Macaulay2 » Documentation
Packages » Jets » jetsProjection
next | previous | forward | backward | up | index | toc

# jetsProjection -- canonical map between jets rings

- 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Jets.m2:1666:0.