Revision history [back]
 | 1 | initial version |
Related question: https:// mathoverflow.net/questions/181350/fast-computation-of-a-groebner-basis-what-is-possible
In general, such a big system may easily be hopeless. There are examples with way fewer variables and equations that do not terminate in reasonable time. You may want to try different monomial orders and Groebner basis algorithms within and beyond SAGE.
And lastly, any additional mathematical knowledge you have will also increase your chance of success. Do you always suspect the ideal to be (1)? Then it might help to find out how 1 is expressed in terms of the generators over F_2.
About the solutions over the rationals: if an equation system over the integers has a solution, then also mod p for every p. But you already know that there is no solution over F_2.
| | 2 | No.2 Revision |
Related question: https:// mathoverflow.net/questions/181350/fast-computation-of-a-groebner-basis-what-is-possible
In general, such a big system may easily be hopeless. There are examples with way fewer variables and equations that do not terminate in reasonable time. You may want to try different monomial orders and Groebner basis algorithms within and beyond SAGE.
And lastly, any additional mathematical knowledge you have will also increase your chance of success. Do you always suspect the ideal to be (1)? Then it might help to find out how 1 is expressed in terms of the generators over F_2.
About the solutions over the rationals: if an equation system over the integers has a solution, then also mod p for every p. But you already know does knowing that there is no solution over F_2. F_2 help here?
| | 3 | No.3 Revision |
Related question: https:// mathoverflow.net/questions/181350/fast-computation-of-a-groebner-basis-what-is-possible
In general, such a big system may easily be hopeless. There are examples with way fewer variables and equations that do not terminate in reasonable time. You may want to try different monomial orders and Groebner basis algorithms within and beyond SAGE.
And lastly, any additional mathematical knowledge you have will also increase your chance of success. Do you always suspect the ideal to be (1)? Then it might help to find out how 1 is expressed in terms of the generators over F_2.
About the solutions over the rationals: does do you expect integral solutions so that knowing that there is no solution over F_2 help here?helps?
