The msolve tutorial currently states that, when working over Q,
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which corresponds to the elimination of the variable $t$. When the input |
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coefficients lie in the field of rational numbers (hence, characteristic $0$), |
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the returned Gr\"obner basis is the one of the {\em elimination ideal}, i.e. they |
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have partial degree $0$ in the variables to eliminate. |
This limitation makes it hard to use msolve in algorithms that rely on the full Gröbner basis under an elimination order, e.g., Suzuki–Sato's algorithm for comprehensive Gröbner systems. Providing an option to return the full Gröbner basis would therefore be extremely useful.
P.S.: About a month ago, I pushed commits to my branches to add an option to lift all polynomials instead of just those with partial degree 0 in the variables to eliminate. However, I'm not fully satisfied with my changes, which is why I’m opening this feature request.
The msolve tutorial currently states that, when working over Q,
msolve/doc/msolve-tutorial.tex
Lines 632 to 635 in 7e0ef99
This limitation makes it hard to use msolve in algorithms that rely on the full Gröbner basis under an elimination order, e.g., Suzuki–Sato's algorithm for comprehensive Gröbner systems. Providing an option to return the full Gröbner basis would therefore be extremely useful.
P.S.: About a month ago, I pushed commits to my branches to add an option to lift all polynomials instead of just those with partial degree 0 in the variables to eliminate. However, I'm not fully satisfied with my changes, which is why I’m opening this feature request.