CotangentSchubert -- A package for cotangent Schubert calculus

Description

CotangentSchubert is a package for calculations in cotangent Schubert calculus. Specifically, it allows to compute motivic Chern and Segre classes (as well as their limits in ordinary Schubert calculus, namely Schubert classes), and to independently compute the expansion of their products using puzzles. Puzzles and their "fugacities" are defined and computed using the results of [1,2,3].

References:
[1] A. Knutson and P. Zinn-Justin, Schubert puzzles and integrability I: invariant trilinear forms, arXiv:1706.10019.
[2] A. Knutson and P. Zinn-Justin, Schubert puzzles and integrability II: multiplying motivic Segre classes, arXiv:2102.00563.
[3] A. Knutson and P. Zinn-Justin, Schubert puzzles and integrability III: separated descents, arXiv:2306.13855.

Author

Paul Zinn-Justin <[email protected]>

Certification

Version 0.63 of this package was accepted for publication in volume 14 of Journal of Software for Algebra and Geometry on 2024-02-06, in the article The CotangentSchubert Macaulay2 package (DOI: 10.2140/jsag.2024.14.73). That version can be obtained from the journal.

Version

This documentation describes version 0.71 of CotangentSchubert.

Citation

If you have used this package in your research, please cite it as follows:

@misc{CotangentSchubertSource,
  title = {{CotangentSchubert: Cotangent Schubert calculus. Version~0.71}},
  author = {Paul Zinn-Justin},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

@article{CotangentSchubertArticle,
  title = {{The CotangentSchubert \emph{Macaulay2} package}},
  author = {Paul Zinn-Justin},
  journal = {Journal of Software for Algebra and Geometry},
  volume = {14},
  year = {2024},
}

Exports

Types
- LabelList (missing documentation)
- Puzzle -- see puzzle -- Compute puzzles with given boundaries
Functions and commands
- basisCoeffs -- Expand a finite-dimensional algebra element into its basis
- bottom -- The bottom string of a puzzle
- canonicalClass -- Class of the canonical bundle of a flag variety
- chernClass -- Compute a motivic Chern class
- chernClass' -- see chernClass -- Compute a motivic Chern class
- stableClass -- see chernClass -- Compute a motivic Chern class
- stableClass' -- see chernClass -- Compute a motivic Chern class
- doublePuzzle -- Produces a rhombus puzzle
- dualZeroSection -- Class of the zero section of the tangent bundle of a flag variety
- fugacity -- compute the fugacity of puzzles
- fugacityTally -- see fugacity -- compute the fugacity of puzzles
- fugacityVector -- see fugacity -- compute the fugacity of puzzles
- inversion -- Inversion number of a string
- pushforwardToPoint -- Push forward classes to a point
- pushforwardToPointFromCotangent -- see pushforwardToPoint -- Push forward classes to a point
- puzzle -- Compute puzzles with given boundaries
- restrict -- Restriction to fixed points
- schubertClass -- Compute a Schubert class
- schubertClass' -- see schubertClass -- Compute a Schubert class
- sClass -- see segreClass -- Compute a motivic Segre class
- sClass' -- see segreClass -- Compute a motivic Segre class
- segreClass -- Compute a motivic Segre class
- segreClass' -- see segreClass -- Compute a motivic Segre class
- setupCotangent -- Set up cotangent Schubert calculus rings
- tautoClass -- Compute the class of a tautological bundle
- zeroSection -- Class of the zero section of the cotangent bundle of a flag variety
Methods
- inversion(LabelList) (missing documentation)
- net(LabelList) (missing documentation)
- new LabelList from List (missing documentation)
- new LabelList from String (missing documentation)
- new List from Puzzle (missing documentation)
- Puzzle ++ HashTable (missing documentation)
- Puzzle ++ List (missing documentation)
- Puzzle == Puzzle (missing documentation)
- texMath(LabelList) (missing documentation)
- toExternalString(LabelList) (missing documentation)
- toString(LabelList) (missing documentation)
Symbols
- assoc (missing documentation)

For the programmer

The object CotangentSchubert is a package, defined in CotangentSchubert.m2, with auxiliary files in CotangentSchubert/.

The source of this document is in CotangentSchubert.m2:398:0.