有没有办法在SymPy中处理常量函数参数? [英] Is there a way to handle constant function parameters in SymPy?

问题描述

我正在生成符号函数，并使用SymPy对其进行简化. 现在，我想一种简化"符号的方法，这些符号代表尚未安装的函数中的常量参数. 例如，如果我正在生成多项式，则可能会生成这样的字符串

I am generating symbolic functions and using SymPy to simplify them. Now I would like a way to "simplify" symbols that represent constant parameters in a function that is yet to be fitted. For example, if I am generating a polynomial, I might generate a string like this

C*x*x + C*x + C*x + C,

SymPy将变成哪个

which SymPy would turn into

C*x^2 + 2*C*x + C.

现在，我想找到一种方法来获取此信息:

Now I would like to find a way to get this:

C*x^2 + C*x + C.

换句话说，有一种方法可以告诉SymPy某个符号是常量且未定义，因此

In other words, is there a way to tell SymPy that a certain symbol is constant and undefined, so that

C+C -> C, C*C -> C, etc. Or more generally: f(C) = C, for any f(C)?

我的第一个想法是，也许有一个描述此属性的假设(例如Q.positive)，我也许可以使用优化.但是，事实似乎并非如此. 如果没有别的，我敢肯定有一种方法可以使用preorder_traversal来完成我想要的事情，但是我无法提出一种实现它的策略. 任何帮助或想法都将受到赞赏.

My first idea was that perhaps there is an assumption (such as Q.positive) that describes this property and I might be able to use refine. However, this does not seem to be the case. If nothing else, I'm sure there is a way to use preorder_traversal to do what I want, but I can't come up with a strategy to do it. Any help or ideas are appreciated.

推荐答案

也许是这样(适用于已完全展开的表达式):

Perhaps something like this (applied to an expression that has been fully expanded):

def consim(eq, *v):
    con = numbered_symbols('c', cls=Dummy)
    reps = {}
    for i in preorder_traversal(eq):
        if i.is_Mul or i.is_Add:
            c, d = i.as_independent(*v)
            if c != i.identity and c.free_symbols:
                c = reps.setdefault(c, next(con))
    return eq.subs(reps)


>>> from sympy.abc import a, b, c, d, x
>>> eq = 2*a*x**2 + b*c*x + d + e
>>> consim(eq, x)
         2
c₀ + c₁⋅x  + c₂⋅x

您可能希望编号符号，但并非所有符号都相同.

You probably want numbered symbols, not all symbols the same.

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