Re: How to do quickest
- To: mathgroup at smc.vnet.net
- Subject: [mg116579] Re: How to do quickest
- From: Artur <grafix at csl.pl>
- Date: Sun, 20 Feb 2011 05:27:16 -0500 (EST)
Thank You for procedure! On my computer
{12.312, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25,1}}
Bob try Your quickest steps combined with following which is still
little quickest
{10.313, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25, 1}}
(*Daniel Lichtblau modified by Artur Jasinski*)
Timing[cc = {}; pol = x^8 - x - 1;
nn = Length[CoefficientList[pol, x]] - 1;
pp = IntegerPartitions[nn];
Do[htab[pp[[j]]] = j, {j, Length[pp]}];
aa = Table[0, {Length[pp]}];
n = 1; cn = 0;
While[cn < nn!, p = Prime[n];
n++;
kk = FactorList[pol, Modulus -> p];
ww = Rest[Exponent[kk[[All, 1]], x]];
ww = Reverse[Sort[ww]];
pos = htab[ww];
If[pos == 0, , cn++; aa[[pos]] = aa[[pos]] + 1]];
aa]
{10.313, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25, 1}}
W dniu 2011-02-19 17:37, DrMajorBob pisze:
> This is easier to read, if no faster.
>
> Timing[
> Clear[a, c];
> pol = x^8 - x - 1;
> nn = Length@CoefficientList[pol, x] - 1;
> If[
> IrreduciblePolynomialQ[pol],
> a[i_] = {};
> c[i_] := Length@Flatten[a@i];
> pp = IntegerPartitions@nn;
> b = FactorInteger[Discriminant[pol, x]][[All, 1]];
> n = 1;
> cn = 0;
> While[cn < nn!, p = Prime@n;
> If[! MemberQ[b, p],
> cn++;
> k = Reverse@Rest@FactorList[pol, Modulus -> p][[All, 1]];
> w = Length@CoefficientList[#, x] - 1 & /@ k;
> pos = Position[pp, w, 1, 1][[1, 1]];
> a[pos] = {a[pos], p}];
> n++]];
> Array[c, Length@pp]
> ]
>
> {10.8518, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
> 2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25, 1}}
>
> Bobby
>
> On Sat, 19 Feb 2011 04:12:14 -0600, Sjoerd C. de Vries
> <sjoerd.c.devries at gmail.com> wrote:
>
>> Without changing the basic operation of your algorithm I've changed a
>> couple of details. The difference is not huge, but about 20% of speed
>> gain is still nice.
>>
>> pol = x^8 - x - 1;
>> nn = Length[CoefficientList[pol, x]] - 1;
>> If[IrreduciblePolynomialQ[pol],
>> pp = IntegerPartitions[nn];
>> aa = Table[{}, {n, 1, Length[pp]}]; Print[aa];
>> ff = FactorInteger[Discriminant[pol, x]];
>> bb = Table[ff[[n, 1]], {n, 1, Length[ff]}];
>> n = 1;
>> cn = 0;
>> While[cn < nn!,
>> p = Prime[n];
>> If[MemberQ[bb, p],
>> (*True*),
>> cn++;
>> kk = FactorList[pol, Modulus -> p];
>> ww = Table[
>> Length[CoefficientList[kk[[m, 1]], x]] - 1,
>> {m, Length[kk], 2, -1}
>> ];
>> pos = Position[pp, ww, 1, 1][[1, 1]];
>> aa[[pos]] = {aa[[pos]], p};
>> ];
>> n++
>> ]
>> ]; aa = Map[Flatten, aa, {1}];
>> Table[Length[aa[[m]]], {m, 1, Length[aa]}]
>> ]
>>
>>
>> Cheers -- Sjoerd
>>
>>
>> On Feb 15, 12:33 pm, Artur <gra... at csl.pl> wrote:
>>> Dear Mathematica Gurus,
>>> How to do following procedure quickest?
>>> (*start*)
>>> pol = x^8 - x - 1; nn = Length[CoefficientList[pol, x]] - 1; If[
>>> IrreduciblePolynomialQ[pol], pp = IntegerPartitions[nn]; aa = {};
>>> Do[AppendTo[aa, {}], {n, 1, Length[pp]}]; Print[aa];
>>> ff = FactorInteger[Discriminant[pol, x]]; bb = {};
>>> Do[AppendTo[bb, ff[[n]][[1]]], {n, 1, Length[ff]}]; n = 1; cn = 0;
>>> While[cn < nn!, p = Prime[n];
>>> If[MemberQ[bb, p], , cn = cn + 1;
>>> kk = FactorList[pol, Modulus -> p]; ww = {};
>>> Do[cc = Length[CoefficientList[kk[[m]][[1]], x]];
>>> AppendTo[ww, cc - 1], {m, 2, Length[kk]}]; ww = Reverse[ww];
>>> pos = Position[pp, ww][[1]][[1]]; AppendTo[aa[[pos]], Prime[n]]]=
>> ;
>>> n++]]; Table[Length[aa[[m]]], {m, 1, Length[aa]}]
>>> (*end*)
>>> Best wishes
>>> Artur
>>
>>
>
>