Glitch in NumberFieldFundamentalUnits

*To*: mathgroup at smc.vnet.net*Subject*: [mg92373] Glitch in NumberFieldFundamentalUnits*From*: "Doug Hensley" <dahensley at suddenlink.net>*Date*: Mon, 29 Sep 2008 07:08:46 -0400 (EDT)*References*: <D0D555E836994F10AE26728DDF2AECB2@DougPC> <48DFF283.8080805@gmail.com>

Try this: Timing[NumberFieldFundamentalUnits[Root[x^3+4 x^2-10 x-1,1]]] You'll get something like this: Prepend::normal : Nonatomic expression expected at position 1 in Prepend[System`NumberFieldDump`pvec,AlgebraicNumber[Root[-1-10 #1+4 Slot[â? 1â?¡]2+#13&,1,0],{104,-39,-10}]]. {8491.51,NumberFieldFundamentalUnits[Root[-1-10 #1+4 #12+#13&,1]]} Now try it with another package that offers this functionality, just to get a peek at the answer: a=bnfinit(x^3+4*x^2-10*x-1);a.fu You'll get something like this: (Mod(x,x^3+4x^2-10x-1),Mod(126x^2-184x-81,x^3+4x^2-10x-1)), in far less than one second. (Meaning, that if alpha is one of the roots of p=x^3+4x^2-10x-1, then the set {alpha,126alpha^2-184 alpha-81} comprises a fundamental system of units for Q(alpha). ) Mathematica's NumberFieldFundamentalUnits gets fundamental unit systems for hundreds of comparably complicated inputs, and the outputs it obtains are not ever so much simpler in the other cases. Therefore, there's a bug. It's the better kind of bug, because it doesn't return a wrong answer. It just hangs and then supplies an error message.