#11946: Change iteration order for finite field multiplicative_generator()
------------------------------+---------------------------------------------
Reporter: jdemeyer | Owner: was
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.3
Component: user interface | Keywords: GF
Work_issues: | Upstream: N/A
Reviewer: | Author: Jeroen Demeyer
Merged: | Dependencies:
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Old description:
> In the literature of finite fields, a generator for the multiplicative
> group is often called a "primitive element" (or primitive root). We
> should add a method `primitive_element` which returns the multiplicative
> generator.
New description:
If `K` is a finite field implemented through PARI (the default if q >
2^16^), then we try to find a multiplicative generator by first trying all
elements of `GF(p)` (the prime field). This means the following will
never finish in practice:
{{{
sage: p = next_prime(10^20)
sage: K.<a> = GF(p^2)
sage: K.multiplicative_generator()
}}}
Also, a generator for the multiplicative group is often called a
"primitive element" (or primitive root). We should add a method
`primitive_element` which returns the multiplicative generator.
--
Comment(by jdemeyer):
Replying to [comment:3 kini]:
> {{{
> *** Warning: Mod(a,b)^n with n >> b : wasteful.
> }}}
Nice catch, see new description. New patch fixes this.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11946#comment:7>
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