Bill Allombert on Wed, 5 Mar 2003 21:44:18 +0100 |
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QX_caract |
Hello PARI-DEV, Why not use the modular algorithm of ZX_caract directly in QX_caract instead of removing the content and calling ZX_caract ? The new LLL allows for polred() of polynomials of large degree/coefs and now the QX_caract step is the most consuming. A simple example: ? polred(x^20+2^16)[13] %5 = x^20 + 16 This polynomial is the result of QX_caract(x^20 + 65536,1/32768*x^19,x) %6 = x^20 + 16 which in turn lead to ZX_caract(x^20 + 65536,x^19,x) %7 = x^20 + 32592575621351777380295131014550050576823494298654980010178247189670100796213387298934358016 This lead to a modular computation with a final modulus of 324bits when using a direct modular approach, a final modulus of 6 bits would have lead to the correct result. This is especially true in polred, since the polynomials we get are expected to be small. Of course I have not addressed how to implement this, in particular how to know we have a sufficiently large modulus. Cheers, Bill.