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在Python中，如何重构循环？

发布于 2025-02-06 20:49:25 字数 539 浏览 0 评论 0原文

我为函数构建了牛顿多项式。它具有相当简单的结构：

“牛顿的polyenmial公式”

在这里，y y的deltas是取自String_one list，x_0 - 对于每个块 - 符号都有不同的值（来自X_COL_LIST列表） - 实际上，这是指示的通过方括号中的非步骤：[1] [2] [n]。

我正在尝试构建一个公式，其中：

x保留x而无需获得值（这是由sympy模块提供的）;
每个分数的分母增加一个;
元素（x -x_0）在每个summand -block中，我们添加一个额外的括号，保持已经累积的：
（

原文

I construct a Newton polynomial for a function. It has a fairly simple structure:

Newton 's polynomial formula

Here, the deltas for y are taken from the string_one list, and x_0 - for each block-summands have different values (from the x_col_list list) - actually, this is indicated by non-steps in square brackets: [1] [2] [n].

I'm trying to build a formula where:

x remains x without getting values (this is served by the sympy module);
the denominator of each fraction increases by one;
element (x - x_0) in each summand-block we add one additional bracket, keeping the already accumulated:
(????−0)
(????−0)(????−0.3142)
(????−0)(????−0.3142)(????−0.6283)
with the last term:
(????−0)*(????−0.3142)(????−0.6283)(????−0.9425)(????−1.2566)(????−1.5708)(????−1.885)(????−2.1991)

I'm in trouble right now:

I get too much in the opposite direction: ????(????-2.1991)(????-1.885)...(????−0.3142)
x with zero is immediately truncated to x, and I need (x - 0)
and somehow now it has to be folded.

Code:

from sympy import symbols, prod
from scipy.special import factorial

x = symbols('x')

string_one = [0.3091,-0.0304,-0.0271,0.0054,0.0025,-0.0016,0.0019,-0.0046,0.0099,-0.019]
x_col_list = [0.0, 0.3142, 0.6283, 0.9425, 1.2566, 1.5708, 1.885, 2.1991, 2.5133]
h=1.25665

x = symbols('x')

 # we go along the deltas:
num=1
for delta in string_one:
    # we go along the column of x's: 
    polynom = round( ( delta/(factorial(num)*h**num) ), 4 ) * prod([x - args for args in x_col_list[::-1]])
    num+=1
    print(polynom)

Now the way out is this:
0.246*x*(x - 2.5133)*(x - 2.1991)*(x - 1.885)*(x - 1.5708)*(x - 1.2566)*(x - 0.9425)*(x - 0.6283)*(x - 0.3142) -0.0096*x*(x - 2.5133)*(x - 2.1991)...

As you can see, brackets are attached to each term. And all the other flaws. What can be done? Thanks

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