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:
* invariant_ring:: generators of the invariant ring (i.r.)
* invariant_ring_random:: generators of the i.r., randomized alg.
* primary_invariants:: primary invariants (p.i.)
* primary_invariants_random:: primary invariants, randomized alg.
Auxiliary procedures:
* cyclotomic:: cyclotomic polynomial
* group_reynolds:: finite group and Reynolds operator (R.o.)
* molien:: Molien series (M.s.)
* reynolds_molien:: Reynolds operator and Molien series
* partial_molien:: partial expansion of Molien series
* evaluate_reynolds:: image under the Reynolds operator
* invariant_basis:: basis of homogeneous invariants of a degree
* invariant_basis_reynolds:: as invariant_basis(), with R.o.
* primary_char0:: primary invariants in char 0
* primary_charp:: primary invariant in char p
* primary_char0_no_molien:: p.i., char 0, without Molien series
* primary_charp_no_molien:: p.i., char p, without Molien series
* primary_charp_without:: p.i., char p, without R.o. or Molien series
* primary_char0_random:: primary invariants in char 0, randomized
* primary_charp_random:: primary invariants in char p, randomized
* primary_char0_no_molien_random:: p.i., char 0, without M.s., randomized
* primary_charp_no_molien_random:: p.i., char p, without M.s., randomized
* primary_charp_without_random:: p.i., char p, without R.o. or M.s., random.
* power_products:: exponents for power products
* secondary_char0:: secondary (s.i.) invariants in char 0
* secondary_charp:: secondary invariants in char p
* secondary_no_molien:: secondary invariants, without Molien series
* secondary_and_irreducibles_no_molien:: s.i. & irreducible s.i., without M.s.
* secondary_not_cohen_macaulay:: s.i. when invariant ring not Cohen-Macaulay
* orbit_variety:: ideal of the orbit variety
* relative_orbit_variety:: ideal of a relative orbit variety
* image_of_variety:: ideal of the image of a variety

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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