423 lines
11 KiB
Python
423 lines
11 KiB
Python
#! /usr/bin/env python
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# -*- coding: utf-8 -*-
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# vim:fenc=utf-8
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#
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# Copyright © 2017 lafrite <lafrite@Poivre>
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#
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# Distributed under terms of the MIT license.
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"""
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Expression
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"""
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from functools import partial
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from ..core import AssocialTree, Tree, compute, typing, TypingError
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from ..core.MO import moify
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from .tokens import factory
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from .renders import render
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class Expression(object):
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"""
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Expression class
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:example:
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>>> e = Expression.from_str("2+3*4")
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>>> e2 = e.simplify()
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>>> print(e2)
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14
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>>> for s in e2.explain():
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... print(s)
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2 + 3 * 4
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2 + 12
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14
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"""
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def __init__(self, tree, ancestor=None):
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"""
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"""
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self._tree = tree
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self._ancestor = ancestor
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@classmethod
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def from_str(cls, string, typing=True):
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""" Initiate the expression from a string
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:param string: String to parse to generate the Expression
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:returns: the expression
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:example:
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>>> e = Expression.from_str("2 + 3 * 4")
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>>> e
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<Exp: 2 + 3 * 4>
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>>> e = Expression.from_str("2/3")
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>>> e
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<Fraction 2 / 3>
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>>> e = Expression.from_str("2x + 1")
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>>> e
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<Linear 2x + 1>
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>>> e = Expression.from_str("2x + 1 + 5x^2")
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>>> e
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<Quadratic 5x^2 + 2x + 1>
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>>> e = Expression.from_str("2x + 1 + 5x")
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>>> e
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<Exp: 2x + 1 + 5x>
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"""
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t = Tree.from_str(string)
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if typing:
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return cls._post_processing(t)
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return cls(t)
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@classmethod
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def _post_processing(cls, t):
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""" Post process the tree by typing it """
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tt = cls(t)._typing()
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try:
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return factory(tt)
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except TypeError as e:
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return cls(t)
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def __str__(self):
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return render(self._tree)
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def __repr__(self):
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return f"<Exp: {render(self._tree, 'txt')}>"
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def _order(self, exclude_nodes=["*", "/", "**"]):
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""" Order the expression base on types
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:example:
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>>> e = Expression.from_str("1 + 2x + 3 + 4x")
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>>> print(e)
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1 + 2x + 3 + 4x
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>>> #print(e._order())
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1 + 3 + 2x + 4x
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>>> e = Expression.from_str("x + 6x^3 + 1 + 2x^2 + 3 + 4x^2 + 5x")
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>>> print(e._order())
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x + 5x + 6x^3 + 2x^2 + 4x^2 + 1 + 3
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"""
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def signature(leaf):
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try:
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leaf.node
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except AttributeError:
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try:
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return leaf.signature
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except AttributeError:
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return type(leaf)
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else:
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try:
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typed_leaf = typing(
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leaf.node, leaf.left_value, leaf.right_value)
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return typed_leaf.signature
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except (AttributeError, NotImplementedError, TypingError):
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return type(leaf)
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try:
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self._tree.node
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except AttributeError:
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return self
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organised = AssocialTree.from_any_tree(self._tree).organise_by(
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signature, recursive=True, exclude_nodes=exclude_nodes
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)
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return Expression(organised)
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def _optimize(self, exclude_nodes=["/", "**"]):
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""" Return a copy of self with an optimize tree
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:example:
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>>> e = Expression.from_str("2x^2+2x+3x")
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>>> print(e._tree)
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+
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> +
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| > *
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| | > 2
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| | > ^
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| | | > x
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| | | > 2
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| > *
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| | > 2
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| | > x
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> *
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| > 3
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| > x
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>>> print(e._optimize()._tree)
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+
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> *
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| > 2
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| > ^
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| | > x
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| | > 2
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> +
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| > *
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| | > 2
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| | > x
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| > *
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| | > 3
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| | > x
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"""
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try:
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# TODO: need to test exclude_nodes |ven. oct. 5 08:51:02 CEST 2018
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return Expression(self._tree.balance(exclude_nodes=exclude_nodes))
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except AttributeError:
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return self
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def _typing(self):
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""" Build a copy of self with as much typing as possible
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:example:
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>>> e = Expression.from_str("2x", typing=False)
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>>> print(e._tree.map_on_leaf(lambda x: type(x).__name__))
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*
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> MOnumber
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> MOstr
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>>> typed_e = e._typing()
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>>> print(type(typed_e._tree))
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<class 'mapytex.calculus.core.MO.monomial.MOMonomial'>
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>>> typed_e = e._typing()
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>>> print(type(typed_e._tree))
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<class 'mapytex.calculus.core.MO.monomial.MOMonomial'>
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>>> e = Expression.from_str("2x+3+4/5", typing=False)
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>>> print(e._tree.map_on_leaf(lambda x: type(x).__name__))
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+
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> +
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| > *
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| | > MOnumber
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| | > MOstr
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| > MOnumber
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> /
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| > MOnumber
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| > MOnumber
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>>> typed_e = e._typing()
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>>> print(e._tree.map_on_leaf(lambda x: type(x).__name__))
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+
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> +
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| > *
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| | > MOnumber
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| | > MOstr
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| > MOnumber
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> /
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| > MOnumber
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| > MOnumber
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"""
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try:
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return Expression(self._tree.apply(typing))
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except AttributeError:
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return self
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def _compute(self):
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"""" Compute one step of self
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"""
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try:
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return Expression(self._tree.apply_on_last_level(compute))
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except AttributeError:
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return self
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def set_ancestor(self, ancestor):
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""" Set ancestor """
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self._ancestor = ancestor
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def _simplify(self, optimize=True):
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""" Compute as much as possible the expression
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:param optimize: bool to optimize tree when it's possible
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:return: an expression
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:example:
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>>> e = Expression.from_str("2+3*4")
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>>> e
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<Exp: 2 + 3 * 4>
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>>> f = e._simplify()
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>>> f
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<Exp: 14>
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>>> f._ancestor
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<Exp: 2 + 12>
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"""
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typed_exp = self._typing()
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if optimize:
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organized_exp = typed_exp._order()
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opt_exp = organized_exp._optimize()
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else:
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opt_exp = typed_exp
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comp_exp = opt_exp._compute()
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if typed_exp != comp_exp:
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comp_exp.set_ancestor(self)
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return comp_exp._simplify(optimize=optimize)
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typed_exp.set_ancestor(self._ancestor)
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return typed_exp
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def simplify(self, optimize=True):
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""" Simplify the expression, keep the history and factory child
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:param optimize: bool to optimize tree when it's possible
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:return: an expression
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:example:
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>>> e = Expression.from_str("2+3*4")
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>>> e
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<Exp: 2 + 3 * 4>
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>>> f = e.simplify()
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>>> f
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<Integer 14>
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>>> f._ancestor
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<Exp: 2 + 12>
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"""
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self._child = self._simplify(optimize=optimize)
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return factory(self._child, ancestor=self._child._ancestor)
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def explain(self):
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""" Yield every calculus step which have lead to self
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:example:
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>>> e = Expression.from_str("2+3*4")
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>>> f = e.simplify()
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>>> for s in f.explain():
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... print(s)
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2 + 3 * 4
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2 + 12
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14
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>>> e = Expression.from_str("1+2+3+4+5+6+7+8+9")
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>>> f = e.simplify()
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>>> for s in f.explain():
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... print(s)
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1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
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3 + 7 + 11 + 7 + 17
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10 + 11 + 24
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10 + 35
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45
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>>> e = Expression.from_str("1+2+3+4+5+6+7+8+9")
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>>> f_no_balance = e.simplify(optimize=False)
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>>> for s in f_no_balance.explain():
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... print(s)
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1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9
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3 + 3 + 4 + 5 + 6 + 7 + 8 + 9
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6 + 4 + 5 + 6 + 7 + 8 + 9
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10 + 5 + 6 + 7 + 8 + 9
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15 + 6 + 7 + 8 + 9
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21 + 7 + 8 + 9
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28 + 8 + 9
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36 + 9
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45
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>>> e = Expression.from_str("1+2+3+4+5*6*7*8*9")
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>>> f = e.simplify()
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>>> for s in f.explain():
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... print(s)
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1 + 2 + 3 + 4 + 5 * 6 * 7 * 8 * 9
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3 + 7 + 30 * 7 * 72
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10 + 210 * 72
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10 + 15120
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15130
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>>> e = Expression.from_str("1+2+3+4+5*6*7*8*9")
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>>> f_no_balance = e.simplify(optimize=False)
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>>> for s in f_no_balance.explain():
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... print(s)
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1 + 2 + 3 + 4 + 5 * 6 * 7 * 8 * 9
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3 + 3 + 4 + 30 * 7 * 8 * 9
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6 + 4 + 210 * 8 * 9
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10 + 1680 * 9
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10 + 15120
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15130
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>>> e = Expression.from_str("1+2/3/4/5")
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>>> f = e.simplify()
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>>> for s in f.explain():
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... print(s)
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1 + 2 / 3 / 4 / 5
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1 + (2 / 3 * 1 / 4) / 5
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1 + (2 * 1) / (3 * 4) / 5
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1 + 2 / 12 / 5
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1 + 2 / 12 * 1 / 5
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1 + (2 * 1) / (12 * 5)
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1 + 2 / 60
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1 / 1 + 2 / 60
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(1 * 60) / (1 * 60) + 2 / 60
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60 / 60 + 2 / 60
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(60 + 2) / 60
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62 / 60
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"""
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try:
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yield from self._ancestor.explain()
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except AttributeError:
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yield self
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else:
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yield self
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def __call__(self, value):
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""" Call a Expression to evaluate itself on value
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:param value: evaluate the Expression with this value
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:return: Expression simplified if the value is not a string with a length greater than 1.
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:examples:
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>>> f = Expression.from_str("3*x^2 + 2x + 1")
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>>> for s in f(2).explain():
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... print(s)
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3 * 2^2 + 2 * 2 + 1
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3 * 4 + 4 + 1
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12 + 5
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17
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>>> f(f(2))
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<Integer 902>
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>>> f(17)
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<Integer 902>
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>>> f("n")
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<Quadratic 3n^2 + 2n + 1>
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>>> f("u_n")
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<Exp: 3u_n^2 + 2u_n + 1>
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>>> f(f)
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<Polynomial 27x^4 + 36x^3 + 36x^2 + 16x + 6>
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"""
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tree = self._tree
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variable = (set(tree.get_leafs(extract_variable)) - {None}).pop()
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try:
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dest = value._mo
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except AttributeError:
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dest = moify(value)
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replace_var = partial(replace, origin=variable, dest=dest)
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tree = tree.map_on_leaf(replace_var)
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if isinstance(value, str) and len(value) > 1:
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return Expression(tree)
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return Expression(tree).simplify()
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def extract_variable(leaf):
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try:
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return leaf.variable
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except AttributeError:
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return None
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def replace(leaf, origin, dest):
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""" Recursively replace origin to dest in leaf """
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try:
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leaf.tree
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except AttributeError:
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if leaf == origin:
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return dest
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return leaf
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replace_var = partial(replace, origin=origin, dest=dest)
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return leaf.tree.map_on_leaf(replace_var)
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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