### D.7.1 finvar_lib

Library:
  finvar.lib
Purpose:
  Invariant Rings of Finite Groups
Author:
  Agnes E. Heydtmann, contact via Wolfram Decker: decker@mathematik.uni-kl.de Simon A. King, email: simon.king@nuigalway.ie

Overview:
  A library for computing polynomial invariants of finite matrix groups and generators of related varieties. The algorithms are based on B. Sturmfels, G. Kemper, S. King and W. Decker et al..

Procedures:

> D.7.1.1 invariant_ring |  | generators of the invariant ring (i.r.)
> D.7.1.2 invariant_ring_random |  | generators of the i.r., randomized alg.
> D.7.1.3 primary_invariants |  | primary invariants (p.i.)
> D.7.1.4 primary_invariants_random |  | primary invariants, randomized alg.
> D.7.1.5 invariant_algebra_reynolds |  | minimal generating set for the invariant ring of a finite matrix group, in the non-modular case
> D.7.1.6 invariant_algebra_perm |  | minimal generating set for the invariant ring or a permutation group, in the non-modular case
> D.7.1.7 cyclotomic |  | cyclotomic polynomial
> D.7.1.8 group_reynolds |  | finite group and Reynolds operator (R.o.)
> D.7.1.9 molien |  | Molien series (M.s.)
> D.7.1.10 reynolds_molien |  | Reynolds operator and Molien series
> D.7.1.11 partial_molien |  | partial expansion of Molien series
> D.7.1.12 evaluate_reynolds |  | image under the Reynolds operator
> D.7.1.13 invariant_basis |  | basis of homogeneous invariants of a degree
> D.7.1.14 invariant_basis_reynolds |  | as invariant_basis(), with R.o.
> D.7.1.15 primary_char0 |  | primary invariants (p.i.) in char 0
> D.7.1.16 primary_charp |  | primary invariants in char p
> D.7.1.17 primary_char0_no_molien |  | p.i., char 0, without Molien series
> D.7.1.18 primary_charp_no_molien |  | p.i., char p, without Molien series
> D.7.1.19 primary_charp_without |  | p.i., char p, without R.o. or Molien series
> D.7.1.20 primary_char0_random |  | primary invariants in char 0, randomized
> D.7.1.21 primary_charp_random |  | primary invariants in char p, randomized
> D.7.1.22 primary_char0_no_molien_random |  | p.i., char 0, without M.s., randomized
> D.7.1.23 primary_charp_no_molien_random |  | p.i., char p, without M.s., randomized
> D.7.1.24 primary_charp_without_random |  | p.i., char p, without R.o. or M.s., random.
> D.7.1.25 power_products |  | exponents for power products
> D.7.1.26 secondary_char0 |  | secondary invariants (s.i.) in char 0
> D.7.1.27 irred_secondary_char0 |  | irreducible s.i. in char 0
> D.7.1.28 secondary_charp |  | s.i. in char p, with Molien series and Reynolds operator
> D.7.1.29 secondary_no_molien |  | s.i., without Molien series but with Reynolds operator
> D.7.1.30 irred_secondary_no_molien |  | irreducible s.i., without Molien series but with Reynolds operator
> D.7.1.31 secondary_and_irreducibles_no_molien |  | s.i. & irreducible s.i., without M.s.
> D.7.1.32 secondary_not_cohen_macaulay |  | s.i. when the invariant ring is not Cohen-Macaulay
> D.7.1.33 orbit_variety |  | ideal of the orbit variety
> D.7.1.34 rel_orbit_variety |  | ideal of a relative orbit variety (new version)
> D.7.1.35 relative_orbit_variety |  | ideal of a relative orbit variety (old version)
> D.7.1.36 image_of_variety |  | ideal of the image of a variety orbit_sums orbit sums of a set of monomials under the action of a permutation group

User manual for Singular version 4.4.1, 2025, generated by texi2html.