complete expansion of polynomial substitution

In the following code, I have substituted a polynomial in other polynomial and the result even after using the command ".expand" shows no complete expansion,Is there any other way to get complete expansion of polynomial substitution?

g1=1+ (s^2) ;
g2=g1.subs(s= 1/(z-1) ) ;
g2.expand()


Result: 1+ 1/((z-1)^2) is shown, but not expansion (z^2-z+2)/z^2-z+1.

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Just a command to convert to polynomial fraction is needed additionally:

sage:  g1=1+ (s^2) ; g2=g1.subs(s= 1/(z-1) ) ; g2.expand().fraction(QQ)
(z^2 - 2*z + 2)/(z^2 - 2*z + 1)

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If you want to compute with polynomials, you should rather use polynomial variables:

sage: s = polygen(QQ,'s')
sage: z = polygen(QQ,'z')
sage:  g1=1+s^2 ; g2=g1(s=1/(z-1) ) ; g2
(z^2 - 2*z + 2)/(z^2 - 2*z + 1)


This means using polygen instead of var. You also have to choose a coefficient field.

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Asked: 2015-02-14 13:16:35 -0500

Seen: 1,143 times

Last updated: Feb 16 '15