# jetsProjection -- canonical map between jets rings

## Synopsis

• Usage:
jets(t,s,R)
jets(t,s,Q)
• Inputs:
• Optional inputs:
• Projective => ..., default value false, Option for jets
• Outputs:
• , 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 .