jeanluct / pseudoanosov Goto Github PK

Things are a little murky right now:

• ReciprocalPolynomialBoundedList restricts to Perron root. Is this the best idea? Probably.
• Usage, from LT2010b: "Perron root" is the root itself (signed), "Perron number" is the absolute value.
• PerronRoot doesn't quite do that, since it returns the largest root (in magnitude), even if the polynomial is not Perron. Would it be better to call it LargestRoot or MaximalRoot?

There are several notebooks in the root folder and subfolders:

• stratatest.nb: Title: "Automated Elimination of Strata". Worked out example that refers to tables in the systole paper. Should verify these tables. Link to arXiv version of paper. It doesn't "derive" the polynomials. Why not? Takes too much time? Update: after looking through it it doesn't seem to do things systematically later. Maybe change it so it does?
• TestPseudoAnosov.nb
• delta+.nb
• homologyaction.nb
• newbound.nb
• newminpA_even.nb
• newminpA.nb
• pGolden_genusg_even.nb
• stratatest2.nb
• lite/disc5.nb
• genus3/gup9_elim.nb
• genus3/genus3_systole_polybound.nb
• genus3/genus3_systole.nb
• genus3/genus2_systole.nb
• genus3/gup8_elim.nb
• polybound/polybound.nb
• primitive/polybound_n=6-7.nb
• primitive/primitive_bound_n=3.nb
• primitive/primitive_bound_n=6.nb
• primitive/primitive_bound_n=4_reciprocal.nb
• primitive/polybound_n=5.nb
• primitive/primitive_bound_n=4.nb
• primitive/primitive_bound_n=5.nb
• primitive/ChoHam_primitive_matrices.nb
• primitive/polybound_n=6.nb
• primitive/xn-x-1.nb

Categorize them: some should be moved to subfolders. Keep a few that demonstrate the use of PA.

Right now Regular takes a PerronRootSign option, but the other "expert" functions Singular, SingularPermutations, and SingularStratum take a prs value of +1 or -1.

One reason for this discrepancy, I think, is that the latter can't attempt to figure out the sign (i.e., can't take the Automatic value for PerronRootSign). Still, it's not very elegant to have these two different ways.

Possible solutions:

• Make all these expert functions truly internal, with i prefix.
• Give the flag to the other 3 functions, but disallow Automatic. After that I'm tempted to stop labeling them as "expert" and just move them with the others.

See also issue #3.

PseudoAnosovPerronRootQ[x^2 - 3 x + 1]

Abs::argx: Abs called with 0 arguments; 1 argument is expected. >>

True

Here the optional argument lmax should default to zero, but it doesn't. The argument list of the functions has lmax___:0 (three underscores). Why?

I'm not sure that StratumOrbits deals with the torus s={{}} in the right way. Ditto for marked points. Do some experiments, with things like StratumOrbits[{{}},p] or StratumOrbits[{{0,2}},p]. Then maybe expand help message to clarify that marked points can be used.

Check also that table works:

StratumOrbitsTable[#, 10] & /@ StratumOrbits[{{}}, p0]
First::nofirst: "{} has zero length and no first element."

stratatest.nb contains some really nice functions for making results tables. Add these to the core PseudoAnosov.m file, possibly in a new context? (`Results?)

Two ways of specifying stratum: with or without multiplicities. Easy to do. I think some functions already do it.

Several functions have the line

If[prs == Automatic, prs = Sign[Times @@ Take[L,-2]]];

which attempts to figure out the Perron root sign from the Lefschetz numbers (they eventually alternate). Make this a separate helper function.