180 lines
4.4 KiB
Python
180 lines
4.4 KiB
Python
#!/usr/bin/env python
|
|
# encoding: utf-8
|
|
|
|
from .fraction import Fraction
|
|
from .generic import add_in_dict, remove_in_dict, convolution_dict
|
|
import re
|
|
|
|
class FormalExp(object):
|
|
"""A formal expression (similare to Symbol in Sympy"""
|
|
|
|
def __init__(self, coef = {}, letter = ""):
|
|
"""Initiat the formal expression
|
|
|
|
:param coef: the dictionary representing the expression
|
|
:param letter: minimum expression, a letter
|
|
|
|
"""
|
|
|
|
if coef != {} and letter != "":
|
|
raise ValueError("A FormalExp can't be initiate with dict_exp and a letter")
|
|
elif letter != "":
|
|
self._letter = letter
|
|
self._coef = {letter: 1}
|
|
elif coef != {}:
|
|
self._coef = coef
|
|
else:
|
|
raise ValueError("FormalExp needs a letter or dictionary of coeficients")
|
|
|
|
if len(self) != 1:
|
|
self.mainOp = "+"
|
|
|
|
def master_coef(self):
|
|
"""Return the master coefficient
|
|
/!\ may not work pretty well if there is more than one indeterminate
|
|
:returns: a_n
|
|
|
|
"""
|
|
pattern = "\w\^(\d*)"
|
|
finder = re.compile(pattern)
|
|
power = {}
|
|
for (k,v) in self._coef.items():
|
|
if k=="":
|
|
power[0] = v
|
|
else:
|
|
p = finder.findall(k)
|
|
if p == []:
|
|
power[1] = v
|
|
else:
|
|
power[int(p[0])] = v
|
|
|
|
m_power = max(power)
|
|
return power[m_power]
|
|
|
|
def check_calculous(self, other):
|
|
"""Check if other is a constant and then transform it into a dictionary compatible with FormalExp
|
|
|
|
:param other: The thing to compute with the expression
|
|
:returns: dictionary of this thing
|
|
|
|
"""
|
|
if type(other) in [int, Fraction]:
|
|
return {"":other}
|
|
elif type(other) == FormalExp:
|
|
return other._coef.copy()
|
|
else:
|
|
raise ValueError("Can't add {type} with FormalExp".format(type=type(other)))
|
|
|
|
def const_or_formal(self, d):
|
|
"""Return a constant if there is nothing else, FormalExp otherwise
|
|
|
|
:param d: dictionary descripting the expression
|
|
:returns: a constant or a FormalExp
|
|
|
|
"""
|
|
if list(d.keys()) == ['']:
|
|
return d['']
|
|
else:
|
|
return FormalExp(d)
|
|
|
|
def __add__(self, other):
|
|
d = self.check_calculous(other)
|
|
|
|
d = add_in_dict(self._coef, d)
|
|
d = remove_in_dict(d)
|
|
|
|
return [self.const_or_formal(d)]
|
|
|
|
def __radd__(self, other):
|
|
return self + other
|
|
|
|
def __sub__(self, other):
|
|
o_tmp = -other
|
|
return self + o_tmp
|
|
|
|
def __neg__(self):
|
|
d = {}
|
|
for k,v in self._coef.items():
|
|
d[k] = -v
|
|
return FormalExp(d)
|
|
|
|
def __mul__(self, other):
|
|
d = self.check_calculous(other)
|
|
|
|
d = convolution_dict(self._coef, d, op_key = self.op_key)
|
|
d = remove_in_dict(d)
|
|
|
|
return [self.const_or_formal(d)]
|
|
|
|
def op_key(self, x,y):
|
|
"""Operation on keys for convolution_dict"""
|
|
if x == "" or y == "":
|
|
return x+y
|
|
else:
|
|
return x + "*" + y
|
|
|
|
|
|
def __rmul__(self, other):
|
|
d = self.check_calculous(other)
|
|
|
|
d = convolution_dict(d, self._coef, op_key = self.op_key)
|
|
d = remove_in_dict(d)
|
|
|
|
return [self.const_or_formal(d)]
|
|
|
|
def __div__(self, other):
|
|
# Will never be done :D
|
|
pass
|
|
|
|
def __pow__(self, other):
|
|
# Will never be done :D quoique
|
|
pass
|
|
|
|
def __len__(self):
|
|
return len(list(self._coef.keys()))
|
|
|
|
def __str__(self):
|
|
ans = ""
|
|
for k,v in self._coef.items():
|
|
if v < 0:
|
|
ans += "-"
|
|
else:
|
|
ans += "+"
|
|
|
|
if abs(v) == 1:
|
|
ans += str(k)
|
|
else:
|
|
ans += str(abs(v)) + str(k)
|
|
if ans[0] == "+":
|
|
return ans[1:]
|
|
else:
|
|
return ans
|
|
|
|
if __name__ == '__main__':
|
|
fe1 = FormalExp({"x": -1, "":-2})
|
|
print(fe1)
|
|
fe2 = FormalExp({"x^12": 5, "":2})
|
|
print(fe2)
|
|
fe3 = fe1 * fe2
|
|
for s in fe3:
|
|
print(s)
|
|
fe4 = fe1 * 2
|
|
for s in fe4:
|
|
print(s)
|
|
|
|
fe = FormalExp(letter = "a")
|
|
fe_ = -2 * fe
|
|
print(fe_[0])
|
|
|
|
fe = FormalExp(letter = "a")
|
|
fe_ = fe * (-2)
|
|
print(fe_[0])
|
|
|
|
|
|
|
|
|
|
# -----------------------------
|
|
# Reglages pour 'vim'
|
|
# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
|
|
# cursor: 16 del
|