Re: How to do quickest
- To: mathgroup at smc.vnet.net
- Subject: [mg116566] Re: How to do quickest
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Sun, 20 Feb 2011 05:24:53 -0500 (EST)
Here's a more readable code (IMHO). I like variable names that mean
something.
Timing[
poly = x^8 - x - 1;
order = Exponent[poly, x];
partitions = IntegerPartitions@order;
np = Length@partitions;
index[_] = 0;
Do[index[partitions[[j]]] = j, {j, np}];
aa = ConstantArray[0, np];
n = total = 0;
While[total < order!,
p = Prime[++n];
factors = FactorList[poly, Modulus -> p][[All, 1]];
ndx = index@Reverse@Sort@Rest@Exponent[factors, x];
Positive@ndx && (total++; aa[[ndx]]++)
];
aa]
{9.84093, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25, 1}}
The following yields the tidbit of information that ndx == 0 EXACTLY ONCE:
Timing[
poly = x^8 - x - 1;
order = Exponent[poly, x];
partitions = IntegerPartitions@order;
np = Length@partitions;
Clear[counts, index];
counts[_] = 0;
index[_] = 0;
Do[index@partitions[[j]] = j, {j, np}];
n = total = 0;
While[total < order!,
p = Prime[++n];
factors = FactorList[poly, Modulus -> p][[All, 1]];
ndx = index@Reverse@Sort@Rest@Exponent[factors, x];
counts[ndx]++;
Positive@ndx && total++
];
Table[counts@i, {i, 0, np}]]
{10.2563, {1, 4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360,
1321, 2470, 412, 1103, 1114, 1652, 1129, 105, 102, 416, 206, 25, 1}}
If we can COUNT on that being so for some reason, the code becomes
Timing[
poly = x^8 - x - 1;
order = Exponent[poly, x];
partitions = IntegerPartitions@order;
np = Length@partitions;
Clear[counts, index];
counts[_] = 0;
index[_] = 0;
Do[index@partitions[[j]] = j, {j, np}];
n = 0;
While[n < order!,
p = Prime[++n];
factors = FactorList[poly, Modulus -> p][[All, 1]];
ndx = index@Reverse@Sort@Rest@Exponent[factors, x];
counts[ndx]++;
ndx == 0 &&
Print@{n, p, factors, Reverse@Sort@Rest@Exponent[factors, x]};
];
Array[counts, np]]
{5,11,{1,9+x,8+5 x+3 x^2+10 x^3+x^4+4 x^5+x^6},{6,1}}
{9.95797, {4996, 5781, 3361, 3449, 2653, 4055, 1360, 1249, 3360, 1321,
2470, 412, 1103, 1114, 1651, 1129, 105, 102, 416, 206, 25, 1}}
where I have shown the exception.
The problem is a black box to me, but finding just ONE exception is not
what I would have expected.
Bobby
On Sat, 19 Feb 2011 12:02:22 -0600, Artur <grafix at csl.pl> wrote:
> 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
>>>
>>>
>>
>>
--
DrMajorBob at yahoo.com