/**/ use P ::= QQ[x,y];
/**/ I := IdealOfPoints(P, mat([[1,2], [3,4], [5,6]]));
/**/ MinPolyQuotDef(x,I,x); -- the smallest x-univariate poly in I
x^3 -9*x^2 +23*x -15
/**/ indent(factor(It));
record[
RemainingFactor := 1,
factors := [x -1, x -3, x -5],
multiplicities := [1, 1, 1]
]
/**/ f := x+y;
/**/ I := ideal(x^2, y^2);
/**/ MinPolyQuotDef(f,I,x);
x^3
/**/ subst(It, x, f) isin I;
true
---- this is how to use an indet in another ring:
/**/ QQt := RingQQt(1);
/**/ MinPolyQuotDef(f, I, indet(RingQQt(1),1));
t^3
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