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
@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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