|Bill Allombert on Tue, 12 Nov 2002 22:47:30 +0100|
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|Re: bug in polredabs?|
On Mon, Oct 14, 2002 at 10:32:25AM -0700, Carl R. Witty wrote: > Version: Debian packages version 2.1.4-1 (x86 linux). > > There is an example in the documentation for polcompositum that > demonstrates taking the result of polcompositum and calling polredabs > on it, and using subst on the result of that. After the last line of > the example, you can type "a^5 - 5" and get 0. > > I'm trying to do exactly the same thing, except with different > polynomials. Here's my example: > > ? z = polcompositum(x^2-3, 12*x^2-1, 1); > ? pol = z > %2 = 12*x^2 - 49 > ? a = z; a^2-3 > %3 = 0 > ? z = polredabs(pol, 1); > ? pol = z > %5 = x^2 - 3 > ? a = subst(a.pol, x, z) > %6 = Mod(-6*x, x^2 - 3) > ? a^2 - 3 > %7 = Mod(105, x^2 - 3) > > I was hoping, based on the polcompositum example, that the last line > would return 0; this would have worked if the second element returned > by polredabs were 7/6*x instead of 7*x. > > I don't know if this is a bug, because the polredabs documentation > says the second element returned by polredabs(..., 1) is > "an element expressed on a root of the polynomial $P$, > whose minimal polynomial is equal to $x$", and I don't know what > "minimal polynomial" means. Karim have fixed this bug in the stable branch of the CVS, so the fix will appear in GP 2.1.5. Thanks for your report ! Cheers, Bill.