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D.6.1 finvar_lib
- Library:
finvar.lib
- Purpose:
Invariant Rings of Finite Groups
- Author:
Agnes E. Heydtmann, email: agnes@math.uni-sb.de
- 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 and W. Decker et al..
Main procedures:
D.6.1.1 invariant_ring generators of the invariant ring (i.r.) D.6.1.2 invariant_ring_random generators of the i.r., randomized alg. D.6.1.3 primary_invariants primary invariants (p.i.) D.6.1.4 primary_invariants_random primary invariants, randomized alg.
Auxiliary procedures:
D.6.1.5 cyclotomic cyclotomic polynomial D.6.1.6 group_reynolds finite group and Reynolds operator (R.o.) D.6.1.7 molien Molien series (M.s.) D.6.1.8 reynolds_molien Reynolds operator and Molien series D.6.1.9 partial_molien partial expansion of Molien series D.6.1.10 evaluate_reynolds image under the Reynolds operator D.6.1.11 invariant_basis basis of homogeneous invariants of a degree D.6.1.12 invariant_basis_reynolds as invariant_basis(), with R.o. D.6.1.13 primary_char0 primary invariants in char 0 D.6.1.14 primary_charp primary invariant in char p D.6.1.15 primary_char0_no_molien p.i., char 0, without Molien series D.6.1.16 primary_charp_no_molien p.i., char p, without Molien series D.6.1.17 primary_charp_without p.i., char p, without R.o. or Molien series D.6.1.18 primary_char0_random primary invariants in char 0, randomized D.6.1.19 primary_charp_random primary invariants in char p, randomized D.6.1.20 primary_char0_no_molien_random p.i., char 0, without M.s., randomized D.6.1.21 primary_charp_no_molien_random p.i., char p, without M.s., randomized D.6.1.22 primary_charp_without_random p.i., char p, without R.o. or M.s., random. D.6.1.23 power_products exponents for power products D.6.1.24 secondary_char0 secondary (s.i.) invariants in char 0 D.6.1.25 secondary_charp secondary invariants in char p D.6.1.26 secondary_no_molien secondary invariants, without Molien series D.6.1.27 secondary_and_irreducibles_no_molien s.i. & irreducible s.i., without M.s. D.6.1.28 secondary_not_cohen_macaulay s.i. when invariant ring not Cohen-Macaulay D.6.1.29 orbit_variety ideal of the orbit variety D.6.1.30 relative_orbit_variety ideal of a relative orbit variety D.6.1.31 image_of_variety ideal of the image of a variety