These are the things I'll get to do when I get to do them:
$Id: TODO,v 1.21 2010/03/03 20:01:01 gap Exp $

ALL:
  * extend alphabet by natural embedding, "skip levels" in tree
  * quotient alphabets
  * check alphabets not [1..n]
  * should stateset be an attribute or an operation?
  * in e.g. Nucleus, keep track of words along with mealy machine; this
    will speed up FabrykowskiGuptaGroups which reconstructs the nucleus's words

frmachine:
  * add or remove generator

frelement:
  * order and cycles for transformations, with period and preperiod
  * recognize at least some machines that are not finite-state

mealy:

group:
  * smarter "branch" detection, with commutators and quotients
  * find explicit isomorphism between contracting groups, incl. non-trivial
  * Exponent, IsSolvable, IsNilpotent, IsSimple
  * smarter IsTorsion, IsTorsionFree, HasCongruenceProperty
  * SubexponentialGrowth
  * SEARCH@.BALL should not compute full balls if #gens is large (>100)

vhgroup:
  * IsLevelTransitiveOnPatterns

examples:
  * mother groups for polynomial growth, construct embeddings into such group

helpers:
  * interval arithmetic
  * maybe use InputOutputLocalProcess

img:
  * blow-ups, tuning of IMG
  * adding machines of fractional (e.g. 1/7) amplitude, for more tunings & matings
  * "dilute" FR machine by multiplying stateset with {1..n} and chaining them in sequence
  * formal matings
  * given obstruction, compute quotient machine. More generally, find a common format for obstructions

linear, vector:
  * stategrowth limitmachine nucleus nucleusmachine
  * Minimize, nice vectors for algebra elements
  * extend / restrict scalars
  * "in" method
  
algebra:
  * test membership in an algebra
  * test nillity of algebra (akin to IsTorsion for groups)
