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Slug #1739

IsHomog for ideals

Added by Anna Maria Bigatti 12 months ago. Updated about 2 months ago.

Status:
Closed
Priority:
Normal
Assignee:
Anna Maria Bigatti
Category:
Improving
Target version:
CoCoALib-0.99850
Start date:
05 May 2023
Due date:
% Done:

100%

Estimated time:
2.01 h
Spent time:
1.75 h

Description

the function IsHomog for ideals might take a long time computing a GBasis, but if
the check IsHomog(gens(I)) gives true, it should immediately return true without further computations.

Related issues

Related to CoCoALib - Feature #1784: Add flag IhaveHomogGensValue for ideals in SparsePolyRing?New2024-03-01

Related to CoCoALib - Feature #1785: Add function IsHomog3(I)?New2024-03-01

History

#1 Updated by John Abbott 3 months ago

  • Target version changed from CoCoALib-0.99800 to CoCoALib-0.99850

This should be easy to implement, right?
I was wondering how often one would want to know whether an ideal is homog without shortly afterwards wanting a GBasis?
I presume that if the ideal is not homog then one must compute the GBasis, right?

#2 Updated by John Abbott 3 months ago

  • Status changed from New to In Progress

I say impl the suggestion in the main description: it should be very little code, and may make some computations faster.

Are there any other short-cuts?
If IsZeroDim(I) then it is not homog. I can think of other possible short-cuts, but would they ever be applicable? For instance, if there is a non-homog generator using indets x[1],...,x[n] and all other gens use only other indets... How often does this happen?

reply IsZeroDim(I) requires a GBasis, so it's not a real shortcut.

#3 Updated by John Abbott 3 months ago

Source is in SparsePolyOps-ideal.C:908 more or less

#4 Updated by John Abbott 3 months ago

Could it be useful to have also IsHomog3 which returns a bool3?

#5 Updated by Anna Maria Bigatti 3 months ago

Fixed. Now checking if gens are monomial, then if gens are homogeneous.

/**/ use R ::= QQ[a,b,c,d,e,f];
/**/ L := monomials(sum(indets(R))^25);  len(L);
142506
/**/ IL := ideal(L);  t0 := CpuTime(); IsHomog(IL); TimeFrom(t0); -- monomial gens
true
0.003
/**/ L[len(L)] := a+b;
/**/ IL := ideal(L);  t0 := CpuTime(); IsHomog(IL); TimeFrom(t0); -- last gen non monomial
true
0.028
/**/ IL := ideal(L);  t0 := CpuTime(); GB := GBasis(IL); TimeFrom(t0);
--> very long time

#6 Updated by Anna Maria Bigatti 2 months ago

  • Status changed from In Progress to Resolved
  • % Done changed from 10 to 80

check if there is a "homog" flag to be set

#7 Updated by Anna Maria Bigatti about 2 months ago

  • Related to Feature #1784: Add flag IhaveHomogGensValue for ideals in SparsePolyRing? added

#8 Updated by Anna Maria Bigatti about 2 months ago

Anna Maria Bigatti wrote:

check if there is a "homog" flag to be set

The answer is "no" (#1784).

#9 Updated by Anna Maria Bigatti about 2 months ago

John Abbott wrote:

Could it be useful to have also IsHomog3(I) which returns a bool3?

it could be handy to have a function: it is not entirely trivial to write a quick check on the generators, if one needs it.
On the other hand, it is useful anywhere?

Usual philosophical question: it is good to add functions whose utility is uncertain?
I'm inclined to postpone this into a new issue.

#10 Updated by Anna Maria Bigatti about 2 months ago

#11 Updated by Anna Maria Bigatti about 2 months ago

  • Status changed from Resolved to Closed
  • % Done changed from 80 to 100
  • Estimated time changed from 1.00 h to 2.01 h

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