I agree to all of your 3 points :-)
On Thursday, 13 January 2022 at 15:34:02 UTC+1 john.c...@gmail.com wrote:
> On Thu, 13 Jan 2022 at 14:05, 'Martin R' via sage-devel
> <sage-...@googlegroups.com> wrote:
> >
> > I have some very strange behaviour of a substitution, which I don't know
> how to reproduce, but it happens from time to time, and is REALLY
> disturbing. I don't even know what to write into a ticket, so I'm asking
> here first. The definition of CSP is at the end of the mail.
> >
> > sage: R.<q> = ZZ[]
> > sage: p = q^21 + q^20 + q^19 + q^18 + q^17 + q^16 + q^15 + q^14 + q^13 +
> q^12 + q^11 + 2*q^10 + 2*q^9 + 2*q^8 + 2*q^7 + 2*q^6 + 2*q^5 + 2*q^4 +
> 2*q^3 + 2*q^2 + 3*q + 4
> > sage: p == CSP(22)
> > True
> > sage: CSP(22).subs({q:QQbar.zeta(2)})
> > -28
> > sage: CSP(22).subs({q:QQbar.zeta(2)})
> > 2
> > sage: CSP(22).parent()
> > Univariate Polynomial Ring in q over Integer Ring
> >
> > Sometimes I also get a complex number.
> >
> > Martin
> >
> > ###################
> > def cycle_power(g, e):
> > """
> > Return k such that g^k = e
> > """
> > if e.is_one():
> > return 0
> > k = 1
> > p = g
> > while True:
> > if e == p:
> > return k
> > p *= g
> > k += 1
> >
>
> 1. You could be using discrete_log() or one of its variants instead of
> your cycle_power() function.
>
> 2. In CSP() would it not be faster to work out for each power h=g^k,
> how many times h will arise and hence the coefficient of q^k? The
> pattern in your example is fairly simple to see.
>
> I know that neither of these points answers your actual question...
>
> John
>
> > @cached_function
> > def CSP(n):
> > C = groups.permutation.Cyclic(n)
> > g = C.gen()
> > R.<q> = ZZ[]
> > return sum(q^min(cycle_power(g, e) for e in coset) for H in
> C.subgroups() for coset in C.cosets(H))
> >
> > --
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> .
>
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