Ask Your Question

What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variables

asked 2016-12-03 11:50:01 +0200

Nilesh gravatar image

I am doing calculations of finding Groebner basis of a toric ideal associated with one matrix. At the end I am getting output as Polynomial Sequence with 634 Polynomials in 35 Variables . I want a complete output which involves all these polynomials. Is there any command to do this?

edit retag flag offensive close merge delete

1 Answer

Sort by » oldest newest most voted

answered 2016-12-03 12:30:18 +0200

slelievre gravatar image

updated 2016-12-03 12:54:50 +0200

The documentation for polynomial sequences is here:

It says

We call a finite list of polynomials a Polynomial Sequence.

To see all the polynomials in the sequence, you can use the list command.


sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)

This outputs the list of all polynomials in the polynomial sequence.

Note that the representation of F is a string of the list itself if the sequence F has less than 20 elements, while if F has 20 elements or more, a summary is printed.

Example: compare

sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]


sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables

Note that this information is in the documentation for the _repr_ method of F, which you can access by typing

sage: F._repr_?

See also the source code by typing

sage: F._repr_??
edit flag offensive delete link more


Dear Sir, I had again done sage computations for finding a Groebner basis of an ideal in polynomial ring in 35 variables with coefficients from finite field with 2 elements. This time as soon as I enter a command I.groebner_basis() No output is coming. Why this is so? What to do , to get an output?

Nilesh gravatar imageNilesh ( 2016-12-04 13:51:41 +0200 )edit

It could be that the computation is taking a long time. Please ask this as a separate question. Be sure to provide code to define the ideal in question.

slelievre gravatar imageslelievre ( 2016-12-05 07:25:49 +0200 )edit

Dear Sir, as per your suggestion I asked this as a separate question.Please go through it. Thanks.

Nilesh gravatar imageNilesh ( 2016-12-05 11:08:09 +0200 )edit

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

Question Tools

1 follower


Asked: 2016-12-03 11:50:01 +0200

Seen: 633 times

Last updated: Dec 03 '16