Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

asked 2016-12-05 11:03:07 +0100

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.

click to hide/show revision 3
None

updated 2016-12-06 10:42:28 +0100

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.
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
about | faq | help | privacy policy | terms of service
Powered by Askbot version 0.7.59