resultant(RingElement,TriaSystem) -- iterated resultant by a triangular set

Synopsis

Function: resultant
Usage:

resultant(f,T)
Inputs:
- f, a ring element,
- T, an instance of the type TriaSystem,
Optional inputs:
- Algorithm (missing documentation) => ..., default value null,
Outputs:
- a ring element, iterated resultant of f by T

Description

Returns the iterated resultant of $f$ by a triangular set $T$. Let $T = (t_1,t_2,\cdots,t_k)$ where $mvar(t_1)>\cdots>mvar(t_k)$. The resultant of $f$ by $T$ is $$resultant(f,T) = resultant(\cdots(resultant(resultant(f,t_1),t_2)\cdots,t_k)$$

i1 : R = QQ[x,y,t,s,MonomialOrder=>Lex];

i2 : F = {x + y^2 - t, t^2 -s};

i3 : T = triaSystem(R,F,{});

i4 : f = x*y*t;

i5 : resultant(f,T)

        6     2 2
o5 = - y s + y s

o5 : R

Ways to use this method: