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Feature #48

Feature #39: Squarefree factorization

Feature #43: Squarefree factorization - for polynomials

Feature #47: Squarefree factorization - multivariate polynomials

Squarefree factorization - multivariate polynomials, char 0

Added by John Abbott over 12 years ago. Updated over 8 years ago.

Status:
Closed
Priority:
Normal
Assignee:
John Abbott
Category:
New Function
Target version:
CoCoALib-0.99531
Start date:
30 Nov 2011
Due date:
% Done:

100%

Estimated time:
Spent time:
0.45 h

Description

No obvious new conceptual problems. Efficiency may be an issue. Consider modular approach?

What happens if coeffs are not in QQ? Consider the ring QQ[x][y,z]

History

#1 Updated by John Abbott over 10 years ago

  • Status changed from New to Closed
  • Assignee set to John Abbott
  • % Done changed from 0 to 100

This case is effectively covered by the porting of d'Ali's code.

Might still need some tweaking to handle "strange" cases such as QQ[x][y,z].

#2 Updated by Anna Maria Bigatti over 10 years ago

  • Target version set to CoCoALib-0.99531

#3 Updated by Anna Maria Bigatti over 8 years ago

In factor.C there is the line:

    if (IsQQ(R)) return SqFreeFactorChar0(f);

is it ok to substitute it with
    if (characteristic(R)==0) return SqFreeFactorChar0(f);

?

#4 Updated by John Abbott over 8 years ago

I'm not sure; I suspect it will not work in every case.

What coeff ring did you have in mind? Were you thinking of a polynomial in a ring like QQ[x][y]? In this case we could "flatten" the ring to QQ[x,y], compute the answer there, and then map it back to the original ring.

The existing code may work for algebraic extensions of QQ... I'm too tired to check now.

#5 Updated by Anna Maria Bigatti over 8 years ago

John Abbott wrote:

I'm not sure; I suspect it will not work in every case.

I thought it would: in char 0 the square free (or radical) of a polynomial f is f/gcd(f,f').
So I imagined your algorithm does not actually depend on the specific (char 0) coefficient ring.

#6 Updated by John Abbott over 8 years ago

Good point! So if gcd works then we can expect that squarefree decomposition works.

#7 Updated by Anna Maria Bigatti over 8 years ago

Anna Maria Bigatti wrote:

John Abbott wrote:

I'm not sure; I suspect it will not work in every case.

I thought it would: in char 0 the square free (or radical) of a polynomial f is f/gcd(f,f').
So I imagined your algorithm does not actually depend on the specific (char 0) coefficient ring.

Ah! here is where I got confused: this algorithm is for the univariate case!!
so, maybe we could give the answer for univariate polynomials (at least..)

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