This method returns the product of degrees of the polynomial in $T$ (the degree in the main variables). In the zero-dimensional case, this agrees with degree of the saturated ideal of $T$.
i1 : R = QQ[a,b,c,d,e,f,g,h, MonomialOrder=>Lex]; |
i2 : F = {a^2*d - b, c*f*h - d*e, e^3*h - f*g}; |
i3 : T = triaSystem(R,F) 2 3 o3 = {a d - b, c*f*h - d*e, e h - f*g} / {d, f*h, h} o3 : TriaSystem |
i4 : degree T o4 = 6 |
i5 : for f in F list degree(mvar f, f) o5 = {2, 1, 3} o5 : List |
It is assumed that the triangular set is a regular chain