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Feature #585

(Hilbert-) quasi-polynomials

Added by Christof Soeger about 10 years ago. Updated almost 10 years ago.

Status:
Closed
Priority:
Normal
Assignee:
John Abbott
Category:
New Function
Target version:
CoCoALib-0.99534 Seoul14
Start date:
10 Jul 2014
Due date:
% Done:

100%

Estimated time:
2.70 h
Spent time:
2.60 h

Description

For objects (cones, algebras,..) which are not generated in degree 1 the Hilbert function is not a polynomial anymore, but a quasi-polynomial.
A quasi-polynomial Q of period p is a polynomial with periodic coefficients, in other word, a collection of polynomials Q_0 , . . . , Q_{p-1} with Q(i) = Q_j(i) when i is congruent j mod pi.

How to represent them? (in CoCoALib and also CoCoA5)

Easy possibility: A vector of regular polynomials. It can be combined with an evaluation function that chooses the right Q_i.

History

#1 Updated by John Abbott about 10 years ago

  • Category set to New Function
  • Status changed from New to Feedback
  • Assignee set to John Abbott
  • Target version set to CoCoALib-0.99534 Seoul14
  • % Done changed from 0 to 90
  • Estimated time set to 2.70 h

Implemented; tested; documented; checked in. So status-->FEEDBACK!

#2 Updated by John Abbott almost 10 years ago

  • Status changed from Feedback to Closed
  • % Done changed from 90 to 100

Christof has reported no problems, so closing.

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