将方程改写为多项式 [英] Rewrite equation as polynomial

问题描述

from sympy import *
K, T, s = symbols('K T s')
G = K/(1+s*T)
Eq1 =Eq(G+1,0)

我想用sympy作为多项式重写方程Eq1:1+K+T*s==0

I want to rewrite equation Eq1 with sympy as polynomial: 1+K+T*s==0

我该怎么做?

我花了几个小时搜索和尝试简化方法，但找不到优雅、简短的解决方案.

I spent some hours of searching and trying simplifications methods but could not find a elegant, short solution.

SymPy 中的实际问题:

The actual problem in SymPy:

from IPython.display import display 
import sympy as sp
sp.init_printing(use_unicode=True,use_latex=True,euler=True)
Kf,Td0s,Ke,Te,Tv,Kv,s= sp.symbols("K_f,T_d0^',K_e,T_e,T_v,K_v,s")
Ga= Kf/(1+s*Tv)
Gb= Ke/(1+s*Te)
Gc= Kf/(1+s*Td0s)
G0=Ga*Gb*Gc
G1=sp.Eq(G0+1,0)
display(G1) 

如何告诉 Sympy 将方程 G1 重写为多项式，形状为 s^3*(...)+s^2*(...)+s*(...)+(...)=... ?

How to tell Sympy to rewrite equation G1 as polynomial in shape s^3*(...)+s^2*(...)+s*(...)+(...)=... ?

教科书的实际问题:http://i.imgur.com/J1MYo9H.png

它应该是什么样子:http://i.imgur.com/RqEDo7H.png

这两个等式是等价的.

推荐答案

这是您可以执行的操作.

Here's what you can do.

import sympy as sp
Kf,Td0s,Ke,Te,Tv,Kv,s= sp.symbols("K_f,T_d0^',K_e,T_e,T_v,K_v,s")
Ga= Kf/(1+s*Tv)
Gb= Ke/(1+s*Te)
Gc= Kf/(1+s*Td0s)
G0=Ga*Gb*Gc

扔掉分母

eq = (G0 + 1).as_numer_denom()[0]

展开方程并收集具有 s 次幂的项.

Expand the equation and collect terms with powers of s.

eq = eq.expand().collect(s)

最终方程

Eq(eq, 0)
Eq(K_e*K_f**2 + T_d0^'*T_e*T_v*s**3 + s**2*(T_d0^'*T_e + T_d0^'*T_v + T_e*T_v) + s*(T_d0^' + T_e + T_v) + 1, 0)

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