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D.7.1 finvar_lib

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

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..


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