Question

# python 2.7.10
# sympy 0.7.6
import sympy as sym
a, b, c, x = sym.symbols('a b c x')
F = sym.symbols('F', cls=sym.Function)

假设我们有一个表达式：

expr = F(a - b) - F(b**2 - c)

有没有办法用已知函数F替换未知函数F(x) = x**0.5 + 1？例如：

result = expr.subs(F(_), _**0.5 + 1)

哪会导致：

(a - b)**0.5 - (b**2 - c)**0.5

Answer 1

In [1]: import sympy as sm
In [2]: a, b, c, x = sm.symbols('a b c x')
In [3]: F = sm.symbols('F', cls=sm.Function)
In [4]: expr = F(a - b) - F(b**2 - c)

您可以使用SymPy的Lambda函数来定义自定义函数。

In [5]: G = sm.Lambda(x, sqrt(x) + 1)
In [6]: expr.subs(F, G)
Out[6]: sqrt(a - b) - sqrt(b**2 - c)

Answer 2

replace就是出于此目的：

>>> import sympy as sym
>>> a, b, c, x = sym.symbols('a b c x')
>>> F = sym.symbols('F', cls=sym.Function)
>>> expr = F(a - b) - F(b**2 - c)
>>> arg=Wild('arg')
>>> expr.replace(F(arg), sqrt(arg) + 1)
sqrt(a - b) - sqrt(b**2 - c)

Answer 3

这可以通过继承Function并定义正确的eval方法（http://docs.sympy.org/dev/modules/core.html#id50）

来完成

In [1]: from sympy import Function, sqrt

In [2]: from sympy.abc import x, y, z, a, b, c

In [4]: f = Function('f')

In [5]: expr = f(a-b)+f(b**2-c)

In [6]: expr
Out[6]: f(a - b) + f(b**2 - c)

In [11]: class F(Function):
   ....:     
   ....:     @classmethod
   ....:     def eval(cls, x):
   ....:        return sqrt(x)+1
   ....:    

In [12]: expr.subs(f, F)
Out[12]: sqrt(a - b) + sqrt(b**2 - c) + 2

Python的type函数可用于缩短F

的定义

In [13]: G = type('G', (Function, ),
        {'eval' : classmethod(lambda self, x : sqrt(x)+1)})

In [14]: expr.subs(f, G)
Out[14]: sqrt(a - b) + sqrt(b**2 - c) + 2

In [15]:

占位符功能在同情中

3 个答案: