jetsProjection -- canonical map between jets rings

Synopsis

Usage:

jets(t,s,R)

jets(t,s,Q)
Inputs:
- t, an integer,
- s, an integer,
- R, a polynomial ring, or a quotient of
Optional inputs:
- Projective => ..., default value false, Option for jets
Outputs:
- a ring map, between jets orders

Description

This function is provided by the package Jets. Generates an inclusion map from the order s into the order t jets of a (quotient of a) polynomial ring. Throws an error if t<s.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : f = jetsProjection(5,2,R)

o2 = map (QQ[x0, y0][x1, y1][x2, y2][x3, y3][x4, y4][x5, y5], QQ[x0, y0][x1, y1][x2, y2], {x2, y2, x1, y1, x0, y0})

o2 : RingMap QQ[x0, y0][x1, y1][x2, y2][x3, y3][x4, y4][x5, y5] <-- QQ[x0, y0][x1, y1][x2, y2]

i3 : use jets(2,R)

o3 = QQ[x0, y0][x1, y1][x2, y2]

o3 : PolynomialRing

i4 : p = (x2 + 2*x1*y1 + x0*y2^2)

          2
o4 = x0*y2  + x2 + 2x1*y1

o4 : QQ[x0, y0][x1, y1][x2, y2]

i5 : f p

          2
o5 = x0*y2  + x2 + 2x1*y1

o5 : QQ[x0, y0][x1, y1][x2, y2][x3, y3][x4, y4][x5, y5]

Ways to use jetsProjection :

jetsProjection(ZZ,ZZ,PolynomialRing)
jetsProjection(ZZ,ZZ,QuotientRing)

For the programmer

The object jetsProjection is a method function with options.