# 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.
```

I do not have a

`check_mat`

method for`C`

, which version of Sage are you using ?@Nilesh -- what is the output of

`version()`

?What do you mean with

`Output: No output is coming`

, is it running, i.e. takes too long to compute the Groebner basis?