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Feature #1299

New fn ConstantTerm?

Added by John Abbott over 4 years ago. Updated almost 4 years ago.

Status:
Closed
Priority:
Normal
Assignee:
John Abbott
Category:
New Function
Target version:
CoCoALib-0.99710
Start date:
29 Jul 2019
Due date:
% Done:

100%

Estimated time:
1.66 h
Spent time:
1.50 h

Description

In some prototype code I would like to use a function which gives me the "constant term" of a polynomial. The result may be 0.

One way is to call CoeffOfTerm(f,1); well, actually CoeffOfTerm(f, one(RingOf(f))).
But this is likely to be needlessly slow.

Is it a good idea to have a dedicated function? If so, what should it be called?

History

#1 Updated by John Abbott over 4 years ago

Possible names include ConstTerm and ConstantTerm. The result should be an element of CoeffRing.

Implementing in CoCoALib should be quick; I do not recall now, but maybe CoCoALib has (almost direct) access to the last term in a poly.
It would be good if the code can avoid traversing the whole poly. If we do have to traverse, note that we should first check whether the "next" pointer is null; if it is not, we go to the next term; if it is null, then we check whether the PP is 1 (no need to check for other PPs being equal to 1).

#2 Updated by Anna Maria Bigatti over 4 years ago

  • % Done changed from 0 to 10

I think it could be useful.
But I wouldn't call it ConstantTerm, because term in CoCoA usually (always?) is equivalent to "power-product", so it would cause ambiguity.
Call it constant(f)?

#3 Updated by John Abbott over 4 years ago

  • Status changed from New to In Progress
Other candidates:
  • ConstantPart
  • ValueAtZero or ValueAt0
  • ConstantCoeff or ConstantCoefficient

Further ideas?

JAA quite likes ConstantCoeff at the moment...

#4 Updated by John Abbott over 4 years ago

  • Target version changed from CoCoALib-0.99700 to CoCoALib-0.99800

#5 Updated by John Abbott about 4 years ago

This is a little bit like HomogCompt(f,0). See issue #1439.

#6 Updated by John Abbott about 4 years ago

  • Assignee set to John Abbott
  • % Done changed from 10 to 40

I have a prototype impl, much like the impl for HomogCompt.

It is disappointingly slow for larger polynomials:

use QQ[x,y,z];
f := 1+x+y+z;
g := f^200; -- takes about 90s, occupies about 400Mbytes
ConstantCoeff(g); -- takes about 0.4s; had hoped it'd be faster

UPDATE: (2020-04-19) NumTerms(g) takes about 0.48s; result is 1373701

#7 Updated by John Abbott about 4 years ago

  • Status changed from In Progress to Feedback
  • % Done changed from 40 to 90
  • Estimated time set to 1.66 h

I have now checked in my code... since I was checking CVS anyway.
Also added doc to CoCoAHelp.xml.

#8 Updated by Redmine Admin almost 4 years ago

  • Target version changed from CoCoALib-0.99800 to CoCoALib-0.99710

#9 Updated by John Abbott almost 4 years ago

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

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