Re: Ugly expressions. Was: Toghether, Apart ?
- To: mathgroup at smc.vnet.net
- Subject: [mg17287] Re: Ugly expressions. Was: Toghether, Apart ?
- From: "F. Mittermayr" <mitterma at linz.vai.co.at>
- Date: Fri, 30 Apr 1999 23:22:23 -0400
- Organization: IBM Global Services - Remote Access Mail & News Services
- References: <7f1di1$kop@smc.vnet.net> <7f9k7n$596@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I tried your FactorCommon and FactorCommon2: FactorCommon[a a b b + a b + a d b] but no factor was seen in the result. Did I do something wrong? Allan Hayes wrote in message <7f9k7n$596 at smc.vnet.net>... >Tobias, >Some variants on your code, FactorCommon > >Clear[FactorCommon2]; >FactorCommon2[HoldPattern[Plus[e__Times]]] := > ( #(Plus @@ ( {e}/#))) &[Intersection[e] >]; >FactorCommon2[HoldPattern[Plus[e__]]] := > With[{ d = d1 d2 }, > ( #(Plus @@ ( {e}/#))) &[cc = (Intersection @@ ( d{e}))/d] >]; > FactorCommon2[expr_] := expr > >Here id FactorCommon: > >Clear[FactorCommon]; > FactorCommon[expr_Plus] := > Block[{(*com, dummy1, dummy2*)}, >com = Apply[Intersection, dummy1 dummy2 Apply[List, expr]] /. >{dummy1 -> 1, dummy2 -> 1}; >com Map[#/com &, expr] >] > FactorCommon[expr_] := expr > >Some timings > >a b c d e f >Apply[Plus, Apply[Times, Table[e[i + j*10], {j, 0, 20}, {i, 0, 20}], {1}]]]; > >Do[FactorCommon2[ex], {100}] // Timing > >{3.74 Second, Null} > >Do[FactorCommon2[ex + a ], {100}] // Timing > >{5.77 Second, Null} > >Do[FactorCommon2[ex + 3], {100}] // Timing > >{2.48 Second, Null} > >Do[FactorCommon[ex], {100}] // Timing > >{6.48 Second, Null} > >Do[FactorCommon[ex + a], {100}] // Timing > >{5.71 Second, Null} > >Do[FactorCommon[ex + 3], {100}] // Timing > >{2.42 Second, Null} > > ><tobiasoed at my-dejanews.com> wrote in message news:7f1di1$kop at smc.vnet.net... >> Hi all. >> There was a post about handling long expressions (leafcount > 10^7). I am >> manipulating the same kind of nasty things and am interested in any little >> function that deals with them (without running out of memory) - like the >> following FactorCommon. that pulls out common factors of sums. >> >> FactorCommon[expr_Plus]:=Block[{com,dummy1,dummy2}, >> com=Apply[Intersection,dummy1 dummy2 Apply[List,expr]] >> /. {dummy1->1,dummy2->1}; >> com Map[#/com &,expr] >> ] >> >> FactorCommon[expr_]:=expr >> >> an example use: >> >> In[1]:= FactorCommon[expr_Plus]:=Block[{com,dummy1,dummy2}, >> com=Apply[Intersection,dummy1 dummy2 Apply[List,expr]] /. >> {dummy1->1,dummy2->1}; >> com Map[#/com &,expr] >> ] >> >> In[2]:= FactorCommon[expr_]:=expr >> >> In[3]:= ex = Expand[a b >> Apply[Plus,Apply[Times,Table[e[i+j*10],{j,0,8},{i,0,9}],{1}]]] >> >> Out[3]= a b e[0] e[1] e[2] e[3] e[4] e[5] e[6] e[7] e[8] e[9] + >> >> > a b e[10] e[11] e[12] e[13] e[14] e[15] e[16] e[17] e[18] e[19] + >> >> > a b e[20] e[21] e[22] e[23] e[24] e[25] e[26] e[27] e[28] e[29] + >> >> > a b e[30] e[31] e[32] e[33] e[34] e[35] e[36] e[37] e[38] e[39] + >> >> > a b e[40] e[41] e[42] e[43] e[44] e[45] e[46] e[47] e[48] e[49] + >> >> > a b e[50] e[51] e[52] e[53] e[54] e[55] e[56] e[57] e[58] e[59] + >> >> > a b e[60] e[61] e[62] e[63] e[64] e[65] e[66] e[67] e[68] e[69] + >> >> > a b e[70] e[71] e[72] e[73] e[74] e[75] e[76] e[77] e[78] e[79] + >> >> > a b e[80] e[81] e[82] e[83] e[84] e[85] e[86] e[87] e[88] e[89] >> >> In[4]:= Timing[FactorCommon[ex]][[1]] >> >> Out[4]= 0.04 Second >> >> In[5]:= Timing[Factor[ex]][[1]] >> >> Out[5]= 0.73 Second >> >> Sure, FactorCommon is not as powerfull as Factor, but sometimes it's the >only >> way I found to reduce some of my exprssions. >> Hope this can help some others too, Tobias. >> >> -----------== Posted via Deja News, The Discussion Network ==---------- >> http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own >> > >