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asked 2016-12-05 11:03:07 +0200

Nilesh gravatar image

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 (-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28 + z34, -z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 + z33, -z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 + z32, -z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 + z31, -z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 + z30, -z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 + 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([-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28 + z34, -z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 + z33, -z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 + z32, -z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 + z31, -z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 + z30, -z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 + 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.

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 (-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28 + z34, -z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 + z33, -z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 + z32, -z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 + z31, -z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 + z30, -z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 + 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([-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28 + z34, -z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 + z33, -z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 + z32, -z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 + z31, -z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 + z30, -z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 + 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.

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updated 2016-12-06 10:42:28 +0200

tmonteil gravatar image

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? 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 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 (-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28 (-z0*z1*z2*z3*z4*z13*z14*z16*z17*z18*z19*z22*z23*z27*z28 + z34,
-z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 -z0*z1*z3*z4*z5*z7*z8*z15*z16*z18*z20*z23*z24*z26*z27 + z33,
-z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 -z0*z1*z2*z3*z5*z10*z11*z15*z17*z18*z21*z22*z24*z26*z28 + z32,
-z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 -z0*z2*z3*z4*z5*z6*z8*z12*z13*z19*z20*z23*z25*z26*z28 + z31,
-z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 -z0*z1*z2*z4*z5*z9*z11*z12*z14*z19*z21*z22*z25*z26*z27 + z30,
-z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 -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
 
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([-z0z1z2z3z4z13z14z16z17z18z19z22z23z27z28
 + z34,
-z0z1z3z4z5z7z8z15z16z18z20z23z24z26z27 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,
-z0z1z2z3z5z10z11z15z17z18z21z22z24z26z28 -z0*z1*z2*z3*z5*z10*z11*z15*z17*z18*z21*z22*z24*z26*z28 + z32,
-z0z2z3z4z5z6z8z12z13z19z20z23z25z26z28 -z0*z2*z3*z4*z5*z6*z8*z12*z13*z19*z20*z23*z25*z26*z28 + z31,
-z0z1z2z4z5z9z11z12z14z19z21z22z25z26z27 -z0*z1*z2*z4*z5*z9*z11*z12*z14*z19*z21*z22*z25*z26*z27 + z30,
-z1z2z3z4z5z6z7z9z10z20z21z24z25z27z28 -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.
coming.
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