My Math Forum Calculator Question

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 June 19th, 2009, 07:36 PM #1 Newbie   Joined: Jun 2009 Posts: 6 Thanks: 0 Calculator Question Hello, Does anyone know of a calculator, preferably online, that will calculate to at least 50 or so decimal places? I would like to convert phi to a base 12 number with at least 45 duodecimal places. I've done some searching, but I still haven't found a calculator that is better than the Windows calculator which calculates to about 30 decimal places. Thank you.
 June 19th, 2009, 07:47 PM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Calculator Question Check my .sig.
 June 19th, 2009, 08:11 PM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Calculator Question I hacked together some code for converting to duodecimal for you: Code: duodigit(n)=["0","1","2","3","4","5","6","7","8","9","A","B"][n+1] duoint(n)=my(out="");if(n<=0,return(if(n<0,concat("-",duoint(-n)),"0")));while(n>0,out=concat(duodigit(n%12),out);n\=12);out duodecimal(x)=my(out=duodigit(if(x<0,-floor(-x),floor(x))),k);if(x==floor(x),return(out));out=concat(out,".");k=floor(precision(x)*log(10)/log(12)-2);for(i=1,k,x=(x-floor(x))*12;out=concat(out,duodigit(floor(x))));out You can just copy this and past it into Pari. (You'll need to turn on QuickEdit mode if you're using Windows: right-click the shortcut to Pari, choose Properties, and check "QuickEdit" on one of the tabs, I forget what it's called, maybe the second tab. This lets you paste by right-clicking, very useful.) Then it's just two commands to get phi to lots of decimal places. First, change the precision to (say) 100 decimal places: Code: \p 100 Then calculate phi, converting to duodecimal with my script above: Code: duodecimal((1 + sqrt(5))/2)
 June 19th, 2009, 08:43 PM #4 Newbie   Joined: Jun 2009 Posts: 6 Thanks: 0 Re: Calculator Question Thanks for the response! Unfortunately I don't have a computer that I can download PARI to. Would it be too much for me to ask for you to post phi in base 12 to however many places you can stand to calculate? Thanks again.
June 19th, 2009, 09:05 PM   #5
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Re: Calculator Question

Quote:
 Originally Posted by at phi Thanks for the response! Unfortunately I don't have a computer that I can download PARI to.
Are you at an Internet cafe or something?

Quote:
 Originally Posted by at phi Would it be too much for me to ask for you to post phi in base 12 to however many places you can stand to calculate?
My code isn't optimized for large numbers of digits, but I'm attaching a zip file of 7 seconds' worth of calculation, about 9200 duodecimal digits.

 June 19th, 2009, 09:18 PM #6 Newbie   Joined: Jun 2009 Posts: 6 Thanks: 0 Re: Calculator Question Actually, I tried to download PARI but the install file is a GZ file which I can't open because I don't have WinZip. Eventually, I'll probably just buy WinZip so that I can install PARI. Thanks a ton for the file! That helps a lot.
June 19th, 2009, 09:21 PM   #7
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Re: Calculator Question

Quote:
 Originally Posted by at phi Actually, I tried to download PARI but the install file is a GZ file which I can't open because I don't have WinZip. Eventually, I'll probably just buy WinZip so that I can install PARI.
You're doing it wrong! You need to download the Windows binary. Even if you could read the .tar.gz file (which you could... download 7zip, it's free and better than WinZip) you couldn't do anything with it. Edit: I edited my .sig to include a direct link to the binary.

Pari/GP is *really* worth it. You have no idea how easy it makes questions like this.

 June 19th, 2009, 09:57 PM #8 Newbie   Joined: Jun 2009 Posts: 6 Thanks: 0 Re: Calculator Question Great; I got PARI installed now. I'm sure I'll have a bit of a learning curve to go through before I can really utilize the program but I know this will help me out with a lot of stuff. Thanks!
 June 19th, 2009, 10:15 PM #9 Newbie   Joined: Jun 2009 Posts: 6 Thanks: 0 Re: Calculator Question So, after I've defined the duodecimal function (or any function), is there any way to get PARI to retain the function after I close the program? It seems that it wipes out the function after I close PARI and re-open.
June 19th, 2009, 10:17 PM   #10
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Re: Calculator Question

Quote:
 Originally Posted by at phi Great; I got PARI installed now. I'm sure I'll have a bit of a learning curve to go through before I can really utilize the program but I know this will help me out with a lot of stuff.
A bit, but not as much as you'd think. The basics are pretty much the same as the standard plan-text math conventions:
1+1
2^7+3/2
7%2 (the remainder of 7 when divided by 2)
10!

Then you just pick up named functions that apply to you:
isprime(3^494+2)
zeta(3)
factor(20!+1)

Looping functions are also good:
for(k=1,10,print(k))
sum(n=1,10,n^2)
forprime(p=2,100,print1(p" "))
forstep(n=3,21,2,print1(n", "))

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### duodecimal of phi

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