Rewrite equation as polynomial

问题

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

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

How would I do this?

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

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) 

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

The actual problem from textbook: http://i.imgur.com/J1MYo9H.png

How it should look like: http://i.imgur.com/RqEDo7H.png

The two equations are equivalent.

回答1:

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

Throw away the denominator

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

Expand the equation and collect terms with powers of s.

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

Final Equation

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)

来源：https://stackoverflow.com/questions/31207395/rewrite-equation-as-polynomial