Hi,

Is there a cube root (as Cube root - Wikipedia)

function in Ruby? Math module seems not offer it… except a

Math.sqrt().

Thanks.

Hi,

Is there a cube root (as Cube root - Wikipedia)

function in Ruby? Math module seems not offer it… except a

Math.sqrt().

Thanks.

def cube_root(x)

Math.exp(Math.log(x.to_f)/3.to_f)

end

Cheers,

Serabe

P.D. Proof:

Cube root of x is equal to x^(1/3)

x^(1/3) = y

ln(x^(1/3)) = ln y

(1/3)ln x = ln y

Ergo

y = e^((ln x)/3)

So, so sorry.

Even easier.

def cube_root(x)

x**(1/3.0)

end

Cheers,

Serabe

2009/7/11 Fabian S. [email protected]:

but nice math anyways

Four years studying maths at the university should be useful for

something, should’nt it?

Cheers,

Serabe

one might argue that way, I guess *g*

gives me the satisfaction that what I’m getting into my head

right now for the next exam is not entirely useless *g*

2009/7/11 Sergio A. [email protected]

So, so sorry.

Even easier.

but nice math anyways

Greetz

2009/7/11 Zangief I. [email protected]

Hi,

Is there a cube root (as Cube root - Wikipedia)

class Numeric

def root(arg)

arg**(1.0/self)

end

end

p 3.root 27

p 2.root 9

Thomas P.

[email protected]

http://thopre.googlepages.com/

http://thopre.wordpress.com/

Jack Benny http://www.brainyquote.com/quotes/authors/j/jack_benny.html

“I don’t deserve this award, but I have arthritis and I don’t deserve

that

either.”

Hi,

Am Samstag, 11. Jul 2009, 19:48:50 +0900 schrieb Zangief I.:

Is there a cube root (as Cube root - Wikipedia)

function in Ruby? Math module seems not offer it… except a

Math.sqrt().

I suppose you mean the method mentioned under “Cube root on standard

calculator”. Here’s an implementation:

class Numeric

def sqrt

Math.sqrt self

end

def cbrt

neg = self < 0

c = abs.sqrt.sqrt

i = 2

loop do

w = c

i.times { w = w.sqrt }

i *= 2

w *= c

break if c == w

c = w

end

neg ? -c : c

end

end

If you like it in C (only Ruby 1.8):

http://bertram-scharpf.homelinux.com:8808/doc_root/bs-ruby-2.3/rdoc/classes/Numeric.src/M000033.html

Bertram

On Jul 11, 3:58 pm, Thomas P. [email protected] wrote:

`arg**(1.0/self)`

“I don’t deserve this award, but I have arthritis and I don’t deserve that

either.”

Correction:

class Numeric

def root(arg); self**(1.0/arg) end

end

Thanks you! Thomas P.'s method is perfect.

There is no correction to do jzakiya.

How can you explain this:

```
$ irb
1.9.2p180 (main):001:0> 1000 ** (1.0/3)
9.999999999999998
1.9.2p180 (main):002:0> Math.sqrt(100)
10.0
```

On Wed, 11 May 2011 21:45:42 +0200, Sergey Avseyev

[email protected] wrote:

How can you explain this:

`$ irb 1.9.2p180 (main):001:0> 1000 ** (1.0/3) 9.999999999999998 1.9.2p180 (main):002:0> Math.sqrt(100) 10.0`

Floating-point numbers have a finite precision. As a result, the outcome

of a numerical (computer) calculation usually differs from the outcome

of

the mathematical calculation. Assume you only can operate with integers

and want to compute the square root of 133. You may then end up with

either 11 (11² = 121) or 12 (12² = 144) while the actual result is

approximately 11.5 (11.5² = 121 + 11 + 0.25 = 132.25; more precisely

11.5325625947).

You may like to use formatted output of numbers that suppresses digits

beyond the actual precision:

jupp@pen2:~ $ irb

irb(main):001:0> “%.15f” % 1000 ** (1.0/3)

=> “9.999999999999998”

irb(main):002:0> “%.14f” % 1000 ** (1.0/3)

=> “10.00000000000000”

The above example turns the numerical value into a string displaying a

fractional part with 15 and 14 digits, respectively. Assuming that IEEE

754 double precision floating point numbers (i.e. those used by Ruby)

have

a precision of a little less than 16 (decimal) digits it is safe to

assume

that the complexity of operation you perform results in a value that is

precise to a little less than 15 digits - which means that you can

assume

14 digits to be correct. By chance it MAY be precise to more digits as

it

is the case for Math.sqrt(100) - but that is nothing you can rely on

unless you learn some gory details of numerical mathematics.

HTH

On Thu, May 12, 2011 at 8:25 AM, Josef ‘Jupp’ Schugt [email protected]

wrote:

instead of using floats you can try to use rational numbers in ruby:

ruby-1.9.2-p180 :001 > require ‘mathn’

=> true

ruby-1.9.2-p180 :002 > 1000 ** (1.0/3)

=> 9.999999999999998

ruby-1.9.2-p180 :003 > 1000 ** (1/3)

=> 10

ruby-1.9.2-p180 :004 > 1.0/3

=> 0.3333333333333333

ruby-1.9.2-p180 :005 > 1/3

=> (1/3)

you need to require ‘mathn’ which will change integer division (and make

all

the numbers play nicely together) but other than that things will work

better. the only down side to this whole thing is that rationals are

slower

than floats (probably significantly so) because it is a pair of

integers.

and some values when you look at them wont seem to make sense as a

rational, like PI:

ruby-1.9.2-p180 :011 > Math::PI

=> 3.141592653589793

ruby-1.9.2-p180 :012 > Math::PI.to_r

=> (884279719003555/281474976710656)

you can always num.to_f back but that also takes time. one last thing:

if

your inputs are floats i’m not sure there is a nice way to convert them

to

rationals:

ruby-1.9.2-p180 :016 > (1.0/3).to_r

=> (6004799503160661/18014398509481984)

ruby-1.9.2-p180 :017 > 1/3

=> (1/3)

so this entire e-mail may be moot

hex

On Thu, May 12, 2011 at 2:54 PM, serialhex [email protected] wrote:

…

instead of using floats you can try to use rational numbers in ruby:

ruby-1.9.2-p180 :001 > require ‘mathn’

which also changes this:

(-1) ** (1.0 / 3) #=> NaN

to:

(-1) ** (1.0 / 3) #=> (0.5+0.866025403784439i)

so we can also get complex roots if we want them!

…

one last thing: if your inputs are floats i’m not sure there is a nice way

to convert them to rationals:

(1.0/3).to_r #=> (6004799503160661/18014398509481984)

I think that is a nice way! It’s telling us (I think) what is the

exact rational represented by the float. After all, a float is just a

special type of rational, or rather floats are a subset of the subset

of the rationals defined by them have powers of two as denominators in

their representation using the smallest positive denominator. (I hope

that’s correct.)

Whether it’s a *good* idea to be able to convert floats to “ordinary”

rationals is another question, and I’m sceptical about that: I think

one should probably only want to do it if one fully understands

floating point representation, and if one fully understands floating

point representation, I suspect one wouldn’t want to do it!

On Thu, May 12, 2011 at 10:26 AM, Colin B.

[email protected]wrote:

Which we don’t here, given that the cube root of -1 isn’t imaginary

On 5/11/2011 14:45, Sergey Avseyev wrote:

How can you explain this:

`$ irb 1.9.2p180 (main):001:0> 1000 ** (1.0/3) 9.999999999999998 1.9.2p180 (main):002:0> Math.sqrt(100) 10.0`

You’re using floating point arithmetic which is always inexact. The

1.0/3 part cannot be represented with infinite precision, so it’s

basically rounded at a certain point. The result is then used for the

rest of the operation, which may compound the inaccuracy introduced by

the initial rounding.

If you must use floating point operations, be prepared to accept results

that are only *close* to what you expect, where close is largely

dependent on the operations being performed.

-Jeremy

On Thu, May 12, 2011 at 2:30 PM, Josh C. [email protected]

wrote:

Which we don’t here, given that the cube root of -1 isn’t imaginary

there are actually 3 cube roots of -1 (and 4 quad roots of -1, and 5

penta

roots of -1 and…)

behold the code:

ruby-1.9.2-p180 :004 > a = (-1)**(1/3)
=> (0.5000000000000001+0.8660254037844386i)
ruby-1.9.2-p180 :005 > a.conj
=> (0.5000000000000001-0.8660254037844386i)
ruby-1.9.2-p180 :006 > a.conj**3

=> (-1.0-3.885780586188048e-16i)

ruby-1.9.2-p180 :007 > a**3

=> (-1.0+3.885780586188048e-16i)

ruby-1.9.2-p180 :008 > (-1)**3

=> -1

(conjugation simply flips the sign of the imaginary number, which is

helpful

for a bunch of things) so while there may be 1 *real* root for a given

number, there are n roots for any number taken to the (1/n)th power.

and

while most people will want the (simple) (-1)**(1/3) == (-1) answer,

they

are all right (minus the floating-point rounding errors… which is kind

of

odd cause i would think that i would be getting the rational

representation

of the complex numbers instead of floats… idfk… whatev!)

hex

On May 12, 2011, at 2:30 PM, Josh C. wrote:

to:

(-1) ** (1.0 / 3) #=> (0.5+0.866025403784439i)

so we can also get complex roots if we want them!Which we don’t here, given that the cube root of -1 isn’t imaginary

ONE of the cube roots of -1 isn’t imaginary, but the other two are.

Since (1.0/3) isn’t exactly one-third, raising -1 to (1.0/3) isn’t

exactly the same as taking the cube root either.

-Rob

Rob B.

[email protected] http://AgileConsultingLLC.com/

[email protected] http://GaslightSoftware.com/

On May 12, 2:53pm, Rob B. [email protected]

wrote:

On Thu, May 12, 2011 at 10:26 AM, Colin B. <[email protected]

(-1) ** (1.0 / 3) #=> (0.5+0.866025403784439i)

Rob B.

[email protected] http://AgileConsultingLLC.com/

[email protected] http://GaslightSoftware.com/

See my Roots Module.

It allows you to easily (and accurately) get all n values for a root

n,

for all number classes.

Instead of: 1000**3**-1 of 1000**(1.0/3) to get only default root

Instead do: 1000.root(3) or 1000.roots(3), for all 3 cube roots

Jabari Zakiya

On Thu, May 12, 2011 at 4:25 PM, jzakiya [email protected] wrote:

See my Roots Module.

roots.rb · GitHub

spiffy!!!

hex

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