# Math errors

(-3)**3 => -27

(-27)**(1/3.0) give NaN instead of -3

All odd roots (1/3,1/5,1/7 etc) of negative numbers should give
negative root values, as above, but ruby (in irb) gives NaN (not a
number), even when I require ‘complex’ .

Is this considered an error in Ruby?

2009/12/18 jzakiya [email protected]:

(-3)**3 => -27

(-27)**(1/3.0) give NaN instead of -3

Ruby 1.9 has Math.cbrt.

% ruby -e ‘p Math.cbrt(-27)’
-3.0

IN 1.9.2 I got:

~ \$> ruby -ve ‘p v=Math.cbrt(-27); p v**3’
ruby 1.9.2dev (2009-12-11 trunk 26067) [x86_64-darwin10.2.0]
-3.0
-27.0

~ \$> ruby -ve ‘p v=(-27)(1/3.0); p v3’
(1.5000000000000004+2.598076211353316i)
(-27.000000000000007+1.2434497875801753e-14i)

~ \$> ruby -ve ‘p v=(-27)(Rational(1,3)); p v3’
(1.5+2.5980762113533156i)
(-26.99999999999999+3.552713678800501e-15i)

Got easy results, but with all different values …
So, the first is right, of course.
The second is a good approximation, for floats …
And the last is almost good, while I would expect to be exact (I think
it
should use Math.cbrt in this case)

I would probably interested to use BigDecimal, but it’s impossible I
think
to use it for Complex. (And actually it accept only Fixnum exponent)

Another error in the exception:
TypeError: wrong argument type BigDecimal (expected Fixnum)

But it accept Float, really 2009/12/18 Tanaka A. [email protected]

jzakiya wrote:

(-3)**3 => -27

(-27)**(1/3.0) give NaN instead of -3

All odd roots (1/3,1/5,1/7 etc) of negative numbers should give
negative root values, as above, but ruby (in irb) gives NaN (not a
number), even when I require ‘complex’ .

Is this considered an error in Ruby?

irb(main):001:0> 1/3.0
=> 0.333333333333333

Hi,

In message “Re: Math errors”
on Fri, 18 Dec 2009 17:30:15 +0900, “W. James” [email protected]
writes:

|irb(main):007:0> -27 ** (1/3.0)
|=> -3.0

It’s -(27 ** (1/3.0)).

``          matz.``

jzakiya wrote:

(-3)**3 => -27

(-27)**(1/3.0) give NaN instead of -3

All odd roots (1/3,1/5,1/7 etc) of negative numbers should give
negative root values, as above, but ruby (in irb) gives NaN (not a
number), even when I require ‘complex’ .

Is this considered an error in Ruby?

irb(main):006:0> (-27)**(1/3.0)
=> NaN
irb(main):007:0> -27 ** (1/3.0)
=> -3.0

irb(main):012:0> RUBY_VERSION
=> “1.8.7”

jzakiya wrote:

(-3)**3 => -27

(-27)**(1/3.0) give NaN instead of -3

All odd roots (1/3,1/5,1/7 etc) of negative numbers should give
negative root values, as above, but ruby (in irb) gives NaN (not a
number), even when I require ‘complex’ .

Is this considered an error in Ruby?

I guess, you are right. THIS IS A ‘MATH ERROR’ in Ruby.

The ** method is not able to handle negative numbers raised to Floating
points (that are not Integers)

On Dec 18, 4:52 am, “Dasson, Raghav” [email protected] wrote:

I guess, you are right. THIS IS A ‘MATH ERROR’ in Ruby.

The ** method is not able to handle negative numbers raised to Floating points (that are not Integers)

This behavior was shown in ruby ree 1.8.6, 1.8.6, 1.8.7, 1.9.1

-271/3.0 => -9.0
-27 ** 1/3.0 => -9.0
-27 ** (1/3.0) => -3.0
-27
(1/3.0) => -3.0
(-27)**(1/3.0) => NaN
(-27) ** (1/3.0) => NaN

OK, the first two expression are evaluated as (-27**1)/3 => -9
The second two are correct (what I expected).
But the last two, WHY??

Removing the brackets across -27.0 does the trick, though would need to
find the logic behind the same
(-27)**(1/3.0) gives NaN

-27**(1/3.0) gives -3

Regards,
Raghav

Hello,

The second two are correct (what I expected).
But the last two, WHY??

As Matz said, the second two are evaluated as - (27**(1/3.0)), that is
you take the cubic root of +27 which is 3 and then distribute the
minus.
That way, you take the cubic root of a positive number which does not
raise any problem.

Cheers,

On Dec 18, 10:51 am, jzakiya [email protected] wrote:

-27 ** (1/3.0) => -3.0
-27**(1/3.0) => -3.0
(-27)**(1/3.0) => NaN
(-27) ** (1/3.0) => NaN

OK, the first two expression are evaluated as (-27**1)/3 => -9
The second two are correct (what I expected).
But the last two, WHY??

And just to verify:

(27)**(1/3.0) => 3.0

So Ruby is messing up parsing (-27)**(1/3.0)

On Dec 18, 11:05 am, Fleck Jean-Julien [email protected]
wrote:

Cheers,

JJ Fleck
PCSI1 Lycée Kléber

That is WRONG, you cannot do that.
That only works for odd roots of negative numbers.
The even root of negative numbers are imaginary.

-273-1 => -3 correct
-27
2**-1 => -5.19615242270663 **WRONG, its 5.196152i

That is WRONG, you cannot do that.

Well, I never said that you should do that, I just explained how Ruby
interpreted it…

That only works for odd roots of negative numbers.
The even root of negative numbers are imaginary.

-273-1 => -3 correct
-27
2**-1 => -5.19615242270663 **WRONG, its 5.196152i

Sure. That’s quite a hint why ** does not accept a negative number
with a non integer exponent. To take into account all the special
cases, you should first see if your exponent is a rational and in that
case, see if the denominator is odd (after all due simplifications of
course). In this case (and only this case), you could try to decipher
a root for this negative number.

Cheers,

On Dec 18, 2:13 pm, “William J.” <> wrote:

-272-1 => -5.19615242270663 **WRONG, its 5.196152i
def root base, n
exp = 1.0/n
return base ** exp if base >= 0 or n.even?
-( base.abs ** exp )
end

Remember

i = (-1)^(1/2)

i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
Then it repeats, for example: i^5 = i*(i^4) = i

For negative real value roots:

x = (-a)^(1/n) where n is odd integer => x = -[a^(1/n)]

But for negative real value roots where n is even:

x = (-a)^(1/n) where n is even gives

x = |a^(1/n)|(-1)^(1/n)
x = |a^(1/n)|
(i^2)^(1/n)
x = |a^(1/n)|(i)^(2/n)
from e^(i
x) = cos(x) + isin(x) where x = PI/2
x = |a^{1/n)|e^(PIi/2)^(2/n)
x = |a^(1/n)|e^(PIi/n)
x = |a^(1/n)|
(cos(PI/n) + i*sin(PI/n)) for n even

(-256)^(1/2) = |256^(1/2)|(cos(PI/2) + isin(PI/2))
= (16)(0 + i) = 16i

(-256)^(/4) = |256^(1/4)|(cos(PI/4) + isin(PI/4))
= (4)(0.707 + 0.707i)
= 2.828 + i2.828
= 2.828
(1+i)

Check in irb

require ‘complex’
include Math

x = Complex(-256,0)

x**(1/2.0)
=> (9.79685083057902e-16+16.0i)

X**(1/4.0)
=> (2.82842712474619+2.82842712474619i)

On Dec 18, 8:02 pm, jzakiya [email protected] wrote:

interpreted it…
case, see if the denominator is odd (after all due simplifications of

Then it repeats, for example: i^5 = i*(i^4) = i
x = |a^(1/n)|(i^2)^(1/n)
= (4)
(0.707 + 0.707*i)
x**(1/2.0)

Complex(-3,0)**3
For even odd, you get one real root and n/2 Complex Conjugate Pairs
Thus for n even there are no real roots.

So, I think it’s more intuitive (for most people)
to expect Complex(-27,0)**(1/n-odd) to return the real
root x1 only (i.e. (-3)(-3)(-3) = -27), so have it
act as Complex(-27,0).real (for n odd) be the default.

I guess complex variables aren’t called complex for nothing. Oooh, I just noticed:
Complex(-27**(1/3.0),0) => (-3.0+0i).

So that acts I expected/want.

So maybe it would be nice to be able to do:

Complex(-a**(1/n),0).roots or
Complex(a**(1/n)).roots where a is already complex
and have this return all the roots in an array so you
can see/pick which one(s) you want.

On Dec 18, 5:24 pm, jzakiya [email protected] wrote:

That only works for odd roots of negative numbers.
a root for this negative number.

For negative real value roots:
from e^(ix) = cos(x) + isin(x) where x = PI/2
= 2.828*(1+i)

X**(1/4.0)
=> (2.82842712474619+2.82842712474619i)

BTW there is an error (sort of) in ‘complex’ too

require ‘complex’
include Math

x = Complex(-27,0)
=> (-27+0i)

y = x**(1/3.0) # or x3-1
=> (1.5+2.59807621135332i) # should be (-3+0i)

y**3
=> (-27.0+1.24344978758018e-14i)

Complex(-3,0)**3
=> -27

Whenever you take the root n of a number you actually
get n values. If the value is positive you get n copies
of the same positive real value.

When you take the root of a negative real value you
get n roots too, for n even and odd.

For even odd, you get one real root and n/2 Complex Conjugate Pairs
(CCP).

Thus, for n=3 for (-27)^(1/3) the real root is x1=-3
and x2 is y above and x3 is the CCP of y.

For n=5, you get one real root and 2 pairs of CCPs, etc.

For n even, you get n/2 CCPs only.
So, for n=2 there is one pair of CCP roots.
For n=4 you get 2 different CCP roots, etc,
Thus for n even there are no real roots.

So, I think it’s more intuitive (for most people)
to expect Complex(-27,0)**(1/n-odd) to return the real
root x1 only (i.e. (-3)(-3)(-3) = -27), so have it
act as Complex(-27,0).real (for n odd) be the default.

I guess complex variables aren’t called complex for nothing. On Dec 18, 8:26 pm, jzakiya [email protected] wrote:

with a non integer exponent. To take into account all the special
-( base.abs ** exp )
i^3 = -i

x = Complex(-256,0)
include Math
=> (-27.0+1.24344978758018e-14i)
get n roots too, for n even and odd.
So, for n=2 there is one pair of CCP roots.
Oooh, I just noticed:
Complex(-27**(1/3.0),0) => (-3.0+0i).

So that acts I expected/want.

So maybe it would be nice to be able to do:

Complex(-a**(1/n),0).roots or
Complex(a**(1/n)).roots where a is already complex
and have this return all the roots in an array so you
can see/pick which one(s) you want.

So if you have these methods:

Complex(a).root(n).roots # all the roots of a
Complex(a).root(n).real # the real root(s) if exists

Then for any value a (real or complex) you will get
what you want under the different conditions.