Jets -- compute jets of various algebraic, geometric and combinatorial objects

Description

This package enables computations with jet functors. It introduces the jets method to compute jets of polynomial rings, ideals, quotients, ring homomorphisms, and varieties. The construction of jets follows an algebraic procedure discussed in several sources, including the first three references below.

Additional features include an alternative algorithm to compute the radical of jets of monomial ideals, a function to construct jets of graphs, a method for principal components of jets, and an option for jets with "projective" gradings.

References

L. Ein and M. Mustaţă, Jet schemes and singularities.

F. Galetto, E. Helmick, and M. Walsh, Jet graphs.

R.A. Goward and K.E. Smith, The jet scheme of a monomial scheme.

P. Vojta, Jets via Hasse-Schmidt Derivations.

Authors

Federico Galetto <galetto.federico@gmail.com>
Nicholas Iammarino <nickiammarino@gmail.com>

Version

This documentation describes version 1.1 of Jets.

Source code

The source code from which this documentation is derived is in the file Jets.m2. The auxiliary files accompanying it are in the directory Jets/.

Exports

Functions and commands
- jets -- compute the jets of an object
- jetsProjection -- canonical map between jets rings
- jetsRadical -- compute radicals of jets ideals
- principalComponent -- compute principal component of jets
Methods
- jets(ZZ,AffineVariety) -- the jets of an affine variety
- jets(ZZ,Graph) -- the jets of a graph
- "jets(ZZ,HyperGraph)" -- see jets(ZZ,Graph) -- the jets of a graph
- jets(ZZ,Ideal) -- compute jets of a an ideal in a polynomial ring
- jets(ZZ,PolynomialRing) -- compute jets of a polynomial ring
- jets(ZZ,QuotientRing) -- the jets of an affine algebra
- jets(ZZ,RingMap) -- the jets of a homomorphism of rings
- "jetsProjection(ZZ,ZZ,PolynomialRing)" -- see jetsProjection -- canonical map between jets rings
- "jetsProjection(ZZ,ZZ,QuotientRing)" -- see jetsProjection -- canonical map between jets rings
- "jetsRadical(ZZ,Ideal)" -- see jetsRadical -- compute radicals of jets ideals
- "principalComponent(ZZ,Ideal)" -- see principalComponent -- compute principal component of jets
Symbols
- jet -- hashtable key
- jetsBase -- hashtable value
- jetsInfo -- hashtable key
- jetsMatrix -- hashtable value
- jetsMaxOrder -- hashtable value
- jetsRing -- hashtable value
- projet -- hashtable key
- Saturate -- option for principal components
Other things
- JJ -- scripted functor associated with jets

For the programmer

The object Jets is a package.

Jets -- compute jets of various algebraic, geometric and combinatorial objects

Description

References

Authors

Version

Source code

Exports

For the programmer

Menu

Package methods

Examples from the literature

Technical information