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MathGroup Archive 2004

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Re: why the overflow problems when using assigned values a,b,c vs. actual numbers?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47286] Re: why the overflow problems when using assigned values a,b,c vs. actual numbers?
  • From: adam.smith at hillsdale.edu (Adam Smith)
  • Date: Fri, 2 Apr 2004 03:30:40 -0500 (EST)
  • References: <c3udjo$9oa$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

The problem is in interpreting the hierachy of operations.  Although
it is a bit confusing from your post, I believe that the overflow
message occurred for

55^66^9999

Following the strict rule for functions this is interpreted as:

55^(66^9999) and does result in an overflow because it is 55^"some
very large #"

When you did it "by hand" you actually calculated:

(55^66)^9999

Which although large is less than 55^(66^9999)

As an illustration, look at the following:

In[1]:=
2^3^5 - (2^3)^5

Out[1]=
14134776518227074636666380005943348126619871175004951664972849610340925440

In[2]:=
2^3^5 - 2^(3^5)

Out[2]=
0

Adam Smith
angelomuscat at hotmail.com (Angelomuscot) wrote in message news:<c3udjo$9oa$1 at smc.vnet.net>...
> In[4]:=
> a^b^c
> 
> From In[4]:=
> \!\(\*
>   RowBox[{\(General::"ovfl"\), \(\(:\)\(\ \)\), "\<\"Overflow occurred in 
>       computation. \\!\\(\\*
>       ButtonBox[\\\"More?\\\", ButtonStyle->\\\"RefGuideLinkText\\\", \
> ButtonFrame->None, ButtonData:>\\\"General::ovfl\\\"]\\)\"\>"}]\)
> 
> Out[4]=
> Overflow[]
> 
> 
> BUT:
> 
> 
> In[5]:=
> 55^66
> 
> Out[5]=
> 731033882825428434868476575930782273126401013456960378520411040255228224491595\
> 9896758295144536532461643218994140625
> 
> AND:
> 
> 
> In[6]:=
> 731033882825428434868476575930782273126401013456960378520411040255228224491595\
> 9896758295144536532461643218994140625^9999
> 
> Out[6]=
> 324435743026028411717137084061237264526219685216276129069023086825090331034660\
> 676665460723467189974666799995743247466131925812897291499441793137947555612536\
> 092421118314787654069082988115339735757216388900285000082086886335511569652852\
> 500263751674419665228680993690435411655145421410867274348110658556086214283365\
> 487135310798129419106466657959487644096476639904142566621230014860021099758543\
> 910954184101810811243635968105694215589199277340922844665229795860970932927093\
> 903345342752805464134966818654081439739120197946231129464627625012794671009998\
> 274359074530338140109206089638200488364546090150940246659339109043696118031372\
> 530229742420103382591767900803138236103333789801675407210281125877301931298582\
> 300805788634261795727656073447660759207065107223222708688839651995612311889355\
> 907880386641679940642234768258450802716406293806036524748397672748983611445384\
> 903487466762791631032467508663336994739192371927330510682138180717769732067749\
> 813501627841812758363929902531268898592878366178908663561750678535422233327625\
> 309575011655608248360131500306432201250794818750558867930521429337718150047296\
> 888336494742592017263553596945560876788157860833558579449016137257870975373087\
> 228356365814869002266730157625647704291110893516697268716876172879316855159957\
> 249338111919269666676887164960924916445306418866716796634486117175329048684133\
> 301016184440562120694227194264220575350962432082369096353855300481550347098452\
> 159840773974548827666680165398142221744568827681254444318727439225820408470415\
> 862655480837303079223588987494927630307638662080907343807292397894202706574609\
> 442396217212137554114074188711173060955489002935067115527269579691249441940347\
> ETC........


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