On 25/04/2012 16:45, Graham Gerrard wrote:
Finding occasional inconsistencies when using matrices with cyclotomic
entries, though works well most of the time...
sage: s=CyclotomicField(24,'s').gen()
sage: (8*s^6-1)^10
-1098715216*s^6 - 372960063
sage: xb=matrix(1,1,[8*s^6-1])
sage: xb^10
[1036922553*s^6 - 372960063]
I can confirm this behaviour.
Above example is trivial computation, though problem recurs in several
contexts. I believe that scalar multiplication is correct and xb^10
incorrect.
Yes, I've checked with Magma and you're right.
Any suggestions?
Sage has a special algorithm for multiplying matrices over cyclotomic
fields which works modulo primes and then does a Chinese remainder to
put the answer together. There is presumably a problem somewhere in
this algorithm but I don't know where. A rather unpleasant workaround
is to do
xb.sparse_matrix()^10
Sage just uses a generic algorithm for multiplying the sparse matrices
so this gives the correct answer. However, the performance probably
won't be as good.
Alastair
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