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The goal of reduction
is to rewrite the system into an equivalent
one (i.e.: with the same finite solutions) that has a lower total degree,
so that fewer solution paths need to be followed. Sometimes reduction
can already detect whether a system has no solutions or an infinite
number of solutions.
- Linear Reduction
- performs row-reduction
on the coefficient matrix of the system.
- Sparse Linear Reduction
- brings the coefficient matrix of the system in a diagonal format.
- Nonlinear Reduction
- replaces polynomials by Subtraction-polynomials to eliminate
This type of reduction is more powerful, but also more expensive.
Bounds have to be set to limit the combinatorial enumeration.