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How to substitute polynomials into another polynomial?
http://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1292
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Author:  Gert-Martin Greuel [ Thu Aug 11, 2005 5:31 pm ]
Post subject:  How to substitute polynomials into another polynomial?

>Dear Singular Team,
>Having defined a ring S=0,(x,y,a,b),lp;
>I want to define polys f,g, in x,y, and h in a,h, and
>then substitute h(f,g) to get another poly k in x,y.
>Then I am going to examine the grobner basis for
>ideal i=a-f,b-g;
>and find
>poly l=NF(k,i);
>
>This should recover h.
>
>But how do I substitute a polynomial in given variables
>into another polynomial?

Use map (from S to itself), eg:

ring S=0,(x,y,a,b),lp;
poly f = x3+y5;
poly g = xy5-x2;
poly h = a2-b3;
map F = S,ideal(x,y,f,g);
ideal i =a-f,b-g;
poly k = F(h);
NF(k,std(i));

Best,
Gert-Martin Greuel (Singular team)

email: greuel@mathematik.uni-kl.de
Posted in old Singular Forum on: 2001-05-15 13:23:43+02

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