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Lafrite
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formal.py
179
formal.py
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#!/usr/bin/env python
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# encoding: utf-8
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from fraction import Fraction
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from generic import add_in_dict, remove_in_dict, convolution_dict
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import re
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class FormalExp(object):
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"""A formal expression (similare to Symbol in Sympy"""
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def __init__(self, coef = {}, letter = ""):
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"""Initiat the formal expression
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:param coef: the dictionary representing the expression
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:param letter: minimum expression, a letter
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"""
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if coef != {} and letter != "":
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raise ValueError("A FormalExp can't be initiate with dict_exp and a letter")
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elif letter != "":
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self._letter = letter
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self._coef = {letter: 1}
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elif coef != {}:
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self._coef = coef
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else:
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raise ValueError("FormalExp needs a letter or dictionary of coeficients")
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if len(self) != 1:
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self.mainOp = "+"
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def master_coef(self):
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"""Return the master coefficient
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/!\ may not work pretty well if there is more than one indeterminate
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:returns: a_n
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"""
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pattern = "\w\^(\d*)"
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finder = re.compile(pattern)
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power = {}
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for (k,v) in self._coef.items():
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if k=="":
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power[0] = v
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else:
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p = finder.findall(k)
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if p == []:
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power[1] = v
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else:
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power[int(p[0])] = v
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m_power = max(power)
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return power[m_power]
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def check_calculous(self, other):
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"""Check if other is a constant and then transform it into a dictionary compatible with FormalExp
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:param other: The thing to compute with the expression
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:returns: dictionary of this thing
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"""
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if type(other) in [int, Fraction]:
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return {"":other}
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elif type(other) == FormalExp:
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return other._coef.copy()
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else:
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raise ValueError("Can't add {type} with FormalExp".format(type=type(other)))
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def const_or_formal(self, d):
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"""Return a constant if there is nothing else, FormalExp otherwise
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:param d: dictionary descripting the expression
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:returns: a constant or a FormalExp
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"""
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if list(d.keys()) == ['']:
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return d['']
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else:
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return FormalExp(d)
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def __add__(self, other):
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d = self.check_calculous(other)
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d = add_in_dict(self._coef, d)
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d = remove_in_dict(d)
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return [self.const_or_formal(d)]
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def __radd__(self, other):
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return self + other
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def __sub__(self, other):
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o_tmp = -other
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return self + o_tmp
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def __neg__(self):
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d = {}
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for k,v in self._coef.items():
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d[k] = -v
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return FormalExp(d)
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def __mul__(self, other):
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d = self.check_calculous(other)
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d = convolution_dict(self._coef, d, op_key = self.op_key)
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d = remove_in_dict(d)
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return [self.const_or_formal(d)]
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def op_key(self, x,y):
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"""Operation on keys for convolution_dict"""
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if x == "" or y == "":
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return x+y
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else:
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return x + "*" + y
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def __rmul__(self, other):
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d = self.check_calculous(other)
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d = convolution_dict(d, self._coef, op_key = self.op_key)
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d = remove_in_dict(d)
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return [self.const_or_formal(d)]
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def __div__(self, other):
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# Will never be done :D
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pass
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def __pow__(self, other):
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# Will never be done :D quoique
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pass
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def __len__(self):
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return len(list(self._coef.keys()))
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def __str__(self):
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ans = ""
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for k,v in self._coef.items():
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if v < 0:
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ans += "-"
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else:
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ans += "+"
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if abs(v) == 1:
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ans += str(k)
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else:
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ans += str(abs(v)) + str(k)
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if ans[0] == "+":
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return ans[1:]
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else:
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return ans
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if __name__ == '__main__':
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fe1 = FormalExp({"x": -1, "":-2})
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print(fe1)
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fe2 = FormalExp({"x^12": 5, "":2})
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print(fe2)
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fe3 = fe1 * fe2
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for s in fe3:
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print(s)
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fe4 = fe1 * 2
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for s in fe4:
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print(s)
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fe = FormalExp(letter = "a")
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fe_ = -2 * fe
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print(fe_[0])
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fe = FormalExp(letter = "a")
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fe_ = fe * (-2)
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print(fe_[0])
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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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