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Merge branch 'fraction' into dev

This commit is contained in:
Lafrite 2014-12-28 10:48:29 +01:00
parent 35f2b46521 02df267acf
commit 61bc284805
3 changed files with 90 additions and 73 deletions
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52
pymath/expression.py
View File

@ -28,6 +28,46 @@ class Expression(object):
def set_default_render(cls): def set_default_render(cls):
cls.set_render(cls.DEFAULT_RENDER) cls.set_render(cls.DEFAULT_RENDER)
@classmethod
def tmp_render(cls, render = lambda _,x:Expression(x)):
""" Create a container in which Expression render is temporary modify
The default temporary render is Expression in order to perform calculus inside numbers
>>> exp = Expression("2*3/5")
>>> print(exp)
\\frac{ 2 \\times 3 }{ 5 }
>>> for i in exp.simplify():
... print(i)
\\frac{ 2 \\times 3 }{ 5 }
\\frac{ 6 }{ 5 }
>>> with Expression.tmp_render():
... for i in exp.simplify():
... i
< Expression [2, 3, '*', 5, '/']>
< Expression [6, 5, '/']>
< Fraction 6 / 5>
>>> with Expression.tmp_render(txt):
... for i in exp.simplify():
... print(i)
2 * 3 / 5
6 / 5
>>> for i in exp.simplify():
... print(i)
\\frac{ 2 \\times 3 }{ 5 }
\\frac{ 6 }{ 5 }
"""
class TmpRenderEnv(object):
def __enter__(self):
self.old_render = Expression.get_render()
Expression.set_render(render)
def __exit__(self, type, value, traceback):
Expression.set_render(self.old_render)
return TmpRenderEnv()
@classmethod @classmethod
def random(self, form="", conditions=[], val_min = -10, val_max=10): def random(self, form="", conditions=[], val_min = -10, val_max=10):
"""Create a random expression from form and with conditions """Create a random expression from form and with conditions
@ -299,10 +339,10 @@ def test(exp):
print("\n") print("\n")
if __name__ == '__main__': if __name__ == '__main__':
render = lambda _,x : str(x) #render = lambda _,x : str(x)
Expression.set_render(render) #Expression.set_render(render)
exp = Expression("1/2 - 4") #exp = Expression("1/2 - 4")
print(list(exp.simplify())) #print(list(exp.simplify()))
#Expression.set_render(txt) #Expression.set_render(txt)
#exp = "2 ^ 3 * 5" #exp = "2 ^ 3 * 5"
@ -386,8 +426,8 @@ if __name__ == '__main__':
#for i in exp.simplify(): #for i in exp.simplify():
# print(i) # print(i)
#import doctest import doctest
#doctest.testmod() doctest.testmod()
# ----------------------------- # -----------------------------
# Reglages pour 'vim' # Reglages pour 'vim'

87
pymath/fraction.py
View File

@ -119,13 +119,13 @@ class Fraction(object):
>>> f = Fraction(1, 2) >>> f = Fraction(1, 2)
>>> g = Fraction(2, 3) >>> g = Fraction(2, 3)
>>> f + g >>> f + g
[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+']>, < Expression [3, 4, '+', 6, '/']>, < Fraction 7 / 6>] [< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '+']>, < Expression [3, 6, '/', 4, 6, '/', '+']>, < Expression [< Fraction 3 / 6>, < Fraction 4 / 6>, '+']>, < Expression [3, 4, '+', 6, '/']>, < Expression [7, 6, '/']>, < Fraction 7 / 6>]
>>> f + 2 >>> f + 2
[< Expression [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+']>, < Expression [1, 4, '+', 2, '/']>, < Fraction 5 / 2>] [< Expression [1, 1, '*', 2, 1, '*', '/', 2, 2, '*', 1, 2, '*', '/', '+']>, < Expression [1, 2, '/', 4, 2, '/', '+']>, < Expression [< Fraction 1 / 2>, < Fraction 4 / 2>, '+']>, < Expression [1, 4, '+', 2, '/']>, < Expression [5, 2, '/']>, < Fraction 5 / 2>]
>>> f = Fraction(3, 4) >>> f = Fraction(3, 4)
>>> g = Fraction(5, 4) >>> g = Fraction(5, 4)
>>> f + g >>> f + g
[< Expression [3, 5, '+', 4, '/']>, < Fraction 8 / 4>, 2] [< Expression [3, 5, '+', 4, '/']>, < Expression [8, 4, '/']>, 2]
""" """
@ -134,31 +134,22 @@ class Fraction(object):
number = self.convert2fraction(other) number = self.convert2fraction(other)
steps = []
if self._denom == number._denom: if self._denom == number._denom:
com_denom = self._denom com_denom = self._denom
num1 = self._num num1 = self._num
num2 = number._num num2 = number._num
exp = Expression([num1, num2, op.add, com_denom, op.div])
else: else:
gcd_denom = gcd(self._denom, number._denom) gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
steps.append(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])
com_denom = self._denom * coef1 with Expression.tmp_render():
num1 = self._num * coef1 steps = list(exp.simplify())
num2 = number._num * coef2
steps.append(Expression([num1, num2, op.add, com_denom, op.div]))
num = num1 + num2
ans_frac = Fraction(num, com_denom)
steps.append(ans_frac)
steps += ans_frac.simplify()
return steps return steps
@ -176,7 +167,7 @@ class Fraction(object):
>>> f = Fraction(1, 2) >>> f = Fraction(1, 2)
>>> g = Fraction(2, 3) >>> g = Fraction(2, 3)
>>> f - g >>> f - g
[< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-']>, < Expression [3, 4, '-', 6, '/']>, < Fraction -1 / 6>] [< Expression [1, 3, '*', 2, 3, '*', '/', 2, 2, '*', 3, 2, '*', '/', '-']>, < Expression [3, 6, '/', 4, 6, '/', '-']>, < Expression [< Fraction 3 / 6>, < Fraction 4 / 6>, '-']>, < Expression [3, 4, '-', 6, '/']>, < Expression [-1, 6, '/']>, < Fraction -1 / 6>]
""" """
if other == 0: if other == 0:
@ -184,31 +175,22 @@ class Fraction(object):
number = self.convert2fraction(other) number = self.convert2fraction(other)
steps = []
if self._denom == number._denom: if self._denom == number._denom:
com_denom = self._denom com_denom = self._denom
num1 = self._num num1 = self._num
num2 = number._num num2 = number._num
exp = Expression([num1, num2, op.sub, com_denom, op.div])
else: else:
gcd_denom = gcd(self._denom, number._denom) gcd_denom = gcd(self._denom, number._denom)
coef1 = number._denom // gcd_denom coef1 = number._denom // gcd_denom
coef2 = self._denom // gcd_denom coef2 = self._denom // gcd_denom
steps.append(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])
com_denom = self._denom * coef1 with Expression.tmp_render():
num1 = self._num * coef1 steps = list(exp.simplify())
num2 = number._num * coef2
steps.append(Expression([num1, num2, op.sub, com_denom, op.div]))
num = num1 - num2
ans_frac = Fraction(num, com_denom)
steps.append(ans_frac)
steps += ans_frac.simplify()
return steps return steps
@ -234,7 +216,11 @@ class Fraction(object):
""" """
f = Fraction(-self._num, self._denom) f = Fraction(-self._num, self._denom)
return [f] + f.simplify()
with Expression.tmp_render():
steps = [f] + f.simplify()
return steps
def __mul__(self, other): def __mul__(self, other):
""" overload * """ overload *
@ -242,13 +228,13 @@ class Fraction(object):
>>> f = Fraction(1, 2) >>> f = Fraction(1, 2)
>>> g = Fraction(2, 3) >>> g = Fraction(2, 3)
>>> f*g >>> f*g
[< Expression [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/']>, < Fraction 1 / 3>] [< Expression [1, 1, 2, '*', '*', 1, 2, '*', 3, '*', '/']>, < Expression [1, 2, '*', 2, 3, '*', '/']>, < Expression [2, 6, '/']>, < Expression [1, 2, '*', 3, 2, '*', '/']>, < Fraction 1 / 3>]
>>> f * 0 >>> f * 0
[0] [0]
>>> f*1 >>> f*1
[< Fraction 1 / 2>] [< Fraction 1 / 2>]
>>> f*4 >>> f*4
[< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Fraction 2 / 1>, 2] [< Expression [1, 2, '*', 2, '*', 1, 2, '*', '/']>, < Expression [2, 2, '*', 2, '/']>, < Expression [4, 2, '/']>, 2]
""" """
steps = [] steps = []
@ -258,6 +244,8 @@ class Fraction(object):
elif other == 1: elif other == 1:
return [self] return [self]
# 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 type(other) == int:
gcd1 = gcd(other, self._denom) gcd1 = gcd(other, self._denom)
if gcd1 != 1: if gcd1 != 1:
@ -266,10 +254,8 @@ class Fraction(object):
else: else:
num = [self._num, other, op.mul] num = [self._num, other, op.mul]
denom = [self._denom] denom = [self._denom]
steps.append(Expression(num + denom + [op.div]))
num = int(self._num * other / gcd1) exp = Expression(num + denom + [op.div])
denom = int(self._denom / gcd1)
else: else:
number = self.convert2fraction(other) number = self.convert2fraction(other)
@ -291,14 +277,10 @@ class Fraction(object):
denom1 = [self._denom] denom1 = [self._denom]
steps.append(Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])) exp = Expression(num1 + num2 + [ op.mul] + denom1 + denom2 + [op.mul, op.div])
num = int(self._num * number._num / (gcd1 * gcd2)) with Expression.tmp_render():
denom = int(self._denom * number._denom / (gcd1 * gcd2)) steps = list(exp.simplify())
ans_frac = Fraction(num, denom)
steps.append(ans_frac)
steps += ans_frac.simplify()
return steps return steps
@ -334,10 +316,10 @@ class Fraction(object):
>>> f**1 >>> f**1
[< Fraction 3 / 4>] [< Fraction 3 / 4>]
>>> f**3 >>> f**3
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>] [< Expression [3, 3, '^', 4, 3, '^', '/']>, < Expression [27, 64, '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4) >>> f = Fraction(6, 4)
>>> f**3 >>> f**3
[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>] [< Expression [6, 3, '^', 4, 3, '^', '/']>, < Expression [216, 64, '/']>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
""" """
if not type(power) == int: if not type(power) == int:
@ -348,10 +330,9 @@ class Fraction(object):
elif power == 1: elif power == 1:
return [self] return [self]
else: else:
steps = [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_frac = Fraction(self._num ** power, self._denom ** power) with Expression.tmp_render():
steps.append(ans_frac) steps = list(exp.simplify())
steps += ans_frac.simplify()
return steps return steps
def __xor__(self, power): def __xor__(self, power):
@ -364,10 +345,10 @@ class Fraction(object):
>>> f^1 >>> f^1
[< Fraction 3 / 4>] [< Fraction 3 / 4>]
>>> f^3 >>> f^3
[< Expression [3, 3, '^', 4, 3, '^', '/']>, < Fraction 27 / 64>] [< Expression [3, 3, '^', 4, 3, '^', '/']>, < Expression [27, 64, '/']>, < Fraction 27 / 64>]
>>> f = Fraction(6, 4) >>> f = Fraction(6, 4)
>>> f^3 >>> f^3
[< Expression [6, 3, '^', 4, 3, '^', '/']>, < Fraction 216 / 64>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>] [< Expression [6, 3, '^', 4, 3, '^', '/']>, < Expression [216, 64, '/']>, < Expression [27, 8, '*', 8, 8, '*', '/']>, < Fraction 27 / 8>]
""" """

10
pymath/polynom.py
View File

@ -291,19 +291,15 @@ class Polynom(object):
# On converti en Expression # On converti en Expression
coef_exp = Expression(postfix_add) coef_exp = Expression(postfix_add)
old_render = Expression.get_render() with Expression.tmp_render():
Expression.set_render(lambda _,x:Expression(x))
coef_steps = list(coef_exp.simplify()) coef_steps = list(coef_exp.simplify())
Expression.set_render(old_render)
#print('\t 1.coef_steps -> ', coef_steps) #print('\t 1.coef_steps -> ', coef_steps)
elif type(coef) == Expression: elif type(coef) == Expression:
old_render = Expression.get_render() with Expression.tmp_render():
Expression.set_render(lambda _,x:Expression(x))
coef_steps = list(coef.simplify()) coef_steps = list(coef.simplify())
Expression.set_render(old_render)
#print('\t 2.coef_steps -> ', coef_steps) #print('\t 2.coef_steps -> ', coef_steps)
@ -524,7 +520,7 @@ def test(p,q):
if __name__ == '__main__': if __name__ == '__main__':
#from .fraction import Fraction #from .fraction import Fraction
Expression.set_render(txt) with Expression.tmp_render(txt):
p = Polynom([10, -5]) p = Polynom([10, -5])
q = Polynom([3, -9]) q = Polynom([3, -9])
print(p-q) print(p-q)