laziness, impatience, and hubris PerlMonks

### Converting a Number into a Radical

by slinky773 (Sexton)
 on Dec 18, 2013 at 03:32 UTC Need Help??
slinky773 has asked for the wisdom of the Perl Monks concerning the following question:

On the TI-Nspire calculator, every division answer given, unless irrational, is given in exact form, either as an integer or as a fraction. I can do this in Perl with the fraction module. Every square root answer given is also given in exact form, either as an integer or as a radical. I do not know how to do this in perl. How do you convert a number to a radical?

Replies are listed 'Best First'.
Re: Converting a Number into a Radical
by syphilis (Chancellor) on Dec 18, 2013 at 05:50 UTC
I gather we're concerned only with square roots of integers and that, for example, if the answer is sqrt(18), you want to see it presented as 3 x sqrt(2) instead of simply sqrt(18).
To achieve this you'll first want to factorise the integer - you could use something like Math::Factor::XS or Math::Prime::Util.

To stick with the above example, 18 factorises to the primes 2,3,3 - multiply those primes together and you end up with 18.
Notice that the "3" occurs twice - hence you can write the solution as 3 * sqrt(2).
For sqrt(1050) - the prime factors are 2,3,5,5,7, with the "5" occurring twice, and the solution is therefore:
```5 * sqrt(2 * 3 * 7) = 5 * sqrt(42)
[download]```
That's essentially how it's done - I don't know if there's a module that does it all for you, or whether you'll have to program a good portion of it yourself. (Perhaps Math::NumSeq might also have something to offer.)

Cheers,
Rob
Thanks, Rob. That actually really helps.

I could not resist to write it out:

```use strict;
use warnings;
use Math::Factor::XS 'prime_factors';

my \$n = shift;
( \$n and \$n > 0 and \$n == int \$n ) or die "Need positive integer as in
+put!\n";

my %p;
\$p{\$_}++ for prime_factors( \$n );

my \$radical = 1;
\$radical *= \$_ for grep { \$p{\$_}%2 } keys %p;
print "sqrt( \$n ) = ", sqrt( \$n/\$radical ), " * sqrt( \$radical )\n";
[download]```

What I was missing is a product function, like sum from List::Util. There is one in the replacement List::Util that comes with Scalar::Util but that means overwriting the standard module which makes me feel uncomfortable.

Awesome, syphilis - I wish it were possible to vote it up by more than than one.

A user level that continues to overstate my experience :-))
Re: Converting a Number into a Radical
by Anonymous Monk on Dec 18, 2013 at 04:49 UTC

I don't know of a Perl solution, but SymPy (see www.sympy.org) can do this kind of thing.

```>>> sqrt(49)
7
>>> sqrt(27)
3*sqrt(3)
>>> simplify(sqrt(4+sqrt(448)))
2*sqrt(1 + 2*sqrt(7))
[download]```

Log In?
 Username: Password:

What's my password?
Create A New User
Node Status?
node history
Node Type: perlquestion [id://1067582]
Approved by ww
Front-paged by davido
help
Chatterbox?
and all is quiet...

How do I use this? | Other CB clients
Other Users?
Others scrutinizing the Monastery: (6)
As of 2017-08-17 16:36 GMT
Sections?
Information?
Find Nodes?
Leftovers?
Voting Booth?
Who is your favorite scientist and why?

Results (290 votes). Check out past polls.

Notices?