Singular

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