This is an archived, read-only copy of the United-TI subforum , including posts and topic from May 2003 to April 2012. If you would like to discuss any of the topics in this forum, you can visit Cemetech's
General Open Topic subforum. Some of these topics may also be directly-linked to active Cemetech topics. If you are a Cemetech member with a linked United-TI account, you can link United-TI topics here with your current Cemetech topics.
Open Topic & United-TI Talk =>
General Open Topic
| Author |
Message |
|
Xeda112358
Active Member
Joined: 19 May 2009
Posts: 520
|
 Posted: 31 Aug 2010 03:28:22 pm Post subject: |
|
|
Okay, I am working on an algorithm (for the TI-89, currently) and I need to test if it works. I had it calculate the summation of X^31 from 1 to 9999999999999999999 (that should be 19 9's) in 8~9 seconds using this algorithm, but it would require a few weeks using the normal method (mine doesn't add 1^31+2^31+3^31...). The result was over 600 digits (607 to be exact). I need to find a calculator that can use the regular method, but at a much, much faster rate than the TI-89.
I saved the stats in a program:
Code:
Prgm
©8 seconds
©sums(x^31,x,0,9999999999999999999)
Pause dim("3124999999999999995000000000000000002583333333333333333333333333333333332958750000000000000000000000000000000067424999999999999999999999999999999989043437500000000000000000000000000001527278409090909090909090909090909090730493321590909090909090909090909090926278665340909090909090909090909090907758735211846590909090909090909090909171894622962662337662337662337662337658604147793605519480519480519480519480644314187368019480519480519480519480516634653617006087662337662337662337662378030845546587662337662337662337662337355573790713079004329004329004329004329936779358875000000000000000000000000000000000000")
EndPrgm
That huge number in quotes is the value for sums(x^31,x,0,9999999999999999999)
sums() is the program I made.
I am still working
Last edited by Guest on 01 Sep 2010 06:21:37 am; edited 1 time in total |
|
| Back to top |
|
|
DrDnar
Member
Joined: 28 Aug 2009
Posts: 116
|
| Posted: 31 Aug 2010 05:04:29 pm Post subject: |
|
|
| There are several programming languages that offer arbitrary precision integers. However, a single PC cannot finish such a long loop in any reasonable time. The good news is that doing the sum number-by-number could easily be split into a parallel computing task. It would still take a long time or a lot of computers. |
|
| Back to top |
|
|
Xeda112358
Active Member
Joined: 19 May 2009
Posts: 520
|
| Posted: 01 Sep 2010 12:51:02 pm Post subject: |
|
|
| Okay. I am starting to work on a way to prove my method works. It was accurate at 9999 and various other testing points, but oh well, I still have to prove it. You did answer another question, I believe. I wanted to ask about how long a computer would take to solve that the normal way. I am guessing even the fastest cannot do 8 seconds, right? |
|
| Back to top |
|
|
Lionel Debroux
Member
Joined: 01 Aug 2009
Posts: 170
|
| Posted: 02 Sep 2010 01:24:40 am Post subject: |
|
|
| Does someone here have access to CAS programs such as Maple or Mathematica ? |
|
| Back to top |
|
|
Weregoose
Authentic INTJ
Super Elite (Last Title)
Joined: 25 Nov 2004
Posts: 3976
|
| Posted: 02 Sep 2010 02:52:14 am Post subject: |
|
|
Lionel Debroux wrote:
Does someone here have access to CAS programs such as Maple or Mathematica ?
Mathematica's Sum[x^31, {x, 0, 9999999999999999999}] gives his quoted number instantly. [url=http://www.wolframalpha.com/input/?i=sum+x^31+from+0+to+9999999999999999999]Alpha[/url] does the same.
The actual computation performed is Zeta[-31]-HurwitzZeta[-31,n+1] (where n=9999999999999999999), which breaks down to:
Code:
7709321041217/16320 -
1/1256640 (593617720173709 - 11717544135366800 n^2 +
38549175163831640 n^4 - 50728681747663920 n^6 +
35762288787254700 n^8 - 15687098041414800 n^10 +
4691683716643560 n^12 - 1017696589998000 n^14 +
167406298338510 n^16 - 21598822014000 n^18 + 2244328723560 n^20 -
191923914000 n^22 + 13768454700 n^24 - 847289520 n^26 +
47071640 n^28 - 3246320 n^30 - 628320 n^31 - 39270 n^32)
http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta/
http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta2/
Last edited by Guest on 02 Sep 2010 04:13:39 am; edited 1 time in total |
|
| Back to top |
|
|
Xeda112358
Active Member
Joined: 19 May 2009
Posts: 520
|
| Posted: 02 Sep 2010 10:19:37 am Post subject: |
|
|
THANK YOU! That is exactly what I was looking for.
I've been working on this for eight months trying to figure out what the heck I was doing... ☺
Last edited by Guest on 02 Sep 2010 10:26:54 am; edited 1 time in total |
|
| Back to top |
|
|
|
Register to Join the Conversation
Have your own thoughts to add to this or any other topic? Want to ask a question, offer a suggestion, share your own programs and projects, upload a file to the file archives, get help with calculator and computer programming, or simply chat with like-minded coders and tech and calculator enthusiasts via the site-wide AJAX SAX widget? Registration for a free Cemetech account only takes a minute.
»
Go to Registration page
