On Wednesday, March 25, 2015 at 1:54:24 AM UTC+2, Luv Agarwal wrote:
>
>
> Is primitive_element doing something similar to simple
> <https://github.com/sympy/sympy/wiki/GSoC-2015-Application-Luv-Agarwal:-Cylindrical-Algebraic-Decomposition#2-simple>?.
>
> If yes, will there be difference in efficiency of both of these as they
> take input in different form?.
>
primitive_element and simple do more or less the same thing. Both construct
an extension containing given
algebraic elements. Their differences are
1. primitive_element takes any number of elements, simple only two.
2. simple computes isolating intervals, primitive_element does not
care.
In more detail, primitive_element uses sqf_norm which is just steps 1
and 2 of simple combined.
(1. norm is computed as a resultant, 2. t is chosen to make norm square
free.)
As to efficiency, I don't think there would be essential difference, since
the algorithms are basically
the same. Setting ex=True (experimental?) in primitive_element leads to a
parallel variant using
Groebner bases. It might be more efficient for a large number of elements.
Kalevi
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