Forcing zero-dimensionality for rational function field computation: Part I, field membership #394
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This PR extends the approach already used in the identifiability assessment (originally inspired by this paper) to membership queries for rational function fields.
The idea is to reduce the Groebner basis computations to zero-dimensional ones. This is based on the observation is that a function
f
algebraic overQ(f_1, ..., f_n)
belongs to this field iff it belongs toQ(f_1,..., f_n, a_1, ..., a_k)
, wherea_1, ..., a_k
is a transcendence basis overQ(f_1, ..., f_n)
. Algebraicity can be checked by Jacobian condition and MQS ideal ofQ(f_1,..., f_n, a_1, ..., a_k)
will be zero-dimensional.Here is an example of the speedup (functions derived from a linear compartment model):
The computation time reduced from 100s to 20s.
Next step would be to make similar arrangements in the simplification functionality.