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lalitkumarj / OMSCategory

Sage Category implementation of OMS
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Fix up OMS families random_element() #39

Open rharron opened 11 years ago

rharron commented 11 years ago

This is mostly just rewriting it the way the non-family one is currently written. But also, figuring out how to handle the way K[0]-1 and K[1] affect the precision.

rpollack9974 commented 11 years ago

OK...so in the case k = 0 (p-1), where we are dividing by K[1], we lose ord_p(c) precision where c is the lower left entry of the matrix. (This is assuming -- as we do now in the code -- that we are using a non-torsion generator.)
Note that we should be finding a generator where c != 0. Hopefully this always exists.

In the case k !=0 (p-1), where we are dividing by K[0]-1, we lose no precision as long as omega^k(a) - 1 is non-zero. We should in fact be finding a generator for which this is true -- and hopefully such a generator always exists. If not, we need to do something different...