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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


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