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UniversalGroebnerBasis

universal Groebner basis of the input ideal

Syntax
UniversalGroebnerBasis(I: IDEAL): LIST of RINGELEM

Description
Returns a universal Groebner basis of the input IDEAL I .

Example
-- The ideal generated by the 3x3 minors of 3x4 matrix of indeterminates
-- has 96 marked reduced Groebner bases
/**/ Use R ::= QQ[a,b,c,d,e,f,g,h,i,j,k,l];
/**/ I:=ideal(Minors(Mat([[a,b,c,d],[e,f,g,h],[i,j,k,l]]),3));
/**/ indent(UniversalGroebnerBasis(I));
[d*g*j -c*h*j -d*f*k +b*h*k +c*f*l -b*g*l,
 d*g*i -c*h*i -d*e*k +a*h*k +c*e*l -a*g*l,
 d*f*i -b*h*i -d*e*j +a*h*j +b*e*l -a*f*l,
 c*f*i -b*g*i -c*e*j +a*g*j +b*e*k -a*f*k,
 -d*g*i +c*h*i +d*e*k -a*h*k -c*e*l +a*g*l,
 -d*f*i +b*h*i +d*e*j -a*h*j -b*e*l +a*f*l,
 -c*f*i +b*g*i +c*e*j -a*g*j -b*e*k +a*f*k,
 -d*g*j +c*h*j +d*f*k -b*h*k -c*f*l +b*g*l]

See Also