如何解决在Python中测试数学表达式的等效性
|| 我在Python中有两个字符串，A m * B s / (A m + C m)
C m * B s / (C m + A m)
解决方法
这是基于我之前的回答的简化方法。
这个想法是，如果两个表达式在置换下是等价的，则将一个表达式携带到另一个表达式的置换必须将第一个字符串中的第ith个符号（按首次出现的索引排序）映射到第二个字符串中的第i个符号（再次按的索引排序）。第一次出现）。此原理可用于构造置换，将其应用于第一个字符串，然后检查与第二个字符串是否相等-如果它们相等，则相等，否则相等。
这是一种可能的实现：
import re
# Unique-ify list,preserving order
def uniquify(l):
return reduce(lambda s,e: s + ([] if e in s else [e]),l,[])
# Replace all keys in replacements with corresponding values in str
def replace_all(str,replacements):
for old,new in replacements.iteritems():
str = str.replace(old,new)
return str
class Expression:
units = [\"m\",\"s\"]
def __init__(self,exp):
self.exp = exp
# Returns a list of symbols in the expression that are preceded
# by the given unit,ordered by first appearance. Assumes the
# symbol and unit are separated by a space. For example:
# Expression(\"A m * B s / (A m + C m)\").symbols_for_unit(\"m\")
# returns [\'A\',\'C\']
def symbols_for_unit(self,unit):
sym_re = re.compile(\"(.) %s\" % unit)
symbols = sym_re.findall(self.exp)
return uniquify(symbols)
# Returns a string with all symbols that have units other than
# unit \"muted\",that is replaced with the empty string. Example:
# Expression(\"A m * B s / (A m + C m)\").mute_symbols_for_other_units(\"m\")
# returns \"A m * s / (A m + C m)\"
def mute_symbols_for_other_units(self,unit):
other_units = \"\".join(set(self.units) - set(unit))
return re.sub(\"(.) ([%s])\" % \"\".join(other_units),\" \\g<2>\",self.exp)
# Returns a string with all symbols that have the given unit
# replaced with tokens of the form $0,$1,...,by order of their
# first appearance in the string,and all other symbols muted.
# For example:
# Expression(\"A m * B s / (A m + C m)\").canonical_form(\"m\")
# returns \"$0 m * s / ($0 m + $1 m)\"
def canonical_form(self,unit):
symbols = self.symbols_for_unit(unit)
muted_self = self.mute_symbols_for_other_units(unit)
for i,sym in enumerate(symbols):
muted_self = muted_self.replace(\"%s %s\" % (sym,unit),\"$%s %s\" % (i,unit))
return muted_self
# Define a permutation,represented as a dictionary,according to
# the following rule: replace $i with the ith distinct symbol
# occurring in the expression with the given unit. For example:
# Expression(\"C m * B s / (C m + A m)\").permutation(\"m\")
# returns {\'$0\':\'C\',\'$1\':\'A\'}
def permutation(self,unit):
enum = enumerate(self.symbols_for_unit(unit))
return dict((\"$%s\" % i,sym) for i,sym in enum)
# Return a string produced from the expression by first converting it
# into canonical form,and then performing the replacements defined
# by the given permutation. For example:
# Expression(\"A m * B s / (A m + C m)\").permute(\"m\",{\"$0\":\"C\",\"$1\":\"A\"})
# returns \"C m * s / (C m + A m)\"
def permute(self,unit,permutation):
new_exp = self.canonical_form(unit)
return replace_all(new_exp,permutation)
# Test for equality under permutation and muting of all other symbols
# than the unit provided.
def eq_under_permutation(self,other_exp):
muted_self = self.mute_symbols_for_other_units(unit)
other_permuted_str = other_exp.permute(unit,self.permutation(unit))
return muted_self == other_permuted_str
# Test for equality under permutation. This is done for each of
# the possible units using eq_under_permutation
def __eq__(self,other):
return all([self.eq_under_permutation(unit,other) for unit in self.units])
e1 = Expression(\"A m * B s / (A m + C m)\")
e2 = Expression(\"C m * B s / (C m + A m)\")
e3 = Expression(\"A s * B s / (A m + C m)\")
f1 = Expression(\"A s * (B s + D s) / (A m + C m)\")
f2 = Expression(\"A s * (D s + B s) / (C m + A m)\")
f3 = Expression(\"D s\")
print \"e1 == e2: \",e1 == e2 # True
print \"e1 == e3: \",e1 == e3 # False
print \"e2 == e3: \",e2 == e3 # False
print \"f1 == f2: \",f1 == f2 # True
print \"f1 == f3: \",f1 == f3 # False
str1 = \"A m * B s / (A m + C m)\"
str2 = \"C m * B s / (C m + A m)\"
X1 = C
X2 = A
Y[1] = A
Y[2] = C
str3 = \"X1 m * B s / (X1 m + X2 m)\"
str3_1 = \"A m * Bs / (A m + X2 m)\"
str3_1[:18] = \"A m * B s / (A m + \"
str1[:18] = \"A m * B s / (A m + \"
str3_2 = \"A m * B s / (A m + C m)\"
sympify()
>>> from sympy import *
>>> x
Traceback (most recent call last):
File \"<stdin>\",line 1,in <module>
NameError: name \'x\' is not defined
>>> sympify(\"x**2 + cos(x)\")
x**2 + cos(x)
>>> sympify(\"diff(x**2 + cos(x),x)\")
2*x - sin(x)
A = 10
B = 20
C = 30
m = Math.e
s = Math.pi
s1 = \'A m * B s / (A m + C m)\'
s2 = \'C m * B s / (C m + A m)\'
if s1 != s2:
print \"Not equivalent\"
else:
print \"Try with another sample\"
#SOURCE FOR HELPERS: https://github.com/sympy/sympy/wiki/Faq
import sympy
import sympy.parsing.sympy_parser
ExampleExpressionString1 = \'exp( i*( (x0 - 1)*(x0 + 2) ) )\'
ExampleExpressionSympy1 = sympy.parsing.sympy_parser.parse_expr(ExampleExpressionString1)
ExampleExpressionString2 = \'i*sin( (x0 - 1)*(x0 + 2) ) + cos( (x0 - 1)*(x0 + 2) )\'
ExampleExpressionSympy2 = sympy.parsing.sympy_parser.parse_expr(ExampleExpressionString2)
print \'(ExampleExpressionSympy1 == ExampleExpressionSympy2):\'
print \' \',(ExampleExpressionSympy1 == ExampleExpressionSympy2)
print \'(ExampleExpressionSympy1.simplify() == ExampleExpressionSympy2.simplify()):\'
print \' \',(ExampleExpressionSympy1.simplify() == ExampleExpressionSympy2.simplify())
print \'(ExampleExpressionSympy1.expand() == ExampleExpressionSympy2.expand()):\'
print \' \',(ExampleExpressionSympy1.trigsimp() == ExampleExpressionSympy2.trigsimp())
print \'(ExampleExpressionSympy1.trigsimp() == ExampleExpressionSympy2.trigsimp()):\'
print \' \',(ExampleExpressionSympy1.trigsimp() == ExampleExpressionSympy2.trigsimp())
print \'(ExampleExpressionSympy1.simplify().expand().trigsimp() == ExampleExpressionSympy2.simplify().expand().trigsimp()):\'
print \' \',(ExampleExpressionSympy1.simplify().expand().trigsimp() == ExampleExpressionSympy2.simplify().expand().trigsimp())
import sympy
import sympy.parsing.sympy_parser
Expression.simplify().expand().trigsimp()
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