# CotangentSchubert -- A package for contangent 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, in preparation.

## Version

This documentation describes version 0.6 of CotangentSchubert.

## Source code

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

## Exports

• Types
• "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
• 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
• Symbols

## For the programmer

The object CotangentSchubert is .