    else:
        return PRECEDENCE["Mul"]


PRECEDENCE_FUNCTIONS = {
    "Integer": precedence_Integer,
    "Mul": precedence_Mul,
    "Rational": precedence_Rational,
    "Float": precedence_Float,
    "PolyElement": precedence_PolyElement,
    "FracElement": precedence_FracElement,
}


def precedence(item):
    """
    Returns the precedence of a given object.
    """
    if hasattr(item, "precedence"):
        return item.precedence
    try:
        mro = item.__class__.__mro__
    except AttributeError:
        return PRECEDENCE["Atom"]
    for i in mro:
        n = i.__name__
        if n in PRECEDENCE_FUNCTIONS:
            return PRECEDENCE_FUNCTIONS[n](item)
        elif n in PRECEDENCE_VALUES:
            return PRECEDENCE_VALUES[n]
    return PRECEDENCE["Atom"]