Returns the pseudo-remainder, prem(f,T), of f by a triangular set T.
Let T = (t1,t2,…,tk) where mvar(t1)>…>mvar(tk). The pseudo-remainder of f by T is
Remark: If T is a regular chain, then f lies in its saturated ideal iff prem(f,T)=0.
i1 : R = QQ[a,b,c,d,e,f,g,h, MonomialOrder=>Lex]; |
i2 : F = {a*d - b*c, c*f - d*e, e*h - f*g}; |
i3 : H = {d, f, h}; |
i4 : T = triaSystem(R,F,H) o4 = {a*d - b*c, c*f - d*e, e*h - f*g} / {d, f, h} o4 : TriaSystem |
i5 : (a*h - b*g) % T o5 = 0 o5 : R |
i6 : saturate T o6 = ideal (e*h - f*g, c*h - d*g, c*f - d*e, a*h - b*g, a*f - b*e, a*d - b*c) o6 : Ideal of R |