To what power can Matlab compute to?

To what level can Matlab compute? I tried to do a permutation calculation and it only went to 9 digits before erroring. Also, are there limits in the education edition vs. the regular one?

[George Carlisle]

I need to compute this, v = ['gapvilfmsctnqywdekrh']; p = perms(v) I need this in a spreadsheet.

[George Carlisle]

Can I do 20^50 or 20^100?

[Muthu Annamalai]

You will get results upto double precision.

[Steven Lord]

So to compute all permutations of a 20 element vector would require a matrix with this many rows and 20 columns:

 >> nrows = factorial(20)
 nrows =
   2.4329e+18

How much memory would this matrix require, assuming 2 bytes per element?

 >> ncols = 20;
 >> bytes = 2*nrows*ncols;
 >> exabytes = bytes/(1000^6)
 exabytes =
    97.3161

According to Wikipedia that's roughly between 50000 and 300000 Libraries of Congress worth of data. So how long would it take you to process all those rows at one row per second?

 >> processingOnePermutationPerSecond = years(seconds(nrows))
 processingOnePermutationPerSecond =
            77095595549.806

That's 77 billion years. Earth is around 4.5 billion years old. You might want to rethink your approach to the problem that requires all those permutations.

Answer 1

[Sean de Wolski]

What do you need? With Symbolic Math Toolbox, included in Student version, you can symbolically work on very large numbers.

x = sym('pi')
y = x.^234
vpa(y,100000)