jets(ZZ,QuotientRing) -- the jets of an affine algebra

Synopsis

Function: jets
Usage:

jets (n,Q)
Inputs:
- n, an integer,
- Q, a quotient ring,
Optional inputs:
- Projective => ..., default value false, Option for jets
Outputs:
- a quotient ring,

Description

This function is provided by the package Jets. Forms the jets of a QuotientRing by forming the quotient of jets(ZZ,PolynomialRing) of the ambient ring of Q with jets(ZZ,Ideal) of the ideal defining Q

i1 : R= QQ[x,y];

i2 : I= ideal(y^2-x^3);

o2 : Ideal of R

i3 : Q= R/I;

i4 : JQ= jets(2,Q);

i5 : describe JQ

                          QQ[x0, y0][x1, y1][x2, y2]
o5 = -------------------------------------------------------------------
           2                    2     2       2                 3     2
     (- 3x0 x2 + 2y0*y2 - 3x0*x1  + y1 , - 3x0 x1 + 2y0*y1, - x0  + y0 )

Caveat

Forming quotients triggers a Groebner basis computation, which may be time consuming.