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autopep8 on all files but operator.py

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This commit is contained in:
Benjamin Bertrand
2016-02-13 07:04:08 +03:00
parent e43544006e
commit 47d43849d0
15 changed files with 536 additions and 366 deletions
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55
pymath/calculus/abstract_polynom.py
View File

@@ -9,9 +9,11 @@ from .render import txt,tex
from itertools import chain from itertools import chain
from functools import wraps from functools import wraps
def power_cache(fun): def power_cache(fun):
"""Decorator which cache calculated powers of polynoms """ """Decorator which cache calculated powers of polynoms """
cache = {} cache = {}
@wraps(fun) @wraps(fun)
def cached_fun(self, power): def cached_fun(self, power):
#print("cache -> ", cache) #print("cache -> ", cache)
@@ -23,6 +25,7 @@ def power_cache(fun):
return poly_powered return poly_powered
return cached_fun return cached_fun
class AbstractPolynom(Explicable): class AbstractPolynom(Explicable):
"""The mathematic definition of a polynom. It will be the parent class of Polynom (classical polynoms) and later of SquareRoot polynoms""" """The mathematic definition of a polynom. It will be the parent class of Polynom (classical polynoms) and later of SquareRoot polynoms"""
@@ -86,7 +89,7 @@ class AbstractPolynom(Explicable):
""" """
self._coef = [] self._coef = []
for coef in l_coef: for coef in l_coef:
if type(coef) == list and len(coef)==1: if isinstance(coef, list) and len(coef) == 1:
self._coef.append(coef[0]) self._coef.append(coef[0])
else: else:
self._coef.append(coef) self._coef.append(coef)
@@ -164,7 +167,8 @@ class AbstractPolynom(Explicable):
elif i == 1: elif i == 1:
ans = a * (a != [1]) + [self._letter] + [op.mul] * (a != [1]) ans = a * (a != [1]) + [self._letter] + [op.mul] * (a != [1])
else: else:
ans = a * (a!=[1]) + [self._letter, i, op.pw] + [op.mul] * (a!=[1]) ans = a * (a != [1]) + [self._letter, i,
op.pw] + [op.mul] * (a != [1])
return ans return ans
@@ -208,12 +212,13 @@ class AbstractPolynom(Explicable):
""" """
if self == 0: if self == 0:
return [0] return [0]
# TODO: Faudrait factoriser un peu tout ça..! |dim. déc. 21 16:02:34 CET 2014 # TODO: Faudrait factoriser un peu tout ça..! |dim. déc. 21 16:02:34
# CET 2014
postfix = [] postfix = []
for (i, a) in list(enumerate(self._coef))[::-1]: for (i, a) in list(enumerate(self._coef))[::-1]:
operator = [op.add] operator = [op.add]
operator_sub1 = [] operator_sub1 = []
if type(a) == Expression: if isinstance(a, Expression):
# case coef is an arithmetic expression # case coef is an arithmetic expression
c = self.coef_postfix(a.postfix_tokens, i) c = self.coef_postfix(a.postfix_tokens, i)
if c != []: if c != []:
@@ -221,7 +226,7 @@ class AbstractPolynom(Explicable):
if len(postfix) > 1: if len(postfix) > 1:
postfix += operator postfix += operator
elif type(a) == list: elif isinstance(a, list):
# case need to repeat the x^i # case need to repeat the x^i
for b in a: for b in a:
operator = [op.add] operator = [op.add]
@@ -289,7 +294,8 @@ class AbstractPolynom(Explicable):
elif isPolynom(other): elif isPolynom(other):
return other return other
else: else:
raise ValueError(type(other) + " can't be converted into a polynom") raise ValueError(type(other) +
" can't be converted into a polynom")
def reduce(self): def reduce(self):
"""Compute coefficients which have same degree """Compute coefficients which have same degree
@@ -316,14 +322,15 @@ class AbstractPolynom(Explicable):
[< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, 2], [3, 4, 5], 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, 2, '+'] >, < <class 'pymath.calculus.expression.Expression'> [3, 4, '+', 5, '+'] >, 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [3, < <class 'pymath.calculus.expression.Expression'> [7, 5, '+'] >, 6]>] [< <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, 2], [3, 4, 5], 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, 2, '+'] >, < <class 'pymath.calculus.expression.Expression'> [3, 4, '+', 5, '+'] >, 6]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [3, < <class 'pymath.calculus.expression.Expression'> [7, 5, '+'] >, 6]>]
""" """
# TODO: It doesn't not compute quick enough |ven. févr. 27 18:04:01 CET 2015 # TODO: It doesn't not compute quick enough |ven. févr. 27 18:04:01 CET
# 2015
# gather steps for every coefficients # gather steps for every coefficients
coefs_steps = [] coefs_steps = []
for coef in self._coef: for coef in self._coef:
coef_steps = [] coef_steps = []
if type(coef) ==list: if isinstance(coef, list):
# Simplify each element before adding them # Simplify each element before adding them
s = [] s = []
for c in coef: for c in coef:
@@ -393,12 +400,13 @@ class AbstractPolynom(Explicable):
>>> AbstractPolynom.postfix_add([]) >>> AbstractPolynom.postfix_add([])
[0] [0]
""" """
if not type(numbers) == list: if not isinstance(numbers, list):
return [numbers] return [numbers]
elif numbers == []: elif numbers == []:
return [0] return [0]
else: else:
ans = [[a, op.add] if i!=0 else [a] for (i,a) in enumerate(numbers)] ans = [[a, op.add] if i != 0 else [a]
for (i, a) in enumerate(numbers)]
return list(chain.from_iterable(ans)) return list(chain.from_iterable(ans))
def __eq__(self, other): def __eq__(self, other):
@@ -430,7 +438,8 @@ class AbstractPolynom(Explicable):
n_coef = spe_zip(self._coef, o_poly._coef) n_coef = spe_zip(self._coef, o_poly._coef)
p = AbstractPolynom(n_coef, letter=self._letter) p = AbstractPolynom(n_coef, letter=self._letter)
ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.add])] ini_step = [Expression(self.postfix_tokens +
o_poly.postfix_tokens + [op.add])]
ans = p.simplify() ans = p.simplify()
ans.steps = ini_step + ans.steps ans.steps = ini_step + ans.steps
return ans return ans
@@ -450,7 +459,8 @@ class AbstractPolynom(Explicable):
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', '-'] >] [< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', '-'] >]
""" """
ini_step = [Expression(self.postfix_tokens + [op.sub1])] ini_step = [Expression(self.postfix_tokens + [op.sub1])]
ans = AbstractPolynom([-i for i in self._coef], letter = self._letter).simplify() ans = AbstractPolynom([-i for i in self._coef],
letter=self._letter).simplify()
ans.steps = ini_step + ans.steps ans.steps = ini_step + ans.steps
return ans return ans
@@ -473,7 +483,8 @@ class AbstractPolynom(Explicable):
[< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', 5, 'x', '*', '+', 4, '+', '-'] >, < <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', '-', 5, 'x', '*', '-', 4, '-', '+'] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, -4], [2, -5], [3, -6]]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, -4, '+'] >, < <class 'pymath.calculus.expression.Expression'> [2, -5, '+'] >, < <class 'pymath.calculus.expression.Expression'> [3, -6, '+'] >]>] [< <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', 5, 'x', '*', '+', 4, '+', '-'] >, < <class 'pymath.calculus.expression.Expression'> [3, 'x', 2, '^', '*', 2, 'x', '*', '+', 1, '+', 6, 'x', 2, '^', '*', '-', 5, 'x', '*', '-', 4, '-', '+'] >, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [[1, -4], [2, -5], [3, -6]]>, < <class 'pymath.calculus.abstract_polynom.AbstractPolynom'> [< <class 'pymath.calculus.expression.Expression'> [1, -4, '+'] >, < <class 'pymath.calculus.expression.Expression'> [2, -5, '+'] >, < <class 'pymath.calculus.expression.Expression'> [3, -6, '+'] >]>]
""" """
o_poly = self.conv2poly(other) o_poly = self.conv2poly(other)
ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.sub])] ini_step = [Expression(self.postfix_tokens +
o_poly.postfix_tokens + [op.sub])]
o_poly = -o_poly o_poly = -o_poly
#ini_step += o_poly.steps #ini_step += o_poly.steps
@@ -533,13 +544,14 @@ class AbstractPolynom(Explicable):
if coefs[i + j] == 0: if coefs[i + j] == 0:
coefs[i + j] = elem coefs[i + j] = elem
elif elem != 0: elif elem != 0:
if type(coefs[i+j]) == list: if isinstance(coefs[i + j], list):
coefs[i + j] += [elem] coefs[i + j] += [elem]
else: else:
coefs[i + j] = [coefs[i + j], elem] coefs[i + j] = [coefs[i + j], elem]
p = AbstractPolynom(coefs, letter=self._letter) p = AbstractPolynom(coefs, letter=self._letter)
ini_step = [Expression(self.postfix_tokens + o_poly.postfix_tokens + [op.mul])] ini_step = [Expression(self.postfix_tokens +
o_poly.postfix_tokens + [op.mul])]
ans = p.simplify() ans = p.simplify()
ans.steps = [ini_step] + ans.steps ans.steps = [ini_step] + ans.steps
@@ -573,7 +585,9 @@ class AbstractPolynom(Explicable):
""" """
if not type(power): if not type(power):
raise ValueError("Can't raise {obj} to {pw} power".format(obj = self.__class__, pw = str(power))) raise ValueError(
"Can't raise {obj} to {pw} power".format(
obj=self.__class__, pw=str(power)))
ini_step = [Expression(self.postfix_tokens + [power, op.pw])] ini_step = [Expression(self.postfix_tokens + [power, op.pw])]
@@ -583,15 +597,18 @@ class AbstractPolynom(Explicable):
p = AbstractPolynom(coefs, letter=self._letter) p = AbstractPolynom(coefs, letter=self._letter)
ans = p ans = p
else: else:
coefs = [0]*self.degree*power + [Expression([self._coef[self.degree] , power, op.pw])] coefs = [0] * self.degree * power + \
[Expression([self._coef[self.degree], power, op.pw])]
p = AbstractPolynom(coefs, letter=self._letter) p = AbstractPolynom(coefs, letter=self._letter)
ans = p.simplify() ans = p.simplify()
else: else:
if power == 2: if power == 2:
ans = self * self ans = self * self
else: else:
# TODO: faudrait changer ça c'est pas très sérieux |ven. févr. 27 22:08:00 CET 2015 # TODO: faudrait changer ça c'est pas très sérieux |ven. févr.
raise AttributeError("__pw__ not implemented yet when power is greatter than 2") # 27 22:08:00 CET 2015
raise AttributeError(
"__pw__ not implemented yet when power is greatter than 2")
ans.steps = ini_step + ans.steps ans.steps = ini_step + ans.steps
return ans return ans

1
pymath/calculus/arithmetic.py
View File

@@ -4,6 +4,7 @@
__all__ = ['gcd'] __all__ = ['gcd']
def gcd(a, b): def gcd(a, b):
"""Compute gcd(a,b) """Compute gcd(a,b)

7
pymath/calculus/explicable.py
View File

@@ -3,6 +3,7 @@
from .render import txt, tex from .render import txt, tex
class Renderable(object): class Renderable(object):
""" """
A Renderable object is an object which can work with Render class. It means that it has to have attribute postfix_tokens. A Renderable object is an object which can work with Render class. It means that it has to have attribute postfix_tokens.
@@ -56,6 +57,7 @@ class Renderable(object):
""" """
class TmpRenderEnv(object): class TmpRenderEnv(object):
def __enter__(self): def __enter__(self):
self.old_render = Renderable.get_render() self.old_render = Renderable.get_render()
Renderable.set_render(render) Renderable.set_render(render)
@@ -72,7 +74,6 @@ class Renderable(object):
return False return False
class Explicable(Renderable): class Explicable(Renderable):
""" An Explicable object is an object which can be explicable! """ An Explicable object is an object which can be explicable!
@@ -82,6 +83,7 @@ class Explicable(Renderable):
* explain: Generator which return steps which leed to himself * explain: Generator which return steps which leed to himself
""" """
def __init__(self, *args, **kwargs): def __init__(self, *args, **kwargs):
self.steps = [] self.steps = []
@@ -126,9 +128,6 @@ class Explicable(Renderable):
return False return False
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

75
pymath/calculus/expression.py
View File

@@ -13,13 +13,16 @@ from .random_expression import RdExpression
__all__ = ['Expression'] __all__ = ['Expression']
class Fake_int(int, Explicable): class Fake_int(int, Explicable):
isNumber = True isNumber = True
def __init__(self, val): def __init__(self, val):
super(Fake_int, self).__init__(val) super(Fake_int, self).__init__(val)
self._val = val self._val = val
self.postfix_tokens = [self] self.postfix_tokens = [self]
self.steps = [] self.steps = []
def simplify(self): def simplify(self):
return Fake_int(self._val) return Fake_int(self._val)
@@ -87,44 +90,56 @@ class Expression(Explicable):
""" """
expression = object.__new__(cls) expression = object.__new__(cls)
if type(exp) == str: if isinstance(exp, str):
expression.postfix_tokens = str2tokens(exp) expression.postfix_tokens = str2tokens(exp)
elif type(exp) == list: elif isinstance(exp, list):
# Ici on ne peut convertir les "+" en opérateur que s'ils sont d'arité 2. # Ici on ne peut convertir les "+" en opérateur que s'ils sont
exp_mod_op = [op.get_op(i) if op.can_be_operator(i) else i for i in exp] # d'arité 2.
expression.postfix_tokens = flatten_list([tok.postfix_tokens if Expression.isExpression(tok) else tok for tok in exp_mod_op]) 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 type(exp) == Expression: elif isinstance(exp, Expression):
return exp return exp
elif isNumerand(exp): elif isNumerand(exp):
expression.postfix_tokens = [exp] expression.postfix_tokens = [exp]
else: else:
raise ValueError("Can't build Expression with {} object".format(type(exp))) raise ValueError(
"Can't build Expression with {} object".format(
type(exp)))
if len(expression.postfix_tokens) == 1: if len(expression.postfix_tokens) == 1:
token = expression.postfix_tokens[0] token = expression.postfix_tokens[0]
if type(token) == Fake_int or type(token) == int: if isinstance(token, Fake_int) or isinstance(token, int):
return Fake_int(token) return Fake_int(token)
elif hasattr(token, 'simplify') and hasattr(token, 'explain'): elif hasattr(token, 'simplify') and hasattr(token, 'explain'):
ans = expression.postfix_tokens[0] ans = expression.postfix_tokens[0]
return ans return ans
elif type(token) == str: elif isinstance(token, str):
# TODO: Pourquoi ne pas créer directement un polynom ici? |jeu. févr. 26 18:59:24 CET 2015 # TODO: Pourquoi ne pas créer directement un polynom ici? |jeu. févr. 26 18:59:24 CET 2015
# On crée un faux str en ajoutant la méthode simplify et simplified et la caractérisique isNumber # On crée un faux str en ajoutant la méthode simplify et
# simplified et la caractérisique isNumber
simplify = lambda x: [x] simplify = lambda x: [x]
is_polynom = True is_polynom = True
methods_attr = {'simplify':simplify, '_isPolynom': is_polynom, 'postfix_tokens': [token]} methods_attr = {
fake_token = type('fake_str', (str,Explicable, ), methods_attr)(token) 'simplify': simplify,
'_isPolynom': is_polynom,
'postfix_tokens': [token]}
fake_token = type(
'fake_str', (str, Explicable, ), methods_attr)(token)
return fake_token return fake_token
else: else:
raise ValueError("Unknow token type in Expression: {}".format(type(token))) raise ValueError(
"Unknow token type in Expression: {}".format(
type(token)))
else: else:
expression._isExpression = 1 expression._isExpression = 1
@@ -139,7 +154,8 @@ class Expression(Explicable):
return self.STR_RENDER(self.postfix_tokens) return self.STR_RENDER(self.postfix_tokens)
def __repr__(self): def __repr__(self):
return " ".join(["<", str(self.__class__) , str(self.postfix_tokens), ">"]) return " ".join(["<", str(self.__class__),
str(self.postfix_tokens), ">"])
def simplify(self): def simplify(self):
""" Compute entirely the expression and return the result with .steps attribute """ """ Compute entirely the expression and return the result with .steps attribute """
@@ -157,7 +173,8 @@ class Expression(Explicable):
tmpTokenList = [] tmpTokenList = []
while len(tokenList) > 2: while len(tokenList) > 2:
# on va chercher les motifs du genre A B +, quand l'operateur est d'arité 2, pour les calculer # 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]) \ if isNumerand(tokenList[0]) and isNumerand(tokenList[1]) \
and isOperator(tokenList[2]) and tokenList[2].arity == 2: and isOperator(tokenList[2]) and tokenList[2].arity == 2:
@@ -170,7 +187,8 @@ class Expression(Explicable):
tmpTokenList.append(res) tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes # Comme on vient de faire le calcul, on peut détruire aussi les
# deux prochains termes
del tokenList[0:3] del tokenList[0:3]
# Et les motifs du gens A -, quand l'operateur est d'arité 1 # Et les motifs du gens A -, quand l'operateur est d'arité 1
@@ -185,7 +203,8 @@ class Expression(Explicable):
tmpTokenList.append(res) tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes # Comme on vient de faire le calcul, on peut détruire aussi les
# deux prochains termes
del tokenList[0:2] del tokenList[0:2]
else: else:
@@ -203,7 +222,8 @@ class Expression(Explicable):
tmpTokenList.append(res) tmpTokenList.append(res)
# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes # Comme on vient de faire le calcul, on peut détruire aussi les
# deux prochains termes
del tokenList[0:2] del tokenList[0:2]
tmpTokenList += tokenList tmpTokenList += tokenList
@@ -255,17 +275,23 @@ class Expression(Explicable):
# Some math manipulations # Some math manipulations
def operate(self, other, operator): def operate(self, other, operator):
if type(other) == Expression: if isinstance(other, Expression):
return Expression(self.postfix_tokens + other.postfix_tokens + [operator]) return Expression(
elif type(other) == list: self.postfix_tokens +
other.postfix_tokens +
[operator])
elif isinstance(other, list):
return Expression(self.postfix_tokens + other + [operator]) return Expression(self.postfix_tokens + other + [operator])
else: else:
return Expression(self.postfix_tokens + [other] + [operator]) return Expression(self.postfix_tokens + [other] + [operator])
def roperate(self, other, operator): def roperate(self, other, operator):
if type(other) == Expression: if isinstance(other, Expression):
return Expression(other.postfix_tokens + self.postfix_tokens + [operator]) return Expression(
elif type(other) == list: other.postfix_tokens +
self.postfix_tokens +
[operator])
elif isinstance(other, list):
return Expression(other + self.postfix_tokens + [operator]) return Expression(other + self.postfix_tokens + [operator])
else: else:
return Expression([other] + self.postfix_tokens + [operator]) return Expression([other] + self.postfix_tokens + [operator])
@@ -377,7 +403,6 @@ if __name__ == '__main__':
# print(type(Ar)) # print(type(Ar))
# print('\n-----------') # print('\n-----------')
#A = Expression("-6 / 3 + 10 / -5") #A = Expression("-6 / 3 + 10 / -5")
#Ar = A.simplify() #Ar = A.simplify()

83
pymath/calculus/fraction.py
View File

@@ -12,6 +12,7 @@ from copy import copy
__all__ = ['Fraction'] __all__ = ['Fraction']
class Fraction(Explicable): class Fraction(Explicable):
"""Fractions!""" """Fractions!"""
@@ -61,7 +62,7 @@ class Fraction(Explicable):
if self._num == 0: if self._num == 0:
return Expression([0]) return Expression([0])
elif type(self._num) == Fraction or type(self._denom) == Fraction: elif isinstance(self._num, Fraction) or isinstance(self._denom, Fraction):
return self._num / self._denom return self._num / self._denom
elif self._denom < 0: elif self._denom < 0:
@@ -77,7 +78,13 @@ class Fraction(Explicable):
elif gcd_ != 1: elif gcd_ != 1:
n_frac = Fraction(self._num // gcd_, self._denom // gcd_) n_frac = Fraction(self._num // gcd_, self._denom // gcd_)
ini_step += [Expression([n_frac._num, gcd_, op.mul, n_frac._denom, gcd_, op.mul, op.div ])] ini_step += [Expression([n_frac._num,
gcd_,
op.mul,
n_frac._denom,
gcd_,
op.mul,
op.div])]
n_frac.steps = ini_step + n_frac.steps n_frac.steps = ini_step + n_frac.steps
return n_frac return n_frac
@@ -103,7 +110,8 @@ class Fraction(Explicable):
return str(Expression(self.postfix_tokens)) return str(Expression(self.postfix_tokens))
def __repr__(self): def __repr__(self):
return "< Fraction {num} / {denom}>".format(num=self._num, denom = self._denom) return "< Fraction {num} / {denom}>".format(
num=self._num, denom=self._denom)
def __txt__(self): def __txt__(self):
old_render = Expression.get_render() old_render = Expression.get_render()
@@ -126,7 +134,7 @@ class Fraction(Explicable):
def convert2fraction(self, other): def convert2fraction(self, other):
""" Convert a other into a fraction """ """ Convert a other into a fraction """
if type(other) == Fraction: if isinstance(other, Fraction):
# cool # cool
number = other number = other
else: else:
@@ -188,10 +196,25 @@ class Fraction(Explicable):
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
exp = Expression([self._num, coef1, op.mul, self._denom, coef1, op.mul, op.div, number._num, coef2, op.mul, number._denom, coef2, op.mul, op.div,op.add]) exp = Expression([self._num,
coef1,
op.mul,
self._denom,
coef1,
op.mul,
op.div,
number._num,
coef2,
op.mul,
number._denom,
coef2,
op.mul,
op.div,
op.add])
ans = exp.simplify() ans = exp.simplify()
ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.add]) ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.add])
ans.steps = [ini_step] + ans.steps ans.steps = [ini_step] + ans.steps
return ans return ans
@@ -240,9 +263,24 @@ class Fraction(Explicable):
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
exp = Expression([self._num, coef1, op.mul, self._denom, coef1, op.mul, op.div, number._num, coef2, op.mul, number._denom, coef2, op.mul, op.div,op.sub]) exp = Expression([self._num,
coef1,
op.mul,
self._denom,
coef1,
op.mul,
op.div,
number._num,
coef2,
op.mul,
number._denom,
coef2,
op.mul,
op.div,
op.sub])
ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.sub]) ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.sub])
ans = exp.simplify() ans = exp.simplify()
ans.steps = [ini_step] + ans.steps ans.steps = [ini_step] + ans.steps
return ans return ans
@@ -313,9 +351,10 @@ class Fraction(Explicable):
elif other == 1: elif other == 1:
return copy(self) return copy(self)
# TODO: Changer dans le cas où il y a trop de 1 |dim. déc. 28 10:44:10 CET 2014 # TODO: Changer dans le cas où il y a trop de 1 |dim. déc. 28 10:44:10
# CET 2014
elif type(other) == int: elif isinstance(other, int):
gcd1 = gcd(other, self._denom) gcd1 = gcd(other, self._denom)
if gcd1 != 1: if gcd1 != 1:
num = [self._num, int(other / gcd1), op.mul, gcd1, op.mul] num = [self._num, int(other / gcd1), op.mul, gcd1, op.mul]
@@ -346,10 +385,15 @@ class Fraction(Explicable):
num2 = [number._num] num2 = [number._num]
denom1 = [self._denom] denom1 = [self._denom]
exp = Expression(num1 +
num2 +
[op.mul] +
denom1 +
denom2 +
[op.mul, op.div])
exp = Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div]) ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.mul])
ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.mul])
ans = exp.simplify() ans = exp.simplify()
ans.steps = [ini_step] + ans.steps ans.steps = [ini_step] + ans.steps
return ans return ans
@@ -381,7 +425,8 @@ class Fraction(Explicable):
number = self.convert2fraction(other) number = self.convert2fraction(other)
ini_step = Expression(self.postfix_tokens + number.postfix_tokens + [op.div]) ini_step = Expression(self.postfix_tokens +
number.postfix_tokens + [op.div])
number = Fraction(number._denom, number._num) number = Fraction(number._denom, number._num)
ans = self * number ans = self * number
@@ -421,8 +466,10 @@ class Fraction(Explicable):
< <class 'pymath.calculus.expression.Expression'> [27, 8, '*', 8, 8, '*', '/'] > < <class 'pymath.calculus.expression.Expression'> [27, 8, '*', 8, 8, '*', '/'] >
""" """
if not type(power) == int: if not isinstance(power, int):
raise ValueError("Can't raise fraction to power {}".format(str(power))) raise ValueError(
"Can't raise fraction to power {}".format(
str(power)))
if power == 0: if power == 0:
return Expression([1]) return Expression([1])
@@ -430,7 +477,8 @@ class Fraction(Explicable):
return copy(self) return copy(self)
else: else:
ini_step = Expression(self.postfix_tokens + [power, op.pw]) ini_step = Expression(self.postfix_tokens + [power, op.pw])
exp = Expression([self._num, power, op.pw, self._denom, power, op.pw, op.div]) exp = Expression(
[self._num, power, op.pw, self._denom, power, op.pw, op.div])
ans = exp.simplify() ans = exp.simplify()
ans.steps = [ini_step] + ans.steps ans.steps = [ini_step] + ans.steps
@@ -485,7 +533,6 @@ class Fraction(Explicable):
return Fraction(self._num, self._denom) return Fraction(self._num, self._denom)
if __name__ == '__main__': if __name__ == '__main__':
f = Fraction(1, 12) f = Fraction(1, 12)
g = Fraction(6, 12) g = Fraction(6, 12)

29
pymath/calculus/generic.py
View File

@@ -4,6 +4,7 @@
from itertools import zip_longest from itertools import zip_longest
class Stack(object): class Stack(object):
"""Docstring for Stack """ """Docstring for Stack """
@@ -54,6 +55,7 @@ class Stack(object):
def __add__(self, addList): def __add__(self, addList):
return self.items + addList return self.items + addList
def flatten_list(a, result=None): def flatten_list(a, result=None):
"""Flattens a nested list. """Flattens a nested list.
@@ -71,6 +73,7 @@ def flatten_list(a, result=None):
return result return result
def first_elem(ll): def first_elem(ll):
"""Get the first element in imbricates lists """Get the first element in imbricates lists
# TODO: Fonction pourrie mais j'ai pas le temps de faire mieux! |mar. janv. 28 22:32:22 CET 2014 # TODO: Fonction pourrie mais j'ai pas le temps de faire mieux! |mar. janv. 28 22:32:22 CET 2014
@@ -93,13 +96,14 @@ def first_elem(ll):
""" """
if hasattr(ll, '__contains__'): if hasattr(ll, '__contains__'):
if len(ll) == 1 and type(ll) == str: if len(ll) == 1 and isinstance(ll, str):
return ll[0] return ll[0]
else: else:
return first_elem(ll[0]) return first_elem(ll[0])
else: else:
return ll return ll
def last_elem(ll): def last_elem(ll):
"""Get the last element in imbricates lists """Get the last element in imbricates lists
# TODO: Fonction pourrie mais j'ai pas le temps de faire mieux! |mar. janv. 28 22:32:22 CET 2014 # TODO: Fonction pourrie mais j'ai pas le temps de faire mieux! |mar. janv. 28 22:32:22 CET 2014
@@ -122,7 +126,7 @@ def last_elem(ll):
""" """
if hasattr(ll, '__contains__'): if hasattr(ll, '__contains__'):
if len(ll) == 1 and type(ll) == str: if len(ll) == 1 and isinstance(ll, str):
return ll[-1] return ll[-1]
else: else:
return last_elem(ll[-1]) return last_elem(ll[-1])
@@ -139,7 +143,7 @@ def expand_list(list_list):
[[1, 2, 4, 5, 6, 7, 8]] [[1, 2, 4, 5, 6, 7, 8]]
""" """
list_in_list = [i for i in list_list if type(i) == list].copy() list_in_list = [i for i in list_list if isinstance(i, list)].copy()
try: try:
nbr_ans_list = max([len(i) for i in list_in_list]) nbr_ans_list = max([len(i) for i in list_in_list])
@@ -147,7 +151,7 @@ def expand_list(list_list):
ans = [list_list.copy() for i in range(nbr_ans_list)] ans = [list_list.copy() for i in range(nbr_ans_list)]
for (i, l) in enumerate(ans): for (i, l) in enumerate(ans):
for (j, e) in enumerate(l): for (j, e) in enumerate(l):
if type(e) == list: if isinstance(e, list):
ans[i][j] = e[min(i, len(e) - 1)] ans[i][j] = e[min(i, len(e) - 1)]
# S'il n'y a pas de liste dans la liste (2e exemple) # S'il n'y a pas de liste dans la liste (2e exemple)
except ValueError: except ValueError:
@@ -155,6 +159,7 @@ def expand_list(list_list):
return ans return ans
def add_in_dict(dict1, dict2): def add_in_dict(dict1, dict2):
"""Merge dictionary keys and add the content from dict1 and dict2 """Merge dictionary keys and add the content from dict1 and dict2
@@ -180,6 +185,7 @@ def add_in_dict(dict1, dict2):
return new_dict return new_dict
def remove_in_dict(d, value=0): def remove_in_dict(d, value=0):
""" In a dictionary, remove keys which have certain value """ In a dictionary, remove keys which have certain value
@@ -198,8 +204,9 @@ def remove_in_dict(d, value = 0):
new_dict[k] = v new_dict[k] = v
return new_dict return new_dict
def convolution_dict(D1, D2, op = lambda x,y:x*y,\
op_key = lambda x,y: x + y, \ def convolution_dict(D1, D2, op=lambda x, y: x * y,
op_key=lambda x, y: x + y,
commutative=True, op_twice=lambda x, y: x + y): commutative=True, op_twice=lambda x, y: x + y):
"""Convolution of two dictionaries """Convolution of two dictionaries
@@ -240,6 +247,7 @@ def convolution_dict(D1, D2, op = lambda x,y:x*y,\
return new_dict return new_dict
def spe_zip(l1, l2): def spe_zip(l1, l2):
"""Zip two lists, if a list is longer, only it's element are taken """Zip two lists, if a list is longer, only it's element are taken
@@ -252,12 +260,13 @@ def spe_zip(l1,l2):
ans = [] ans = []
for i in tmp: for i in tmp:
if None in i: if None in i:
j = [a for a in i if a != None][-1] j = [a for a in i if a is not None][-1]
else: else:
j = list(i) j = list(i)
ans.append(j) ans.append(j)
return ans return ans
def transpose_fill(list_lists): def transpose_fill(list_lists):
"""Transpose a list of list and if inside list have not the same length, fill with last token """Transpose a list of list and if inside list have not the same length, fill with last token
@@ -277,6 +286,7 @@ def transpose_fill(list_lists):
yield col yield col
def isOperator(exp): def isOperator(exp):
"""Check if the expression is an opération in "+-*/:^" """Check if the expression is an opération in "+-*/:^"
@@ -292,6 +302,7 @@ def isOperator(exp):
return 0 return 0
return 1 return 1
def isNumber(exp): def isNumber(exp):
"""Check if the expression can be a number """Check if the expression can be a number
@@ -302,12 +313,13 @@ def isNumber(exp):
try: try:
exp.isNumber exp.isNumber
except AttributeError: except AttributeError:
if type(exp) == int: if isinstance(exp, int):
return 1 return 1
else: else:
return 0 return 0
return 1 return 1
def isPolynom(exp): def isPolynom(exp):
"""Check if the expression can be a polynom """Check if the expression can be a polynom
@@ -330,6 +342,7 @@ def isPolynom(exp):
return 0 return 0
return 1 return 1
def isNumerand(exp): def isNumerand(exp):
"""Check is the expression is something we can compute with """Check is the expression is something we can compute with

18
pymath/calculus/polynom.py
View File

@@ -13,6 +13,7 @@ import inspect
__all__ = ["Polynom"] __all__ = ["Polynom"]
def polynom_factory(func): def polynom_factory(func):
""" Decorator which specify the type of polynom that the function returns """ """ Decorator which specify the type of polynom that the function returns """
@wraps(func) @wraps(func)
@@ -31,6 +32,7 @@ def polynom_factory(func):
return P return P
return wrapper return wrapper
class Polynom(AbstractPolynom): class Polynom(AbstractPolynom):
"""Polynom view as a function. """Polynom view as a function.
@@ -47,7 +49,13 @@ class Polynom(AbstractPolynom):
""" """
@classmethod @classmethod
def random(self, coefs_form=[], conditions=[], letter = "x", degree = 0, name = "P"): def random(
self,
coefs_form=[],
conditions=[],
letter="x",
degree=0,
name="P"):
""" Create a random polynom from coefs_form and conditions """ Create a random polynom from coefs_form and conditions
:param coefs_form: list of forms (one by coef) (ascending degree sorted) :param coefs_form: list of forms (one by coef) (ascending degree sorted)
@@ -78,7 +86,7 @@ class Polynom(AbstractPolynom):
# On créé les valeurs toutes concaténées dans un string # On créé les valeurs toutes concaténées dans un string
coefs = RdExpression(form, conditions)() coefs = RdExpression(form, conditions)()
# On "parse" ce string pour créer les coefs # On "parse" ce string pour créer les coefs
coefs = [eval(i) if type(i)==str else i for i in eval(coefs)] coefs = [eval(i) if isinstance(i, str) else i for i in eval(coefs)]
# Création du polynom # Création du polynom
return Polynom(coefs=coefs, letter=letter, name=name) return Polynom(coefs=coefs, letter=letter, name=name)
@@ -141,7 +149,8 @@ class Polynom(AbstractPolynom):
# if isNumerand(value) or Expression.isExpression(value): # if isNumerand(value) or Expression.isExpression(value):
# postfix_exp = [value if i==self._letter else i for i in self.postfix_tokens] # postfix_exp = [value if i==self._letter else i for i in self.postfix_tokens]
# else: # else:
postfix_exp = [Expression(value) if i==self._letter else i for i in self.postfix_tokens] postfix_exp = [
Expression(value) if i == self._letter else i for i in self.postfix_tokens]
return Expression(postfix_exp).simplify() return Expression(postfix_exp).simplify()
@@ -194,7 +203,8 @@ if __name__ == '__main__':
# print(p-q) # print(p-q)
# for i in p-q: # for i in p-q:
# print(i) # print(i)
#Polynom.random(degree = 2, conditions=["{b**2-4*a*c}>0"]) # Polynom deg 2 with positive Delta (ax^2 + bx + c) # Polynom.random(degree = 2, conditions=["{b**2-4*a*c}>0"]) # Polynom deg
# 2 with positive Delta (ax^2 + bx + c)
#import doctest #import doctest
# doctest.testmod(optionflags=doctest.ELLIPSIS) # doctest.testmod(optionflags=doctest.ELLIPSIS)

44
pymath/calculus/polynomDeg2.py
View File

@@ -12,6 +12,7 @@ from sympy import sqrt, latex
__all__ = ["Polynom_deg2"] __all__ = ["Polynom_deg2"]
class Polynom_deg2(Polynom): class Polynom_deg2(Polynom):
""" Degree 2 polynoms """ Degree 2 polynoms
@@ -19,7 +20,15 @@ class Polynom_deg2(Polynom):
""" """
@classmethod @classmethod
def random(self, coefs_form = ["{c}", "{b}", "{a}"], conditions = [], letter = "x", name = "P"): def random(
self,
coefs_form=[
"{c}",
"{b}",
"{a}"],
conditions=[],
letter="x",
name="P"):
""" Create a 2nd degree poly from coefs_form ans conditions """ Create a 2nd degree poly from coefs_form ans conditions
:param coefs_form: list of forms (one by coef) (ascending degree sorted) :param coefs_form: list of forms (one by coef) (ascending degree sorted)
@@ -28,13 +37,15 @@ class Polynom_deg2(Polynom):
""" """
if len(coefs_form) != 3: if len(coefs_form) != 3:
raise ValueError("Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(len(coefs_form))) raise ValueError(
"Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(
len(coefs_form)))
form = str(coefs_form) form = str(coefs_form)
# On créé les valeurs toutes concaténées dans un string # On créé les valeurs toutes concaténées dans un string
coefs = RdExpression(form, conditions)() coefs = RdExpression(form, conditions)()
# On "parse" ce string pour créer les coefs # On "parse" ce string pour créer les coefs
coefs = [eval(i) if type(i)==str else i for i in eval(coefs)] coefs = [eval(i) if isinstance(i, str) else i for i in eval(coefs)]
# Création du polynom # Création du polynom
return Polynom_deg2(coefs=coefs, letter=letter, name=name) return Polynom_deg2(coefs=coefs, letter=letter, name=name)
@@ -45,9 +56,12 @@ class Polynom_deg2(Polynom):
name = poly.name name = poly.name
if len(coefs) < 3 or len(coefs) > 4: if len(coefs) < 3 or len(coefs) > 4:
raise ValueError("Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(len(coefs))) raise ValueError(
"Polynom_deg2 have to be degree 2 polynoms, they need 3 coefficients, {} are given".format(
len(coefs)))
if coefs[2] == 0: if coefs[2] == 0:
raise ValueError("Polynom_deg2 have to be degree 2 polynoms, coefficient of x^2 can't be 0") raise ValueError(
"Polynom_deg2 have to be degree 2 polynoms, coefficient of x^2 can't be 0")
Polynom.__init__(self, coefs, letter, name=name) Polynom.__init__(self, coefs, letter, name=name)
@property @property
@@ -78,7 +92,8 @@ class Polynom_deg2(Polynom):
-8 -8
""" """
return Expression([self.b, 2, op.pw, 4, self.a, self.c, op.mul, op.mul, op.sub]).simplify() return Expression([self.b, 2, op.pw, 4, self.a,
self.c, op.mul, op.mul, op.sub]).simplify()
@property @property
def alpha(self): def alpha(self):
@@ -94,7 +109,8 @@ class Polynom_deg2(Polynom):
\\frac{ -1 \\times 2 }{ 3 \\times 2 } \\frac{ -1 \\times 2 }{ 3 \\times 2 }
\\frac{ -1 }{ 3 } \\frac{ -1 }{ 3 }
""" """
return Expression([self.b, op.sub1, 2, self.a, op.mul, op.div]).simplify() return Expression([self.b, op.sub1, 2, self.a,
op.mul, op.div]).simplify()
@property @property
def beta(self): def beta(self):
@@ -146,7 +162,8 @@ class Polynom_deg2(Polynom):
['-2 - \\\\sqrt{3}', '-2 + \\\\sqrt{3}'] ['-2 - \\\\sqrt{3}', '-2 + \\\\sqrt{3}']
""" """
if self.delta > 0: if self.delta > 0:
self._roots = [latex((-self.b - sqrt(self.delta))/(2*self.a)), latex((-self.b + sqrt(self.delta))/(2*self.a))] self._roots = [latex((-self.b - sqrt(self.delta)) / (2 * self.a)),
latex((-self.b + sqrt(self.delta)) / (2 * self.a))]
elif self.delta == 0: elif self.delta == 0:
self._roots = [Fraction(-self.b, 2 * self.a).simplify()] self._roots = [Fraction(-self.b, 2 * self.a).simplify()]
else: else:
@@ -156,7 +173,8 @@ class Polynom_deg2(Polynom):
def tbl_sgn_header(self): def tbl_sgn_header(self):
""" Return header of the sign line for tkzTabLine""" """ Return header of the sign line for tkzTabLine"""
if self.delta > 0: if self.delta > 0:
return "{$-\\infty$, $" + str(min(self.roots())) + "$ , $" + str( max(self.roots())) + "$ , $+\\infty$}" return "{$-\\infty$, $" + str(min(self.roots())) + \
"$ , $" + str(max(self.roots())) + "$ , $+\\infty$}"
elif self.delta == 0: elif self.delta == 0:
return "{$-\\infty$, $" + str(self.roots()[0]) + "$ , $+\\infty$}" return "{$-\\infty$, $" + str(self.roots()[0]) + "$ , $+\\infty$}"
else: else:
@@ -215,9 +233,11 @@ class Polynom_deg2(Polynom):
beta = self.beta beta = self.beta
if limits: if limits:
if self.a > 0: if self.a > 0:
return "\\tkzTabVar{+/{$+\\infty$}, -/{$" + str(beta) + "$}, +/{$+\\infty$}}" return "\\tkzTabVar{+/{$+\\infty$}, -/{$" + \
str(beta) + "$}, +/{$+\\infty$}}"
else: else:
return "\\tkzTabVar{-/{$-\\infty$}, +/{$" + str(beta) + "$}, -/{$-\\infty$}}" return "\\tkzTabVar{-/{$-\\infty$}, +/{$" + \
str(beta) + "$}, -/{$-\\infty$}}"
else: else:
if self.a > 0: if self.a > 0:
return "\\tkzTabVar{+/{}, -/{$" + str(beta) + "$}, +/{}}" return "\\tkzTabVar{+/{}, -/{$" + str(beta) + "$}, +/{}}"
@@ -242,8 +262,6 @@ if __name__ == '__main__':
doctest.testmod() doctest.testmod()
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

28
pymath/calculus/random_expression.py
View File

@@ -8,11 +8,13 @@ from .generic import flatten_list
from .arithmetic import gcd from .arithmetic import gcd
def random_str(form, conditions=[], val_min=-10, val_max=10): def random_str(form, conditions=[], val_min=-10, val_max=10):
""" Create a random string using RdExpression class """ """ Create a random string using RdExpression class """
random_str_generator = RdExpression(form, conditions) random_str_generator = RdExpression(form, conditions)
return random_str_generator(val_min, val_max) return random_str_generator(val_min, val_max)
class RdExpression(object): class RdExpression(object):
""" """
@@ -43,12 +45,14 @@ class RdExpression(object):
#varia_form = re.findall(pattern, self._form) #varia_form = re.findall(pattern, self._form)
# TODO: Bug with varia with spaces |dim. nov. 23 10:44:34 CET 2014 # TODO: Bug with varia with spaces |dim. nov. 23 10:44:34 CET 2014
varia_form = flatten_list([eval(str(i[0])) for i in pyparsing.nestedExpr('{','}').searchString(self._form)]) varia_form = flatten_list([eval(str(i[0])) for i in pyparsing.nestedExpr(
'{', '}').searchString(self._form)])
varia_form = set(varia_form) varia_form = set(varia_form)
varia_cond = set() varia_cond = set()
for c in self._conditions: for c in self._conditions:
c_varia_cond = flatten_list([eval(str(i[0])) for i in pyparsing.nestedExpr('{','}').searchString(c)]) c_varia_cond = flatten_list(
[eval(str(i[0])) for i in pyparsing.nestedExpr('{', '}').searchString(c)])
varia_cond = varia_cond | set(c_varia_cond) varia_cond = varia_cond | set(c_varia_cond)
self._2replaced = varia_cond | varia_form self._2replaced = varia_cond | varia_form
@@ -123,7 +127,6 @@ class RdExpression(object):
while self._gene_varia[l] == 0: while self._gene_varia[l] == 0:
self._gene_varia[l] = randint(val_min, val_max) self._gene_varia[l] = randint(val_min, val_max)
for e in self._2replaced: for e in self._2replaced:
self._gene_2replaced[e] = eval(e, globals(), self._gene_varia) self._gene_2replaced[e] = eval(e, globals(), self._gene_varia)
@@ -133,10 +136,14 @@ class RdExpression(object):
""" """
if self._conditions != []: if self._conditions != []:
return eval(" and ".join(self._conditions).format(**self._gene_2replaced)) return eval(
" and ".join(
self._conditions).format(
**self._gene_2replaced))
else: else:
return True return True
def desc_rdExp(rdExp): def desc_rdExp(rdExp):
print("--------------------") print("--------------------")
print("form: ", rdExp._form) print("form: ", rdExp._form)
@@ -156,18 +163,25 @@ if __name__ == '__main__':
print(random_str(form, cond)) print(random_str(form, cond))
form = "{a+a*10}*4 + {a} + 2*{b}" form = "{a+a*10}*4 + {a} + 2*{b}"
cond = ["{a} + {b} in [1, 2, 3, 4, 5]", "abs({a}) not in [1]", "{b} not in [1]", "gcd({a},{b}) == 1"] cond = [
"{a} + {b} in [1, 2, 3, 4, 5]",
"abs({a}) not in [1]",
"{b} not in [1]",
"gcd({a},{b}) == 1"]
print(random_str(form, cond)) print(random_str(form, cond))
form = "{a+a*10}*4 + {a} + 2*{b}" form = "{a+a*10}*4 + {a} + 2*{b}"
cond = ["{a-b} + {b} in list(range(20))", "abs({a}) not in [1]", "{b} not in [1]", "gcd({a},{b}) == 1"] cond = [
"{a-b} + {b} in list(range(20))",
"abs({a}) not in [1]",
"{b} not in [1]",
"gcd({a},{b}) == 1"]
print(random_str(form, cond)) print(random_str(form, cond))
import doctest import doctest
doctest.testmod() doctest.testmod()
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

15
pymath/calculus/render.py
View File

@@ -5,6 +5,7 @@ from .generic import Stack,isOperator
__all__ = ['txt', 'tex', 'p2i'] __all__ = ['txt', 'tex', 'p2i']
class Render(object): class Render(object):
""" Create functions which know how to render postfix tokens lists """ """ Create functions which know how to render postfix tokens lists """
@@ -15,7 +16,6 @@ class Render(object):
""" """
self.render = render self.render = render
def __call__(self, postfix_tokens): def __call__(self, postfix_tokens):
"""Make the object acting like a function """Make the object acting like a function
@@ -45,6 +45,7 @@ class Render(object):
else: else:
return operandeStack.pop() return operandeStack.pop()
def txt_render(token): def txt_render(token):
def render(*args): def render(*args):
try: try:
@@ -54,6 +55,8 @@ def txt_render(token):
return render return render
txt = Render(txt_render) txt = Render(txt_render)
def tex_render(token): def tex_render(token):
def render(*args): def render(*args):
try: try:
@@ -63,6 +66,7 @@ def tex_render(token):
return render return render
tex = Render(tex_render) tex = Render(tex_render)
def p2i_render(token): def p2i_render(token):
def render(*args): def render(*args):
try: try:
@@ -79,17 +83,16 @@ if __name__ == '__main__':
from pymath import Expression from pymath import Expression
from pymath import Fraction from pymath import Fraction
coefs_p = [[(i - 2), (j - 2)] for i, j in permutations(range(5), 2)] coefs_p = [[(i - 2), (j - 2)] for i, j in permutations(range(5), 2)]
coefs_q = [[2*(i-2),2*(j-2)] for i,j in permutations(range(5),2)] coefs_q = [[2 * (i - 2), 2 * (j - 2)]
for i, j in permutations(range(5), 2)]
l_p = [Polynom(i) for i in coefs_p] l_p = [Polynom(i) for i in coefs_p]
l_q = [Fraction(i, j) for i, j in coefs_q if j != 0] l_q = [Fraction(i, j) for i, j in coefs_q if j != 0]
operations = [Expression([l_p[i],l_q[j],op.mul]) for i,j in permutations(range(len(l_q)),2)] operations = [Expression([l_p[i], l_q[j], op.mul])
for i, j in permutations(range(len(l_q)), 2)]
for i in operations: for i in operations:
print(i) print(i)
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:

24
pymath/calculus/str2tokens.py
View File

@@ -4,6 +4,7 @@
from .generic import Stack, isOperator, isNumber, isPolynom from .generic import Stack, isOperator, isNumber, isPolynom
from .operator import op from .operator import op
def str2tokens(exp): def str2tokens(exp):
""" Parse the string into tokens then turn it into postfix form """ Parse the string into tokens then turn it into postfix form
@@ -19,6 +20,7 @@ def str2tokens(exp):
return post_tokens return post_tokens
def str2in_tokens(exp): def str2in_tokens(exp):
""" Parse the expression, ie tranform a string into a list of tokens """ Parse the expression, ie tranform a string into a list of tokens
@@ -37,14 +39,14 @@ def str2in_tokens(exp):
for character in exp: for character in exp:
if character.isdigit(): if character.isdigit():
# for "big" numbers (like 2345) # for "big" numbers (like 2345)
if type(tokens[-1]) == int: if isinstance(tokens[-1], int):
if tokens[-1] > 0: if tokens[-1] > 0:
tokens[-1] = tokens[-1] * 10 + int(character) tokens[-1] = tokens[-1] * 10 + int(character)
else: else:
tokens[-1] = tokens[-1] * 10 - int(character) tokens[-1] = tokens[-1] * 10 - int(character)
# Special case for "-" at the begining of an expression or before
# Special case for "-" at the begining of an expression or before "(" # "("
elif tokens[-1] == "-" and \ elif tokens[-1] == "-" and \
str(tokens[-2]) in " (+-*/:": str(tokens[-2]) in " (+-*/:":
tokens[-1] = - int(character) tokens[-1] = - int(character)
@@ -83,7 +85,6 @@ def str2in_tokens(exp):
return tokens[1:] return tokens[1:]
def in2post_fix(infix_tokens): def in2post_fix(infix_tokens):
""" From the infix_tokens list compute the corresponding postfix_tokens list """ From the infix_tokens list compute the corresponding postfix_tokens list
@@ -129,9 +130,11 @@ def in2post_fix(infix_tokens):
else: else:
arity = arity_Stack.pop() arity = arity_Stack.pop()
token_op = op.get_op(token, arity + 1) token_op = op.get_op(token, arity + 1)
# Reset arity to 0 in case there is other operators (the real operation would be "-op.arity + 1") # Reset arity to 0 in case there is other operators (the real
# operation would be "-op.arity + 1")
arity_Stack.push(0) arity_Stack.push(0)
while (not opStack.isEmpty()) and opStack.peek().priority >= token_op.priority: while (not opStack.isEmpty()) and opStack.peek(
).priority >= token_op.priority:
next_op = opStack.pop() next_op = opStack.pop()
postfix_tokens.append(next_op) postfix_tokens.append(next_op)
@@ -142,23 +145,24 @@ def in2post_fix(infix_tokens):
arity = arity_Stack.pop() arity = arity_Stack.pop()
arity_Stack.push(arity + 1) arity_Stack.push(arity + 1)
## Pour voir ce qu'il se passe dans cette procédure # Pour voir ce qu'il se passe dans cette procédure
#print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack)) #print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
while not opStack.isEmpty(): while not opStack.isEmpty():
next_op = opStack.pop() next_op = opStack.pop()
postfix_tokens.append(next_op) postfix_tokens.append(next_op)
## Pour voir ce qu'il se passe dans cette procédure # Pour voir ce qu'il se passe dans cette procédure
#print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack)) #print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
if arity_Stack.peek() != 1: if arity_Stack.peek() != 1:
raise ValueError("Unvalid expression. The arity Stack is ", str(arity_Stack)) raise ValueError(
"Unvalid expression. The arity Stack is ",
str(arity_Stack))
return postfix_tokens return postfix_tokens
if __name__ == '__main__': if __name__ == '__main__':
#a, s, m, d, p = Operator("+"), Operator("-"), Operator("*"), Operator("/"), Operator("^") #a, s, m, d, p = Operator("+"), Operator("-"), Operator("*"), Operator("/"), Operator("^")
#in_tokens = str2in_tokens("2+3*4") #in_tokens = str2in_tokens("2+3*4")

35
pymath/stat/dataset.py
View File

@@ -7,12 +7,14 @@
# #
# #
# TODO: Rendre toutes les réponses Explicable!! |mar. janv. 12 09:41:00 EAT 2016 # TODO: Rendre toutes les réponses Explicable!! |mar. janv. 12 09:41:00
# EAT 2016
from math import sqrt, ceil from math import sqrt, ceil
from .number_tools import number_factory from .number_tools import number_factory
from .random_generator import random_generator from .random_generator import random_generator
class Dataset(list): class Dataset(list):
""" A dataset (a list) with statistics and latex rendering methods """ A dataset (a list) with statistics and latex rendering methods
@@ -30,10 +32,10 @@ class Dataset(list):
""" """
@classmethod @classmethod
def random(cls, length, data_name = "Valeurs", \ def random(cls, length, data_name="Valeurs",
distrib = "gauss", rd_args = (0,1), \ distrib="gauss", rd_args=(0, 1),
nbr_format = lambda x:round(x,2), \ nbr_format=lambda x: round(x, 2),
v_min = None, v_max = None, \ v_min=None, v_max=None,
exact_mean=None): exact_mean=None):
""" Generate a random list of value """ Generate a random list of value
@@ -45,10 +47,10 @@ class Dataset(list):
:param v_max: maximum accepted value :param v_max: maximum accepted value
:param exact_mean: if set, the last generated number will be create in order that the computed mean is exacly equal to "exact_mean" :param exact_mean: if set, the last generated number will be create in order that the computed mean is exacly equal to "exact_mean"
""" """
data = random_generator(length,\ data = random_generator(length,
distrib, rd_args, \ distrib, rd_args,
nbr_format, \ nbr_format,
v_min, v_max, \ v_min, v_max,
exact_mean) exact_mean)
return cls(data, data_name=data_name) return cls(data, data_name=data_name)
@@ -113,7 +115,12 @@ class Dataset(list):
>>> w.quartiles() >>> w.quartiles()
(0, 2.5, 5.5, 8.5, 11) (0, 2.5, 5.5, 8.5, 11)
""" """
return (min(self) , self.quartile(1) , self.quartile(2) , self.quartile(3), max(self)) return (
min(self),
self.quartile(1),
self.quartile(2),
self.quartile(3),
max(self))
@number_factory @number_factory
def quartile(self, quartile=1): def quartile(self, quartile=1):
@@ -166,13 +173,15 @@ class Dataset(list):
""" Latex code to display dataset as a tabular """ """ Latex code to display dataset as a tabular """
d_per_line = self.effectif_total() // nbr_lines d_per_line = self.effectif_total() // nbr_lines
d_last_line = self.effectif_total() % d_per_line d_last_line = self.effectif_total() % d_per_line
splited_data = [self[x:x+d_per_line] for x in range(0, self.effectif_total(), d_per_line)] splited_data = [self[x:x + d_per_line]
for x in range(0, self.effectif_total(), d_per_line)]
# On ajoute les éléments manquant pour la dernière line # On ajoute les éléments manquant pour la dernière line
if d_last_line: if d_last_line:
splited_data[-1] += [' '] * (d_per_line - d_last_line) splited_data[-1] += [' '] * (d_per_line - d_last_line)
# Construction du tableau # Construction du tableau
latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(nbr_col = d_per_line) latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(
nbr_col=d_per_line)
latex += "\t\t \hline \n" latex += "\t\t \hline \n"
d_lines = [' & '.join(map(str, l)) for l in splited_data] d_lines = [' & '.join(map(str, l)) for l in splited_data]
@@ -184,9 +193,7 @@ class Dataset(list):
return latex return latex
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del # cursor: 16 del

2
pymath/stat/number_tools.py
View File

@@ -19,9 +19,7 @@ def number_factory(fun):
return wrapper return wrapper
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del # cursor: 16 del

26
pymath/stat/random_generator.py
View File

@@ -4,10 +4,10 @@
from random import randint, uniform, gauss, choice from random import randint, uniform, gauss, choice
def random_generator(length,\ def random_generator(length,
distrib = gauss, rd_args = (0,1), \ distrib=gauss, rd_args=(0, 1),
nbr_format = lambda x:round(x,2), \ nbr_format=lambda x: round(x, 2),
v_min = None, v_max = None, \ v_min=None, v_max=None,
exact_mean=None): exact_mean=None):
""" Generate a random list of value """ Generate a random list of value
@@ -28,22 +28,26 @@ def random_generator(length,\
""" """
# if exact_mean is set, we create automaticaly only length-1 value # if exact_mean is set, we create automaticaly only length-1 value
if exact_mean != None: if exact_mean is not None:
length = length - 1 length = length - 1
# build function to test created values # build function to test created values
if v_min == None: if v_min is None:
v1 = lambda x: True v1 = lambda x: True
else: else:
v1 = lambda x: x >= v_min v1 = lambda x: x >= v_min
if v_max == None: if v_max is None:
v2 = lambda x: True v2 = lambda x: True
else: else:
v2 = lambda x: x <= v_max v2 = lambda x: x <= v_max
validate = lambda x: v1(x) and v2(x) validate = lambda x: v1(x) and v2(x)
# get distrib function # get distrib function
distribs = {"gauss": gauss, "uniform": uniform, "randint":randint, "choice":choice} distribs = {
"gauss": gauss,
"uniform": uniform,
"randint": randint,
"choice": choice}
try: try:
distrib(*rd_args) distrib(*rd_args)
except TypeError: except TypeError:
@@ -59,10 +63,11 @@ def random_generator(length,\
data.append(v) data.append(v)
# Build last value # Build last value
if exact_mean != None: if exact_mean is not None:
last_v = nbr_format((length + 1) * exact_mean - sum(data)) last_v = nbr_format((length + 1) * exact_mean - sum(data))
if not validate(last_v): if not validate(last_v):
raise ValueError("Can't build the last value. Conflict between v_min/v_max and exact_mean") raise ValueError(
"Can't build the last value. Conflict between v_min/v_max and exact_mean")
data.append(last_v) data.append(last_v)
return data return data
@@ -71,4 +76,3 @@ def random_generator(length,\
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del # cursor: 16 del

24
pymath/stat/weightedDataset.py
View File

@@ -35,7 +35,12 @@ class WeightedDataset(dict):
""" """
def __init__(self, datas = [], data_name = "Valeurs", weights = [], weight_name = "Effectifs"): def __init__(
self,
datas=[],
data_name="Valeurs",
weights=[],
weight_name="Effectifs"):
""" """
Initiate the WeightedDataset Initiate the WeightedDataset
""" """
@@ -103,7 +108,11 @@ class WeightedDataset(dict):
(1, 3, 4, 5, 5) (1, 3, 4, 5, 5)
""" """
return (min(self.keys()) , self.quartile(1) , self.quartile(2) , self.quartile(3), max(self.keys())) return (min(self.keys()),
self.quartile(1),
self.quartile(2),
self.quartile(3),
max(self.keys()))
@number_factory @number_factory
def quartile(self, quartile=1): def quartile(self, quartile=1):
@@ -136,7 +145,8 @@ class WeightedDataset(dict):
position = self.posi_quartile(quartile) - 1 position = self.posi_quartile(quartile) - 1
expanded_values = flatten_list([v * [k] for (k, v) in self.items()]) expanded_values = flatten_list([v * [k] for (k, v) in self.items()])
if position.is_integer(): if position.is_integer():
return (expanded_values[int(position)] + expanded_values[int(position)+1])/2 return (expanded_values[int(position)] +
expanded_values[int(position) + 1]) / 2
else: else:
return expanded_values[ceil(position)] return expanded_values[ceil(position)]
@@ -150,18 +160,19 @@ class WeightedDataset(dict):
""" """
return quartile * self.effectif_total() / 4 return quartile * self.effectif_total() / 4
# -------------------------- # --------------------------
# Rendu latex # Rendu latex
def tabular_latex(self): def tabular_latex(self):
""" Latex code to display dataset as a tabular """ """ Latex code to display dataset as a tabular """
latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(nbr_col = len(self.keys())) latex = "\\begin{{tabular}}{{|c|*{{{nbr_col}}}{{c|}}}} \n".format(
nbr_col=len(self.keys()))
latex += "\t \hline \n" latex += "\t \hline \n"
data_line = "\t {data_name} ".format(data_name=self.data_name) data_line = "\t {data_name} ".format(data_name=self.data_name)
weight_line = "\t {weight_name} ".format(weight_name=self.weight_name) weight_line = "\t {weight_name} ".format(weight_name=self.weight_name)
# TODO: Il faudra trouver une solution pour le formatage des données |sam. janv. 9 13:14:26 EAT 2016 # TODO: Il faudra trouver une solution pour le formatage des données
# |sam. janv. 9 13:14:26 EAT 2016
for (v, e) in self.items(): for (v, e) in self.items():
data_line += "& {val} ".format(val=v) data_line += "& {val} ".format(val=v)
weight_line += "& {eff} ".format(eff=e) weight_line += "& {eff} ".format(eff=e)
@@ -177,4 +188,3 @@ class WeightedDataset(dict):
# Reglages pour 'vim' # Reglages pour 'vim'
# vim:set autoindent expandtab tabstop=4 shiftwidth=4: # vim:set autoindent expandtab tabstop=4 shiftwidth=4:
# cursor: 16 del # cursor: 16 del