#5658: Efficiency improvement in generic order_from_multiple()
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Reporter: cremona | Owner: tbd
Type: enhancement | Status: new
Priority: minor | Milestone: sage-3.4.1
Component: algebra | Keywords: generic group order
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Ryan Hinton pointed out that for groups of prime order n every non-
identity element has order n. The current implementation of
order_from_multiple() computes {{{g^n}}} twice when g is not the identity
and n is prime.
The attached patch avoids this: for each prime p dividing the given
multiple M of the order, we avoid the last multiplication/powering by p,
so there is a saving whenever the p-exponent of the order is maximal.
In an example where the order is {{{2^1279-1}}} (a Mersenne prime) the
times was reduced from 100ms to 70ms.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5658>
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