# Revision history [back]

### 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.)

### 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.)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([x1x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35-1,x2x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28-1,x3x11x12x13x15x17x19x20x21x22x23x24x29x30x31x35-1,x4x8x9x10x14x18x19x20x23x24x25x27* x29x30x32x34-1,x5x7x8x10x12x13x19x20x22x24x25x26x29x31x32x33-1,x6x7x9x10x11x13x16x17x18x20x22x23x25x26x29*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();

### 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'); 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([x1x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35-1,x2x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28-1,x3x11x12x13x15x17x19x20x21x22x23x24x29x30x31x35-1,x4x8x9x10x14x18x19x20x23x24x25x27* x29x30x32x34-1,x5x7x8x10x12x13x19x20x22x24x25x26x29x31x32x33-1,x6x7x9x10x11x13x16x17x18x20x22x23x25x26x29*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();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();

 4 None tmonteil 25703 ●30 ●184 ●477 http://wiki.sagemath.o...

### 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'); 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([x1x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35-1,x2x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28-1,x3x11x12x13x15x17x19x20x21x22x23x24x29x30x31x35-1,x4x8x9x10x14x18x19x20x23x24x25x27* x29x27x29x30x32x34-1,x5x7x8x10x12x13x19x20x22x24x25x20x22x24x25x26x29x29x31x32x33-1,x6x7x9x10x11x13x16x17x18x20x22x23x25x20x22x23x25x26x29*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, x29x30-1,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(); I.groebner_basis();

 5 None tmonteil 25703 ●30 ●184 ●477 http://wiki.sagemath.o...

### 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: 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([x1x21x22x23x24x25x26x27x28x29x30x31x32x33x34x35-1,x2x14x15x16x17x18x19x20x21x22x23x24x25x26x27x28-1,x3x11x12x13x15x17x19x20x21x22x23x24x29x30x31x35-1,x4x8x9x10x14x18x19x20x23x24x25x27x29x30x32x34-1,x5x7x8x10x12x13x19x20x22x24x25x26x29x31x32x33-1,x6x7x9x10x11x13x16x17x18x20x22x23x25x26x29x30-1,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,

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]);     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();
I.groebner_basis();