[sage-support] Universal grobner basis and graver basis of an ideal associated to linear code using sage

[NITIN DARKUNDE]

Dear group members,
   I have found out a grobner basis of an ideal associated to some
binary linear code using sage. Output contains 2127  polynomials
(binomials) in 19 variables( I used degrevlex order). Is there any command
in sage via which one can compute Universal Grobner basis and Graver basis
of an ideal with which we started?

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Re: [sage-support] Re: About inclusion of sage commands and output on word file/Latex file

[NITIN DARKUNDE]

I mean that, if there is any way via which one can get the output on word
and then on latex, in order to include in research paper. I am strongly of
opinion that maths writing must be in latex.

On Dec 24, 2016 4:43 PM, "Dima Pasechnik" <dimp...@gmail.com> wrote:

> This is a bit off-topic, but writing maths in word is not really a good
> idea. Every worthwhile
> publication venue in mathematics or CS supports (La)TeX.
>
>
> On Saturday, December 24, 2016 at 7:52:53 AM UTC, NITIN DARKUNDE wrote:
>>
>> Dear group members,
>>I have been using sage since last 01
>> month. I just done some easy commands in it . I want to ask you, how to
>> take these commands and their output on word/latex file?(So that I can
>> include, this stuff in my research paper). Thanks.
>>
>> --
>> --
>> Yours faithfully,
>> ---
>>
>>
>>
>>
>>
>>
>>
>>
>> *Mr. Nitin Shridhar Darkunde.Assistant Professor,Department of
>> Mathematics,School of Mathematical Sciences,Swami Ramanand Teerth
>> Marathwada University,Vishnupuri, Nanded-431 606 (M.S.), India.Mob.
>> No:08275268895Or
>>  09273500312*
>>
>> --
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[sage-support] About inclusion of sage commands and output on word file/Latex file

[NITIN DARKUNDE]

Dear group members,
   I have been using sage since last 01 month.
I just done some easy commands in it . I want to ask you, how to take these
commands and their output on word/latex file?(So that I can include, this
stuff in my research paper). Thanks.

-- 
--
Yours faithfully,
---








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

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[sage-support] Grobner bases of ideals

[NITIN DARKUNDE]

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,Swami Ramanand Teerth
Marathwada University,Vishnupuri, Nanded-431 606 (M.S.), India.Mob.
No:08275268895Or
 09273500312*

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Re: [sage-support] About total degree of polynomial in Grobner basis of an ideal

[NITIN DARKUNDE]

Respected Sir,
Thank you very much. I used this command and got the
result.

On Tue, Dec 20, 2016 at 3:12 PM, John Cremona <john.crem...@gmail.com>
wrote:

> Use the degree() method to compute the degree of any polynomial.  For
> example:
>
> sage: R.<x,y,z>=QQ[]
> sage: I = Ideal(x^2-y,z^3+x^2)
> sage: I.groebner_basis()
> [z^3 + y, x^2 - y]
> sage: [f.degree() for f in I.groebner_basis()]
> [3, 2]
>
> On 20 December 2016 at 08:47, NITIN DARKUNDE <darkundeni...@gmail.com>
> wrote:
> > Dear group members,
> >  Suppose I am working with an ideal in polynomial
> ring
> > with n variables w.r.t. some ordering say degrevlex. If I compute
> groebner
> > basis of that ideal, then is there any tool via which one can compute
> total
> > degree of each of the polynomial in Groebner basis using sage?
> >
> > --
> > --
> > Yours faithfully,
> > ---
> > Mr. Nitin Shridhar Darkunde.
> > Assistant Professor,
> > Department of Mathematics,
> > School of Mathematical Sciences,
> > Swami Ramanand Teerth Marathwada University,
> > Vishnupuri, Nanded-431 606 (M.S.), India.
> > Mob. No:08275268895Or09273500312
> > 
> >
> >
> > --
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> > For more options, visit https://groups.google.com/d/optout.
>
> --
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>



-- 
--
Yours faithfully,
---








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

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[sage-support] About total degree of polynomial in Grobner basis of an ideal

[NITIN DARKUNDE]

Dear group members,
 Suppose I am working with an ideal in polynomial ring
with n variables w.r.t. some ordering say degrevlex. If I compute groebner
basis of that ideal, then is there any tool via which one can compute total
degree of each of the polynomial in Groebner basis using sage?

-- 
--
Yours faithfully,
---








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

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Re: [sage-support] Grobner bases in sage

[NITIN DARKUNDE]

Respected Sir,
 I am talking about remainder of f.

On Dec 16, 2016 6:17 PM, "David Joyner" <wdjoy...@gmail.com> wrote:

> On Fri, Dec 16, 2016 at 5:55 AM, NITIN DARKUNDE <darkundeni...@gmail.com>
> wrote:
> >
> > Dear Group members,
> >Suppose we have been given an ideal say 'I' in
> > multivariate polynomial over a finite field. Then I know , the procedure
> to
> > find a Groebner basis say 'G' of that ideal. Suppose we have one
> polynomial
> > say f which is outside I as well as G, then can we find reduced form(i.e
> > remainder of f) of f modulo G, using Sage, if so what is the procedure?
> >   Thanks.
> >
>
>
> Are you talking about reduce?
>
> http://doc.sagemath.org/html/en/reference/polynomial_rings/
> sage/rings/polynomial/multi_polynomial_ideal.html
>
>
>
> > --
> > --
> > Yours faithfully,
> > ---
> > Mr. Nitin Shridhar Darkunde.
> > Assistant Professor,
> > Department of Mathematics,
> > School of Mathematical Sciences,
> > Swami Ramanand Teerth Marathwada University,
> > Vishnupuri, Nanded-431 606 (M.S.), India.
> > Mob. No:08275268895Or09273500312
> > 
> >
> >
> > --
> > You received this message because you are subscribed to the Google Groups
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> > email to sage-support+unsubscr...@googlegroups.com.
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> > For more options, visit https://groups.google.com/d/optout.
>
> --
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[sage-support] Grobner bases in sage

[NITIN DARKUNDE]

​Dear Group members,
   Suppose we have been given an ideal say 'I' in
multivariate polynomial over a finite field​. Then I know , the procedure
to find a Groebner basis say 'G' of that ideal. Suppose we have one
polynomial say f which is outside I as well as G, then can we find reduced
form(i.e remainder of f) of f modulo G, using Sage, if so what is the
procedure?
  Thanks.

-- 
--
Yours faithfully,
---








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

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Re: [sage-support] Re: Sage crash report 7.0

[NITIN DARKUNDE]

Hello, I have some old version of sage installed two years ago on my
laptop. Also some worksheets are saved on it. How to upgrade it to latest
7.4 version? Whether old saved worksheets will remain saved? or get deleted?

On Dec 14, 2016 9:08 PM, "Dima Pasechnik"  wrote:

Is there any reason you cannot upgrade to a more recent version? The
current stable version is 7.4.


On Wednesday, December 14, 2016 at 1:28:09 PM UTC, Laurent Bakri wrote:
>
>
>
> Hi all,
> I am using sage  on Debian (sid)
> Sagemath 7.0 was working fine until an upgrade of python  to version 3
> Then it stop working with an syntax error due to python 3
> So I (re)lnked pyhton to python 2.7 but now it crashes for a reason I
> cannot determine
> here is the crash report
> Thanks in advance,
>
> --
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[sage-support] About sage commands/programme in Linear algebra/coding theory

[NITIN DARKUNDE]

Dear group members,
 I have the following question. Suppose I have one
non square matrix(i.e. *generator matrix of some linear code over finite
field with 2 elements*)over GF(2), whose rows will span one particular
vector space say V or linear code over GF(2).


G=G=matrix(GF(2),[[1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1],
[0,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0],
[0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1],
[0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0],
[0,0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0]])
Call each of the row as a,b,c,d,e as follows:
a=[1,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1];
b=[0,1,0,0,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0];
c=[0,0,1,0,0,0,1,0,1,1,1,1,0,0,1,0,0,0,1]
d=[0,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]
e=[0,0,0,0,1,1,1,0,0,1,0,1,0,0,1,1,1,0,0]

Now define a norm of a subcode/subspace as:
If D is a subcode of C/subspace of V, then norm of D is defined as:
* norm of D = | {i ∈ {1, . . . , n} : there exists v ∈ D with vi is
non-zero} |. *

e.g. If D={(0,0,0),(1,0,0),(0,1,0),(1,1,0)} which is vector space/linear
code over GF(2), then norm of D=|{1,2}|=2

Then if I take a linear span of any two distinct vectors from above matrix,
then I will get 10 (since there are 5 choose 2 choices for this) two
dimensional subspaces/subcodes of V or C.
*My question is how to find number of subspaces/subcodes in this vector
space/linear code of  dimension two and given norm(i.e.of varying norm from
1,2,...at the most 19 in above example of matrix G) using sage?*

-- 
--
Yours faithfully,
---








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

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Re: [sage-support] Grobner basis for linear codes

[NITIN DARKUNDE]

Respected Sir,
Yes sir, I am supposed to calculate Grobner basis for
an ideal in a polynomial ring in 35 variables with coefficients from GF(2).

On Dec 6, 2016 10:45 PM, "David Joyner" <wdjoy...@gmail.com> wrote:

> On Mon, Dec 5, 2016 at 4:56 AM, NITIN DARKUNDE <darkundeni...@gmail.com>
> wrote:
> > Dear group members,
> > I am doing my research in algebraic coding theory. I have
> > started using sage for computations of Grobner bases, but while doing it
> I
> > have some difficulties.The paper I am reading has been attached herewith.
> >  Attachment number 1 of this mail:On page number 486,
> > authors have defined an ideal  in equation number 9 and 10 and by using
> this
> > information and theorem 3.1, authors computed reduced Groebner basis of
> > ternary Golay code(on page 487 of this paper). I constructed this ideal
> in
> > equation 9 and 10 by using sage and also succeed to get its Grobner
> basis.
> >  Attachment number 2 of this mail:Now I had taken another
> > 6x35 generator matrix of some linear code over GF(2). I computed
> its(linear
>
>
> Just to clarify, are you asking to compute the GB of an ideal in 35
> variables?
>
> > code's) length, but while finding parity check matrix of this linear
> > code(using command H=C.check_mat()), I am not getting the output or
> > sometimes I get the output as string index out of range... Does it mean
> that
> > size of matrix which is 29x35 is too large for sage to show its output.
> But
> > still I want to see and get the output, Please help me in this
> context.Next
> > question is related to finding Groebner basis of this ideal, as soon as I
> > use the command I.groebner_basis(), I am not getting any output, whereas
> in
> > second paragraph example(of this mail), I was getting the output,Please
> help
> > me in this context.
> >
> > --
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