degree(TriaSystem) -- product of the degrees in a triangular set

Synopsis

Function: degree
Usage:

degree T
Inputs:
- T, an instance of the type TriaSystem,
Outputs:
- an integer, product of the main degrees of the polynomials in T

Description

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

Caveat

It is assumed that the triangular set is a regular chain

Ways to use this method: