SINGULAR / A Computer Algebra System for Polynomial Computations / version 2-0-0 0< by: G.-M. Greuel, G. Pfister, H. Schoenemann \ February 2001 FB Mathematik der Universitaet, D-67653 Kaiserslautern \ // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/primdec.lib (1.98.2.1,2001/03/29) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/matrix.lib (1.26,2001/01/18) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/ring.lib (1.17,2001/01/16) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/inout.lib (1.21,2001/01/16) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/random.lib (1.16,2001/01/16) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/poly.lib (1.33,2001/01/16) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/elim.lib (1.14,2001/01/16) // ** loaded /usr/people/wiss/theobald/software/Singular/2-0-0/LIB/general.lib (1.38.2.1,2001/04/24) 4 8 3 20 3 10 2 24 The ideal factors into 8 components, with 4 of degree 2 and 4 of degree 4 Here are the polynomials in each degree 4 component that factor further (4*s^2)*k^2+(4*s)*k*l+(s^2+1)*l^2 ------------------------------------------- (4*s^2)*k^2+(-4*s)*k*l+(s^2+1)*l^2 ------------------------------------------- (4*s^2)*k^2+(4*s)*k*l+(s^2+1)*l^2 ------------------------------------------- (4*s^2)*k^2+(-4*s)*k*l+(s^2+1)*l^2 ------------------------------------------- Note that these components factor over Q[i] 1217 Auf Wiedersehen.