# Singular

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 Post subject: ideal quotientPosted: Thu Jun 09, 2016 12:40 pm

Joined: Fri Jun 24, 2011 10:10 am
Posts: 9
Hello,

I have 3 homogeneous polynomials f, g, h and I have the ideal quotient (colon) K = I:J where I and J are ideals: I = (f, g), J=(h).
I have also the homogeneous polynomial k of minimal degree from ideal quotient K.
From the definition of the ideal quotient, there must be 2 polynomials f_1, g_1 and so we have:
h * k = f * f_1 + g * g_1.
How can I find these two polynomials f_1 and g_1 with Singular?

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 Post subject: Re: ideal quotientPosted: Fri Jun 10, 2016 11:12 am

Joined: Wed May 25, 2005 4:16 pm
Posts: 205
see http://www.singular.uni-kl.de/Manual/4-0-3/sing_334.htm
Code:
matrix T=lit(ideal(h*k),ideal(f,g));
// the factors are:
T[1,1]; // f_1
T[1,2]; // g_1

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