Mapytex/pymath/calculus/expression.py

#!/usr/bin/env python
# encoding: utf-8

# debuging
# from debug.tools import report

from .generic import flatten_list, expand_list, isOperator, isNumerand
from .str2tokens import str2tokens
from .operator import op
from .explicable import Explicable, Explicable_int, Explicable_Decimal
from decimal import Decimal

from .random_expression import RdExpression

__all__ = ['Expression']


def pstf_factory(pstf_tokens):
    """Factory which tranform postfix tokens list into an Expression or the simpliest object type ready to be rendered

    :param pstf_tokens: a postfix tokens list
    :returns: the object

    >>> from .operator import op
    >>> pstf_t = [2, 3, op.add]
    >>> pstf_factory(pstf_t)
    < <class 'pymath.calculus.expression.Expression'> [2, 3, +] >
    >>> pstf_factory([2])
    2
    >>> type(pstf_factory([2]))
    <class 'pymath.calculus.explicable.Explicable_int'>
    >>> pstf_factory([2.45])
    Decimal('2.45')
    >>> type(pstf_factory([2.45]))
    <class 'pymath.calculus.explicable.Explicable_Decimal'>
    >>> from .fraction import Fraction
    >>> f = Fraction(1,2)
    >>> pstf_factory([f])
    < Fraction 1 / 2>

    """
    if len(pstf_tokens) == 1:
        if isinstance(pstf_tokens[0], int):
            return Explicable_int(pstf_tokens[0])
        elif isinstance(pstf_tokens[0], Decimal):
            return Explicable_Decimal(pstf_tokens[0])
        elif isinstance(pstf_tokens[0], float):
            return Explicable_Decimal(Decimal(str(pstf_tokens[0])))
        elif hasattr(pstf_tokens[0], 'STR_RENDER'):
            return pstf_tokens[0]

    return Expression(pstf_tokens)


class Expression(Explicable):
    """A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""

    @classmethod
    def random(self, form="", conditions=[], val_min=-10, val_max=10):
        """Create a random expression from form and with conditions

        :param form: the form of the expression (/!\ variables need to be in brackets {})
        :param conditions: condition on variables (/!\ variables need to be in brackets {})
        :param val_min: min value for generate variables
        :param val_max: max value for generate variables

        """
        random_generator = RdExpression(form, conditions)
        return Expression(random_generator(val_min, val_max))

    @classmethod
    def tmp_render(cls, render=lambda _, x: pstf_factory(x)):
        """ Same ad tmp_render for Renderable but default render is Expression

        >>> exp = Expression("2*3/5")
        >>> print(exp)
        2 \\times \\frac{ 3 }{ 5 }
        >>> for i in exp.simplify().explain():
        ...     print(i)
        2 \\times \\frac{ 3 }{ 5 }
        \\frac{ 3 }{ 5 } \\times 2
        \\frac{ 3 \\times 2 }{ 5 }
        \\frac{ 6 }{ 5 }
        >>> with Expression.tmp_render():
        ...     for i in exp.simplify().explain():
        ...         i
        < <class 'pymath.calculus.expression.Expression'> [2, 3, 5, /, *] >
        < <class 'pymath.calculus.expression.Expression'> [2, < Fraction 3 / 5>, *] >
        < <class 'pymath.calculus.expression.Expression'> [< Fraction 3 / 5>, 2, *] >
        < <class 'pymath.calculus.expression.Expression'> [3, 2, *, 5, /] >
        < <class 'pymath.calculus.expression.Expression'> [6, 5, /] >
        >>> from .render import txt
        >>> with Expression.tmp_render(txt):
        ...     for i in exp.simplify().explain():
        ...         print(i)
        2 * 3 / 5
        3 / 5 * 2
        ( 3 * 2 ) / 5
        6 / 5
        >>> for i in exp.simplify().explain():
        ...     print(i)
        2 \\times \\frac{ 3 }{ 5 }
        \\frac{ 3 }{ 5 } \\times 2
        \\frac{ 3 \\times 2 }{ 5 }
        \\frac{ 6 }{ 5 }

        """
        return super(Expression, cls).tmp_render(render)

    def __new__(cls, exp):
        """Create Expression objects

        :param exp: the expression. It can be a string or a list of postfix tokens.

        """
        expression = object.__new__(cls)

        if isinstance(exp, str):
            expression.postfix_tokens = str2tokens(exp)

        elif isinstance(exp, list):
            # Ici on ne peut convertir les "+-*/..." en opérateur que s'ils sont
            # d'arité 2.
            exp_mod_op = [
                op.get_op(i) if op.can_be_operator(i) else i for i in exp
                ]
            expression.postfix_tokens = flatten_list(
                [tok.postfix_tokens if Expression.isExpression(tok) else tok for tok in exp_mod_op]
                )

        elif isinstance(exp, Expression):
            return exp

        elif isNumerand(exp):
            expression.postfix_tokens = [exp]

        else:
            raise ValueError(
                "Can't build Expression with {} object".format(
                    type(exp)
                    )
                )

        expression._isExpression = 1
        return expression

    def __str__(self):
        """
        Overload str

        If you want to changer render use Expression.set_render(...) or use tmp_render context manager.
        """
        return self.STR_RENDER(self.postfix_tokens)

    def __repr__(self):
        return " ".join(["<", str(self.__class__),
                         str(self.postfix_tokens), ">"])

    def simplify(self):
        """ Compute entirely the expression and return the result with .steps attribute """
        try:
            self.compute_exp()
        except ComputeError:
            try:
                self.simplified = self.postfix_tokens[0].simplify()
            except AttributeError:
                if isinstance(self.postfix_tokens[0], int):
                    self.simplified = Explicable_int(self.postfix_tokens[0])
                elif isinstance(self.postfix_tokens[0], Decimal):
                    self.simplified = Explicable_Decimal(self.postfix_tokens[0])
                else:
                    self.simplified = self

        else:
            self.simplified = self.child.simplify()
            self.simplified.steps = self.child.steps + self.simplified.steps
        return self.simplified

    def compute_exp(self):
        """ Create self.child with and stock steps in it """
        if len(self.postfix_tokens) == 1:
            raise ComputeError("Nothing to compute in {}".format(self.postfix_tokens))
        else:
            ini_step = Expression(self.postfix_tokens)

            tokenList = self.postfix_tokens.copy()
            tmpTokenList = []

            while len(tokenList) > 2:
                # on va chercher les motifs du genre A B +, quand l'operateur est
                # d'arité 2, pour les calculer
                if isNumerand(tokenList[0]) and isNumerand(tokenList[1]) \
                        and isOperator(tokenList[2]) and tokenList[2].arity == 2:

                    # S'il y a une opération à faire
                    op1 = tokenList[0]
                    op2 = tokenList[1]
                    operator = tokenList[2]

                    res = operator(op1, op2)

                    tmpTokenList.append(res)

                    # Comme on vient de faire le calcul, on peut détruire aussi les
                    # deux prochains termes
                    del tokenList[0:3]

                # Et les motifs du gens A -, quand l'operateur est d'arité 1
                elif isNumerand(tokenList[0]) \
                        and isOperator(tokenList[1]) and tokenList[1].arity == 1:

                    # S'il y a une opération à faire
                    op1 = tokenList[0]
                    operator = tokenList[1]

                    res = operator(op1)

                    tmpTokenList.append(res)

                    # Comme on vient de faire le calcul, on peut détruire aussi les
                    # deux prochains termes
                    del tokenList[0:2]

                else:
                    tmpTokenList.append(tokenList[0])

                    del tokenList[0]

            if len(tokenList) == 2 and isNumerand(tokenList[0]) \
                    and isOperator(tokenList[1]) and tokenList[1].arity == 1:
                # S'il reste deux éléments dont un operation d'arité 1
                op1 = tokenList[0]
                operator = tokenList[1]

                res = operator(op1)

                tmpTokenList.append(res)

                # Comme on vient de faire le calcul, on peut détruire aussi les
                # deux prochains termes
                del tokenList[0:2]

            tmpTokenList += tokenList
            self.child = Expression(tmpTokenList)

            steps = Expression.develop_steps(tmpTokenList)

            if self.child.postfix_tokens == ini_step.postfix_tokens:
                self.child.steps = steps
            else:
                self.child.this_append_before([ini_step] + steps)

    @classmethod
    def develop_steps(cls, tokenList):
        """ From a list of tokens, it develops steps of each tokens """
        tmp_steps = []
        for t in tokenList:
            try:
                with Expression.tmp_render():
                    steps = [i for i in t.explain()]
                    if steps:
                        tmp_steps.append(steps)
                    else:
                        tmp_steps.append([t])
            except AttributeError:
                tmp_steps.append([t])

        if max([len(i) for i in tmp_steps]) > 1:
            tmp_steps = expand_list(tmp_steps)[:-1]
            steps = [Expression(s) for s in tmp_steps]
            return steps

        return []

    @classmethod
    def isExpression(cls, other):
        try:
            other._isExpression
        except AttributeError:
            return 0
        return 1

    # -----------
    # Expression act as container from self.postfix_tokens

    def __getitem__(self, index):
        return self.postfix_tokens[index]

    def __setitem__(self, index, value):
        self.postfix_tokens[index] = value

    # -----------
    # Some math manipulations

    def operate(self, other, operator):
        if isinstance(other, Expression):
            return Expression(
                self.postfix_tokens +
                other.postfix_tokens +
                [operator])
        elif isinstance(other, list):
            return Expression(self.postfix_tokens + other + [operator])
        else:
            return Expression(self.postfix_tokens + [other] + [operator])

    def roperate(self, other, operator):
        if isinstance(other, Expression):
            return Expression(
                other.postfix_tokens +
                self.postfix_tokens +
                [operator])
        elif isinstance(other, list):
            return Expression(other + self.postfix_tokens + [operator])
        else:
            return Expression([other] + self.postfix_tokens + [operator])

    def __add__(self, other):
        """ Overload +

        >>> a = Expression("1+2")
        >>> print(a.postfix_tokens)
        [1, 2, +]
        >>> b = Expression("3+4")
        >>> print(b.postfix_tokens)
        [3, 4, +]
        >>> c = a + b
        >>> print(c.postfix_tokens)
        [1, 2, +, 3, 4, +, +]
        """
        return self.operate(other, op.add)

    def __radd__(self, other):
        return self.roperate(other, op.add)

    def __sub__(self, other):
        """ Overload -

        >>> a = Expression("1+2")
        >>> print(a.postfix_tokens)
        [1, 2, +]
        >>> b = Expression("3+4")
        >>> print(b.postfix_tokens)
        [3, 4, +]
        >>> c = a - b
        >>> print(c.postfix_tokens)
        [1, 2, +, 3, 4, +, -]
        """
        return self.operate(other, op.sub)

    def __rsub__(self, other):
        return self.roperate(other, op.sub)

    def __mul__(self, other):
        """ Overload *

        >>> a = Expression("1+2")
        >>> print(a.postfix_tokens)
        [1, 2, +]
        >>> b = Expression("3+4")
        >>> print(b.postfix_tokens)
        [3, 4, +]
        >>> c = a * b
        >>> print(c.postfix_tokens)
        [1, 2, +, 3, 4, +, *]
        """
        return self.operate(other, op.mul)

    def __rmul__(self, other):
        return self.roperate(other, op.mul)

    def __truediv__(self, other):
        """ Overload /

        >>> a = Expression("1+2")
        >>> print(a.postfix_tokens)
        [1, 2, +]
        >>> b = Expression("3+4")
        >>> print(b.postfix_tokens)
        [3, 4, +]
        >>> c = a / b
        >>> print(c.postfix_tokens)
        [1, 2, +, 3, 4, +, /]
        >>>
        """
        return self.operate(other, op.div)

    def __rtruediv__(self, other):
        return self.roperate(other, op.div)

    def __pow__(self, other):
        return self.operate(other, op.pw)

    def __xor__(self, other):
        return self.operate(other, op.pw)

    def __neg__(self):
        return Expression(self.postfix_tokens + [op.sub1])


class ExpressionError(Exception):
    pass


class ComputeError(Exception):
    pass

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