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Feature #761

Evaluating a QuasiPol

Added by Christof Soeger over 8 years ago. Updated about 8 years ago.

Status:
Closed
Priority:
Normal
Assignee:
John Abbott
Category:
CoCoA-5 function: new
Target version:
CoCoA-5.1.3/4 Jan 2016
Start date:
27 Aug 2015
Due date:
% Done:

100%

Estimated time:
2.00 h
Spent time:
0.85 h

Description

There should be an CoCoA5 function for evaluating a QuasiPoly. There is on in CoCoALib but we probably cannot use it easily because QuasiPoly is no CoCoA5 type.

History

#1 Updated by Anna Maria Bigatti over 8 years ago

  • Category set to CoCoA-5 function: new

I don't know how to do it (and if it is possible), but we could return a QuasiPoly in CoCoA-5 as a tagged object (tag "QuasiPoly") this would make it a kind of //CoCoA-5 type//
We'll see next week ;-)

#2 Updated by Christof Soeger over 8 years ago

Here is an example and how you have to evaluate it at the moment

excl := Mat(ZZ, [
[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1],
[-1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1],
[1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1],
[1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1],
[1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1]
]);

ineq := Mat(ZZ, [
[-1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1],
[-1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1]
]);

eq := Mat(ZZ,[[1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1]]);

v := Mat(ZZ,[[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]]);

CondIn := record[excluded_faces := excl, inequalities := ineq, equations := eq, grading := v, signs := v];

T := CpuTime();
C := NmzComputation(CondIn, ["HilbertSeries"]);
"CpuTime = "+DecimalStr(CpuTime()-T) + "s";

Q := C.HilbertQuasiPolynomial;

// Q[0]
eval(Q[1],[0]);

// periode
len(Q);

// Q[13]
eval(Q[2],[13]);

I would like to do just eval(Q,13). Since it is no type we probably have to give it a different clear name, like evalQuasiPoly(Q,13).

#3 Updated by Christof Soeger over 8 years ago

  • % Done changed from 0 to 50

Ups, there is already NmzEvaluateHilbertQuasiPolynomial with exactly that functionality. But it has no documentation.

#4 Updated by Anna Maria Bigatti over 8 years ago

added example to CoCoAHelp

#5 Updated by John Abbott about 8 years ago

  • Status changed from New to Feedback
  • % Done changed from 50 to 90

This has been present for over 6 months.

Just one question before closing: why does the fn name contain Hilbert?
While the quasi-poly is typically produced as a Hilbert fn, the fn which evaluates it does not care where the quasi-poly came from.

I would suggest the shorter name NmzEvalQuasiPoly;
we use the abbrev Eval for "evaluate" in a few other cases (e.g. EvalHilbertFn);
we use the abbrev Poly for "polynomial" in several cases.

The current name is very long; JAA think it is too long.

#6 Updated by John Abbott about 8 years ago

Christof does have a valid point about creating a new "type" (tag?) for QuasiPoly. If we think it is worth considering, we can create a new separate issue (related to this one).

#7 Updated by Christof Soeger about 8 years ago

I already suggested EvalQuasiPoly ;)

The QuasiPoly is a general object in CoCoALib and not in the Normaliz interface. So the evaluation function also shouldn't contain Nmz.

#8 Updated by John Abbott about 8 years ago

  • Status changed from Feedback to Closed
  • Assignee set to John Abbott
  • % Done changed from 90 to 100

I have renamed the fn to EvalQuasiPoly, and updated the C5 documentation (and the Normaliz tests).
Closing.

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