root function

Anonymous Monk has asked for the wisdom of the Perl Monks concerning the following question:

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Re: root function by FunkyMonk (Chancellor) on Jun 21, 2008 at 18:33 UTC
It's just basic maths. The cube root of 27 is 27(1/3). If you really want a function, try `print wop( 8, 3 ); #2 print wop( 27, 3 ); #3 sub wop { my ( $base, $root ) = @_; return $base (1/$root) }` [download] update: s/If/If you/ Unless I state otherwise, all my code runs with strict and warnings	[reply] [d/l]
Re^2: root function by hobbs (Monk) on Jun 24, 2008 at 00:53 UTC
You're going to have to rename that function "whop" for a US audience. :)	[reply]
Re: root function by swampyankee (Parson) on Jun 21, 2008 at 21:18 UTC
FunkyMonk has one way; another is x^(1/y) = e^ln(x)/y. Just beware that 0⁰ should be undefined, and Perl's ** operator is essentially a wrapper around C's "pow" function, so it will almost certainly puke on (-3)^(1/3), even though it shouldn't. Information about American English usage here and here. Floating point issues? Please read this before posting. — emc	[reply]
Re^2: root function by psini (Deacon) on Jun 21, 2008 at 21:33 UTC
Yes it does. (-3)(1/3) results in nan; But so does the log approach, too. The odd roots of negative numbers must be treated separately as they are limit cases. I'd try something like: `if ($base>0) { return $base(1/$root); } elsif ($base==0) { return 0; ## or do manage the special case 00; } elsif ($root)==int($root) && $root%2==1) { return -((-$base)($root)); } else { return 'nan'; }` [download] Not tested, so probably broken :) Careful with that hash Eugene.	[reply] [d/l]
Re^3: root function by swampyankee (Parson) on Jun 21, 2008 at 21:40 UTC
The logarithms of negative numbers are defined; it's just that they require complex numbers to represent. It's not my fault that Perl (and C) can't cope with them ;-). All will become clear when one remembers that e^πi = -1 Information about American English usage here and here. Floating point issues? Please read this before posting. — emc	[reply]
Re^4: root function by psini (Deacon) on Jun 21, 2008 at 21:47 UTC
Re^5: root function by swampyankee (Parson) on Jun 21, 2008 at 23:39 UTC
Re^4: root function by ysth (Canon) on Jun 22, 2008 at 06:53 UTC
Re^5: root function by psini (Deacon) on Jun 22, 2008 at 07:14 UTC
Re^2: root function by ikegami (Patriarch) on Jun 21, 2008 at 21:37 UTC
linux: `$ perl -le'print -3 (1/3)' -1.44224957030741` [download] ActivePerl: `>perl -le"print -3 (1/3)" -1.44224957030741` [download] Update: Oops, precedence problem `$ perl -le'print( (-3) (1/3) )' nan` [download] `>perl -e"print( (-3) (1/3) )" -1.#IND` [download]	[reply] [d/l] [select]
Re^3: root function by psini (Deacon) on Jun 21, 2008 at 21:42 UTC
`sini@ordinalfabetix:~$ perl -le"print ((-3)(1/3));" nan sini@ordinalfabetix:~$` [download] Exponent operator has higher priority than unary minus so you are doing -(3(1/3)) instead of ((-3)(1/3)). This gives you accidentally the right result but it would tell you that square root of -2 == -1.414265... Careful with that hash Eugene.	[reply] [d/l]
Re^4: root function by ikegami (Patriarch) on Jun 21, 2008 at 21:58 UTC
Re^5: root function by sasdrtx (Friar) on Jun 21, 2008 at 23:17 UTC
Re^5: root function by psini (Deacon) on Jun 21, 2008 at 22:03 UTC
Re: root function by Sixtease (Friar) on Jun 21, 2008 at 18:37 UTC
I have also found the Math::NumberCruncher module, which seems to have a function for that. use strict; use warnings; print "Just Another Perl Hacker\n";	[reply]
Re^2: root function by rhesa (Vicar) on Jun 21, 2008 at 19:14 UTC
I'd reach for bignum first (after using the builtins). See Math::BigInt, Math::BigFloat etc. It's a great set of modules.	[reply]
Re: root function by casiano (Pilgrim) on Jun 22, 2008 at 10:35 UTC
Perl with the help of PDL::Complex can cope with Complex Numbers. See below: pp2@nereida:~/.ssh$ perl -wde 0 main::(-e:1): 0 DB<1> use PDL DB<2> use PDL::Complex DB<3> $x = r2C(-27) # From real to complex DB<4> $r = Croots $x, 3 # There are three complex roots DB<5> print $r # It is sad that there is a bug # with "" overload Use of uninitialized value in numeric ... [ 1.5 +2.59807621135332i -3 +3.67381906146713e-16i 1.5 -2.59807621135332i ] DB<6> x $ra # The answer is a PDL object 0 PDL::Complex=SCALAR(0x8a6a0a8) -> 144899352 DB<7> p re $r # Get the "real" components [1.5 -3 1.5] DB<8> p im $r # And the imaginary ones: [ 2.5980762 3.6738191e-16 -2.5980762] DB<9> $y = $r ** 3 # Check the solution: DB<10> p re $y [-27 -27 -27] DB<11> p im $y # Almost 0, as expected [3.3064372e-15 9.9193115e-15 6.8636015e-14] [download] Hope it helps Casiano	[reply] [d/l]
Re^2: root function by etj (Deacon) on Jun 06, 2022 at 02:17 UTC
And PDL 2.040 or so introduced "native" complex numbers, without the visible real/imaginary dimension. It doesn't yet have an analogue of the `Croots` (multiple complex roots), evidently due to a lack of demand. It would not be hard to implement, since the n roots of a complex number can be calculated very easily using https://en.wikipedia.org/wiki/De_Moivre%27s_formula: root_n = r(cos(theta + 2pi/n) + i sin(theta + 2pi/n)). Pull requests welcome!	[reply] [d/l]
Re: root function by igelkott (Priest) on Jun 22, 2008 at 00:55 UTC
calculate the root Besides the suggested home-made functions, you could also try pow in the POSIX module.	[reply]
Re^2: root function by ikegami (Patriarch) on Jun 22, 2008 at 04:31 UTC
Either you're calling `` a home-made function, or they're just as needed for `pow` as for ``.	[reply] [d/l] [select]
Re^3: root function by igelkott (Priest) on Jun 22, 2008 at 09:25 UTC
calling * a home-made function* I wouldn't call the `**` operator a "function" at all. ;-) I didn't mean anything wrong by home-made but just tried to answer the op literally with an alternative solution. Nothing too serious.	[reply] [d/l]
Re^4: root function by ikegami (Patriarch) on Jun 22, 2008 at 15:19 UTC


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