| 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 |