Characteristic Classes: Sequences

[mjungmath]

To each additive/multiplicative characteristic class corresponds a sequence. Namely, due to the fundamental theorem of symmetric polynomials, each symmetric polynomial can be expressed in terms of the elementary symmetric polynomials. In our setup, the k-th elementary symmetric polynomials corresponds to the k-th Chern class. This allows us to express additive/multiplicative characteristic classes in terms of Chern classes (or Pontryagin classes in the real case respectively). This is the sequence.

CC: @slel @egourgoulhon @tscrim

Component: manifolds

Author: Michael Jung

Branch/Commit: 7aa0ec5

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/30211

[mjungmath]

Branch: u/gh-mjungmath/characteristic_classes_sequence

[mjungmath]

Commit: 6972030

[mjungmath]

New commits:

6972030

Trac #30211: sequence function added

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5f25df5

Trac #30211: Merge branch 'develop' into characteristic_classes_sequence

[sagetrac-git]

Changed commit from 6972030 to 5f25df5

[sagetrac-git]

Changed commit from 5f25df5 to c7414bd

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

c7414bd

Trac #30211: docstring syntax

[mjungmath]

comment:5

This ticket is ready for review. Patchbot should turn green after this commit.

[tscrim]

comment:6

Do you have an example that gives something that is not a symmetric function over QQ?

Also, you are better off using

m = Sym.m()
m._from_dict({p: prod(ring(coeff[i]) for i in p)
              for k in range(len(coeff))
              for p in Partitions(k))

which is faster as it more directly creates the symmmetric function you want.

[mjungmath]

comment:7

Replying to @tscrim:

Do you have an example that gives something that is not a symmetric function over QQ?

Sure: x-y is no symmetric function over QQ.

Also, you are better off using

m = Sym.m()
m._from_dict({p: prod(ring(coeff[i]) for i in p)
              for k in range(len(coeff))
              for p in Partitions(k))

which is faster as it more directly creates the symmmetric function you want.

Thanks, I'll try this.