Returns the jets of an AffineVariety as an AffineVariety.
i1 : R=QQ[x,y] o1 = R o1 : PolynomialRing |
i2 : I= ideal(y^2-x^2*(x+1))
3 2 2
o2 = ideal(- x - x + y )
o2 : Ideal of R
|
i3 : A= Spec(R/I) o3 = A o3 : AffineVariety |
i4 : jets(2,A)
/ QQ[x0, y0][x1, y1][x2, y2] \
o4 = Spec|------------------------------------------------------------------------------------------------|
| 2 2 2 2 3 2 2 |
\((- 3x0 - 2x0)x2 + 2y0*y2 + (- 3x0 - 1)x1 + y1 , (- 3x0 - 2x0)x1 + 2y0*y1, - x0 - x0 + y0 )/
o4 : AffineVariety
|
If jets(...,Projective=>...) is set to true, then jets are computed with the grading introduced in Proposition 6.6 (c) of P. Vojta, Jets via Hasse-Schmidt Derivations, and the function returns a ProjectiveVariety.
i5 : jets(2,A,Projective=>true)
/ QQ[x0, y0][x1, y1][x2, y2] \
o5 = Proj|------------------------------------------------------------------------------------------------|
| 2 2 2 2 3 2 2 |
\((- 3x0 - 2x0)x2 + 2y0*y2 + (- 3x0 - 1)x1 + y1 , (- 3x0 - 2x0)x1 + 2y0*y1, - x0 - x0 + y0 )/
o5 : ProjectiveVariety
|
With Projective=>true the jet variables of order zero have degree 0, therefore no heft vector exist for the ambient ring of the jets. As a result, certain computations will not be supported, and others may run more slowly. See heft vectors for more information.
Note: jets of projective varieties are currently not implemented.