# Grobner bases of ideals

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### NITIN DARKUNDE

Dec 21, 2016, 7:14:51 AM12/21/16
to Simon King, David Joyner, sage-s...@googlegroups.com
Respected Sir,
I am trying to find Groebner basis of an ideal in polynomial ring in 35 variables over GF(2)(As per suggestions earlier, I am working over GF(2) instead of GF(3))  but I am not able to see the output using sage. Even it do not shows any error in it. So,how to get the output?(Even I tried singular, but can't succeed.)

--
----------------------------------------------------------------------
Yours faithfully,
-----------------------------------------------------------------------
Mr. Nitin Shridhar Darkunde.
Assistant Professor,
Department of Mathematics,
School of Mathematical Sciences,
Vishnupuri, Nanded-431 606 (M.S.), India.
Mob. No:08275268895    Or    09273500312
********************************************************

### David Joyner

Dec 21, 2016, 7:28:57 AM12/21/16
to NITIN DARKUNDE, Simon King, SAGE support
On Wed, Dec 21, 2016 at 7:14 AM, NITIN DARKUNDE <darkun...@gmail.com> wrote:
> Respected Sir,
> I am trying to find Groebner basis of an ideal in
> polynomial ring in 35 variables over GF(2)(As per suggestions earlier, I am
> working over GF(2) instead of GF(3)) but I am not able to see the output
> using sage. Even it do not shows any error in it. So,how to get the
> output?(Even I tried singular, but can't succeed.)
>

Please copy and paste your input and output into an email, or save it
to a file and attach the file.

### David Joyner

Dec 21, 2016, 9:16:00 AM12/21/16
to NITIN DARKUNDE, Simon King, SAGE support
On Wed, Dec 21, 2016 at 7:28 AM, David Joyner <wdjo...@gmail.com> wrote:
> On Wed, Dec 21, 2016 at 7:14 AM, NITIN DARKUNDE <darkun...@gmail.com> wrote:
>> Respected Sir,
>> I am trying to find Groebner basis of an ideal in
>> polynomial ring in 35 variables over GF(2)(As per suggestions earlier, I am
>> working over GF(2) instead of GF(3)) but I am not able to see the output
>> using sage. Even it do not shows any error in it. So,how to get the
>> output?(Even I tried singular, but can't succeed.)
>>
>
> Please copy and paste your input and output into an email, or save it
> to a file and attach the file.
>

I copy+pasted this from a word doc the OP emailed me privately.

P.<x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35>=PolynomialRing(FiniteField(2),order='lex');
I=Ideal([x1*x21*x22*x23*x24*x25*x26*x27*x28*x29*x30*x31*x32*x33*x34*x35-1,x2*x14*x15*x16*x17*x18*x19*x20*x21*x22*x23*x24*x25*x26*x27*x28-1,x3*x11*x12*x13*x15*x17*x19*x20*x21*x22*x23*x24*x29*x30*x31*x35-1,x4*x8*x9*x10*x14*x18*x19*x20*x23*x24*x25*x27*
x29*x30*x32*x34-1,x5*x7*x8*x10*x12*x13*x19*x20*x22*x24*x25*x26*x29*x31*x32*x33-1,x6*x7*x9*x10*x11*x13*x16*x17*x18*x20*x22*x23*x25*x26*x29*x30-1,x1^2-1,x2^2-1,x3^2-1,x4^2-1,x5^2-1,x6^2-1,x7^2-1,x8^2-1,x9^2-1,x10^2-1,x11^2-1,x12^2-1,x13^2-1,x14^2-1,
x15^2-1,x16^2-1,x17^2-1,x18^2-1,x19^2-1,x20^2-1,x21^2-1,x22^2-1,x23^2-1,x24^2-1,x25^2-1,x26^2-1,x27^2-1,x28^2-1,x29^2-1,x30^2-1,x31^2-1,x32^2-1,x33^2-1,x34^2-1,x35^2-1]);
I.groebner_basis();

### David Joyner

Dec 21, 2016, 9:17:55 AM12/21/16
to NITIN DARKUNDE, Simon King, SAGE support
On Wed, Dec 21, 2016 at 7:14 AM, NITIN DARKUNDE <darkun...@gmail.com> wrote:
> Respected Sir,
> I am trying to find Groebner basis of an ideal in
> polynomial ring in 35 variables over GF(2)(As per suggestions earlier, I am
> working over GF(2) instead of GF(3)) but I am not able to see the output

What happened when you replace 35 variables by <10 vars (also
suggested earlier)? Do you get what you expeced in that case?

### jack

Dec 21, 2016, 12:49:36 PM12/21/16
to sage-support, simon...@uni-jena.de, wdjo...@gmail.com
Try removing the semi-colon;;;;;;;

Best regards,
Jack Fearnley

### Simon King

Dec 22, 2016, 7:17:37 AM12/22/16
On 2016-12-21, jack <ja...@alcor.concordia.ca> wrote:
>> Try removing the semi-colon;;;;;;;

No. I tried the example, using different term orders (the OP uses lex,
I also tried degrevlex), but it didn't finish within 15 minutes. So, I'd
say that simply the problem is very difficult. On the other hand, the
given polynomials have an easy form, in particular they are all
binomials. So, it might work to use a special machinery for binomial
ideals - I don't think that Singular has an optimisation for it.

Best regards,
Simon

### Dima Pasechnik

Dec 24, 2016, 7:00:52 PM12/24/16
to sage-support
as I posted in another thread, 4ti2 (also the Sage package)
supports binomial (aka toric) ideals,
so this seems to be the right tool for the job here.

Best regards,
Simon