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2016-12-22 05:40:09 +0100 commented question Grobner bases of ideals

Dear Sir, as per your suggestion, I edited my earlier question and given the entire code, which I used.

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2016-12-21 13:11:33 +0100 asked a question Grobner bases of ideals

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), since in GF(2) coefficient growth is restricted) 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.) .Even I tried using degrevlex, but can not get any output. Following is the code w.r.t. lex ordering:

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();
2016-12-20 09:49:00 +0100 asked a question Grobner bases using sage

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?

2016-12-05 11:08:09 +0100 commented answer What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variables

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

2016-12-05 11:03:07 +0100 asked a question Grobner basis

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. I am not getting the output of Parity check matrix.Also, 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?

G=matrix(FiniteField(2),[[1,0,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,1,1,0,0,1,1,0,0,0,1,1,0,1,1,1,1,1],
                         [0,1,0,0,0,0,1,0,1,0,0,0,1,1,0,0,0,0,1,0,0,1,1,0,1,0,1,0,1,1,1,0,1,1,1],
                         [0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,0,1],
                         [0,0,0,1,0,0,0,0,0,1,0,1,1,0,1,0,0,0,1,0,1,0,0,1,1,0,1,1,0,1,0,1,1,1,1],
                         [0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,1,0,1,1],
                         [0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,1,1,1,1,1,1,0]])
C=LinearCode(G)
C
Output: Linear code of length 35, dimension 6 over Finite Field of size 2
H=C.check_mat()
Output:  No output is coming
ToricIdeal(H)
Output:     
Ideal (-z0*z1*z2*z3*z4*z13*z14*z16*z17*z18*z19*z22*z23*z27*z28 + z34,
-z0*z1*z3*z4*z5*z7*z8*z15*z16*z18*z20*z23*z24*z26*z27 + z33,
-z0*z1*z2*z3*z5*z10*z11*z15*z17*z18*z21*z22*z24*z26*z28 + z32,
-z0*z2*z3*z4*z5*z6*z8*z12*z13*z19*z20*z23*z25*z26*z28 + z31,
-z0*z1*z2*z4*z5*z9*z11*z12*z14*z19*z21*z22*z25*z26*z27 + z30,
-z1*z2*z3*z4*z5*z6*z7*z9*z10*z20*z21*z24*z25*z27*z28 + z29) of
Multivariate Polynomial Ring in z0, z1, z2, z3, z4, z5, z6, z7, z8, z9,
z10, z11, z12, z13, z14, z15, z16, z17, z18, z19, z20, z21, z22, z23,
z24, z25, z26, z27, z28, z29, z30, z31, z32, z33, z34 over Rational
Field

P.<z0, z1, z2, z3, z4, z5, z6,z7,z8,z9,z10,z11,z12,z13,z14,z15,z16,z17,z18,z19,z20,z21,z22,z23,z24,z25,z26,z27,z28,z29,z30,z31,z32,z33,z34>=PolynomialRing(FiniteField(3),order='lex')
I=Ideal([-z0*z1*z2*z3*z4*z13*z14*z16*z17*z18*z19*z22*z23*z27*z28
 + z34, -z0*z1*z3*z4*z5*z7*z8*z15*z16*z18*z20*z23*z24*z26*z27 + z33,
-z0*z1*z2*z3*z5*z10*z11*z15*z17*z18*z21*z22*z24*z26*z28 + z32,
-z0*z2*z3*z4*z5*z6*z8*z12*z13*z19*z20*z23*z25*z26*z28 + z31,
-z0*z1*z2*z4*z5*z9*z11*z12*z14*z19*z21*z22*z25*z26*z27 + z30,
-z1*z2*z3*z4*z5*z6*z7*z9*z10*z20*z21*z24*z25*z27*z28 + 
z29,z0^3-1,z1^3-1,z2^3-1,z3^3-1,z4^3-1,z5^3-1,z6^3-1,z7^3-1,z8^3-1,z9^3-1,z10^3-1,z11^3-1,z12^3-1,z13^3-1,z14^3-1,z15^3-1,z16^3-1,z17^3-1,z18^3-1,z19^3-1,z20^3-1,z21^3-1,z22^3-1,z23^3-1,z24^3-1,z25^3-1,z26^3-1,z27^3-1,z28^3-1,z29^3-1,z30^3-1,z31^3-1,z32^3-1,z33^3-1,z34^3-1])
I.groebner_basis()
Output: No output is coming.
2016-12-05 02:38:18 +0100 commented answer How to get complete list of polynomials in an ideal, if its generating set is given?

Sir, if I work in a polynomial ring over a finite field with 2 elements in 35 variables, and find out reduced Grobner basis of that ideal, then will it be an ideal having finite generating set?(I think it has to be, by Hilbert basis theorem), I am unable to get that generating set.

2016-12-04 13:51:41 +0100 commented answer What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variables

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?

2016-12-04 13:47:27 +0100 received badge  Editor (source)
2016-12-04 13:46:45 +0100 asked a question What is the meaning of :IndexError:string index out of range

I am dealing with [35,6] linear code over finite filed with 2 elements. I am able to get an output of its generator matrix as 6x35 matrix, but while computing parity check matrix which will be of size 29x35, I am getting following output: IndexError:string index out of range

Does it mean that its size is too large? If still it is so, how to get that matrix in sage??

2016-12-04 13:45:49 +0100 asked a question What is the meaning of string index out of range?

I am dealing with [35,6] linear code over finite filed with 2 elements. I am able to get an output of its generator matrix as 6x35 matrix, but while computing parity check matrix which will be of size 29x35, I am getting following output: IndexError:string index out of range

Does it mean that its size is two large? If still it is so, how to get that matrix in sage??

2016-12-04 07:27:23 +0100 commented question Computation of reduced Grobner basis

No, I am not getting, how to define this ideal? I have created following generator matrix of a linear code i.e.ternary Golay code using sage G2=matrix(FiniteField(3),[[1,0,0,0,0,0,1,1,1,1,1], [0,1,0,0,0,0,0,1,2,2,1], [0,0,1,0,0,0,1,0,1,2,2], [0,0,0,1,0,0,2,1,0,1,2], [0,0,0,0,1,0,2,2,1,0,1], [0,0,0,0,0,1,1,2,2,1,0]]) print(G2) C = LinearCode(G2); C C.length()

But then not able to construct the ideal viz: I=<x^c-x^c' c-c'="" belongs="" to="" c="">+<xi^p-1 1&lt;="i&lt;=n">, I think,once ideal is constructed, then next thing will be easy.

2016-12-03 14:31:57 +0100 asked a question Computation of reduced Grobner basis

Currently I am reading one research paper http://www.ijpam.eu/contents/2010-62-... on page 486 equation 9 and 10 are describing an ideal, whereas on page 487 , Grobner basis has been calculated w.r.t ideal associated with ternary Goaly code.I understood the proof on page 486, but unable to compute the Grobner basis by using sage.

2016-12-03 14:19:18 +0100 commented answer How to get complete list of polynomials in an ideal, if its generating set is given?

I am thinking for an ideal in a polynomial ring in n variables over finite field with 2 elements

2016-12-03 12:31:04 +0100 received badge  Student (source)
2016-12-03 12:27:47 +0100 asked a question How to get complete list of polynomials in an ideal, if its generating set is given?

I am using sage for working in polynomials in several variables. I want to ask, 1) if generating set of an ideal is given, then is there any command which will give me a complete list of polynomials in that ideal. 2) How to compute addition of two ideals in sage?

2016-12-03 12:27:47 +0100 asked a question What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variables

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?