Sympy:删除多项式中的高阶项 [英] Sympy: Drop higher order terms in polynomial

问题描述

使用Sympy，假设我们有一个表达式f，它是符号"x"(以及其他可能的符号)的多项式.

Using Sympy, say we have an expression f, which is a polynomial of the Symbol "x" (and of potentially other symbols).

我想知道是否存在一种有效的方法来删除所有大于f的整数n的f中的所有项.

I would like to know what if there is an efficient way to drop all terms in f of order greater than some integer n.

作为一个特例，我有一个非常复杂的函数，但我只想将x的术语保持在2阶以内.有效的方法是什么?

As a special case I have a very complicated function but i want to only keep terms up to 2nd order in x. What's the efficient way to do this?

一个明显的，不是很有效的方法是对于每个小于n的m，取m个导数并将x设置为0，以获得x ^ m的系数.我们以这种方式获得每个系数，然后重构多项式.但是采用衍生工具并不是最有效的方法.

The obvious, not-very-efficient way to do it would be for each m less than n, take m derivatives and set x to 0 to obtain the coefficient of x^m. We obtain each coefficient this way then reconstruct the polynomial. But taking derivatives is not the most efficient thing.

推荐答案

一种简单的方法是将O(x**n)添加到表达式中，例如

An easy way to do this is to add O(x**n) to the expression, like

In [23]: x + x**2 + x**4 + x**10 + O(x**3)
Out[23]:
     2    ⎛ 3⎞
x + x  + O⎝x ⎠

如果以后要删除它，请使用removeO方法

If you want to later remove it, use the removeO method

In [24]: (x + x**2 + x**4 + x**10 + O(x**3)).removeO()
Out[24]:
 2
x  + x

您还可以使用series进行表达式的系列扩展.此处的区别在于，如果非多项式项以表达式结尾:

You can also use series to take the series expansion of the expression. The difference here is the behavior if a non-polynomial term ends up in the expression:

In [25]: x + sin(x) + O(x**3)
Out[25]:
              ⎛ 3⎞
sin(x) + x + O⎝x ⎠

In [26]: (x + sin(x)).series(x, 0, 3)
Out[26]:
       ⎛ 3⎞
2⋅x + O⎝x ⎠

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