Richard in Reading on Fri, 03 May 2013 18:58:12 +0200

 Problems with elldivpol - will they be fixed in 2.6.0?

• To: pari-users@pari.math.u-bordeaux1.fr
• Subject: Problems with elldivpol - will they be fixed in 2.6.0?
• Date: Fri, 3 May 2013 17:57:58 +0100 (BST)
• Delivery-date: Fri, 03 May 2013 18:58:12 +0200

```I obtained pari-2.6.0.svn13433.tar,gz from the website and built it in an attempt to escape apparently incorrect elldivpol results which plagued previous pari versions for unix.
By contrast I have a version [2.5.1] running on Windows which apparently doesn't suffer from the same problem in this instance.

So on the [2,6,0,"svn-13433"] version, if I do

x=0;factor(eval(elldivpol(ellinit([0,-1,1,-10,-20]),13)))

it prints the factors 2731,185693,57084047 etc...
however if I then do

e=ellinit(Mod([0,-1,1,-10,-20],2731));lift(ellpow(e,[0,ellordinate(e,0)[1]],13))

it prints [1360,2238] which I believe to indicate that 2731 is incorrect. Similar checks of the other factors fail.

On the [2,5,1] version on Windows, two of the factors are
27793 and 5141213801370234316849605048349

and indeed

e=ellinit(Mod([0,-1,1,-10,-20],5141213801370234316849605048349));lift(ellpow(e,[0,ellordinate(e,0)[1]],13))

gives [0] and also

e=ellinit(Mod([0,-1,1,-10,-20],27793));lift(ellpow(e,[0,ellordinate(e,0)[1]],13))

gives the same result which is a strong indication that the at least the last coefficient of the division polynomial is correct in the 2.5.1 version.

Printing out the values for elldivpol(e,13) in both cases shows they are different on the different versions so it's unlikely to be a problem with eval.

Does anyone have a good idea of the state of bugs in elldivpol for 2.6.0 ? I seem to be completely unable to do the relevant work with elldivpol on a non-windows machine.

I would be very grateful to receive instructions on how to build a version that gives the correct results!

Richard

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