Linda, now please consider
ic NB. interval from complex
[: , ([: i: 9&o.) j./ [: i: 11&o.
ic 0j2
0j_2 0j_1 0 0j1 0j2
Kip
Sent from my iPad
On Jan 19, 2013, at 4:53 AM, "Linda Alvord" <[email protected]> wrote:
> C=: 0j_2 0j_1 0 0j1 0j2
> f
> -: /:~
> f C
> 1
>
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of km
> Sent: Friday, January 18, 2013 10:47 PM
> To: [email protected]
> Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
>
> For what it's worth
>
> ic 1j2
> _1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
>
> (-: /:~) ic 1j2
> 1
>
> On ordering the complex numbers, see the penultimate sentence of the
> vocabulary entry for Grade /:
>
> http://www.jsoftware.com/docs/help701/dictionary/d422.htm
>
> Kip
>
> Sent from my iPad
>
>
> On Jan 18, 2013, at 8:28 PM, "Linda Alvord" <[email protected]> wrote:
>
>> At least these are sensible subsets of complex numbers. In their
>> entirety, complex numbers have been considered unorderable (at least
>> when I went to school).
>>
>> Instead of:
>> ic 1j2
>> _1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
>>
>> how about this:
>>
>> ic 1j2
>> 1j_2 1j_1 1 1j1 1j2
>>
>> It seems to match:
>>
>> ic 0j2
>> 0j_2 0j_1 0 0j1 0j2
>>
>> I haven't considered how you got your subsets or how you would get my
>> alternative.
>>
>> Linda
>>
>> -----Original Message-----From:
>> [email protected]
>> [mailto:[email protected]] On Behalf Of km
>> Sent: Friday, January 18, 2013 11:14 AM
>> To: [email protected]
>> Subject: Re: [Jprogramming] Hermitian from triangular
>>
>> Linda, would you buy
>>
>> ic =: 13 : ',(i: 9 o. y) j./ i: 11 o. y'
>> ic 1
>> _1 0 1
>> ic 2
>> _2 _1 0 1 2
>> ic 1j2
>> _1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
>>
>> ic 0j2
>> 0j_2 0j_1 0 0j1 0j2
>>
>> Kip
>>
>> Sent from my iPad
>>
>>
>> On Jan 18, 2013, at 4:33 AM, "Linda Alvord" <[email protected]>
> wrote:
>>
>>> Kip, I just got back to a different and interesting sidetrack on this
>>> long thread. What a simple way to write a proof in J.
>>>
>>> _1 = ^ 0j1 * o. 1
>>> 1
>>>
>>> (0j1 * o.1) = ^. _1
>>> 1
>>>
>>>
>>> Therefore: Negative numbers can have logarithms to the base e
>>>
>>> Can they also have common logs?
>>>
>>> Also, It makes you wonder if there isn't some sequence out there
>>> somewhere where there is an ordered sequence of complex numbers:
>>>
>>> i:2
>>> _2 _1 0 1 2
>>>
>>> i:0j2
>>>
>>> Happy wandering and pondering.
>>>
>>> Linda
>>>
>>>
>>> -----Original Message-----
>>> From: [email protected]
>>> [mailto:[email protected]] On Behalf Of km
>>> Sent: Thursday, January 17, 2013 9:31 AM
>>> To: [email protected]
>>> Subject: Re: [Jprogramming] Hermitian from triangular
>>>
>>> Linda, about logarithms of negative numbers
>>>
>>> First of all, you know the number e =: ^ 1 and you know ^ y is e^y .
>>> You may not know that ^ x j. y by definition is (^ x) * (cos + 0j1
>>> * sin) y where cos =: 2&o. and sin =: 1&o. . I first learned this
>>> in a college math class called Complex Analysis. A good reference is E.
>> B. Saff and A.
>>> D. Snider, Fundamentals of Complex Analysis, Pearson Education, Inc.
> 2003.
>>>
>>> Anyway, a famous identity in higher math is
>>>
>>> _1 = ^ 0j1 * o. 1
>>> 1
>>>
>>> which should tell you that
>>>
>>> (0j1 * o.1) = ^. _1
>>> 1
>>>
>>> i.e., negative numbers can have logarithms to the base e . For more
>>> on this, please see Saff and Snider's Chapter 3.
>>>
>>> Kip Murray
>>>
>>> Sent from my iPad
>>>
>>>
>>> On Jan 17, 2013, at 4:22 AM, "Linda Alvord" <[email protected]>
>> wrote:
>>>
>>>> Isn't the log of negative numbers indefined?
>>>>
>>>> This is a problem:
>>>>
>>>> %1&o.+0
>>>> _
>>>> %1&o.-0
>>>> _
>>>>
>>>> This is nice!
>>>>
>>>> %1&o.%_
>>>> _
>>>> %1&o.%__
>>>> __
>>>>
>>>>
>>>> The csc is very small for negative numbers close to zero and very
>>>> large for very small positive numbers.
>>>>
>>>> Linda
>>>>
>>>> -----Original Message-----
>>>> From: [email protected]
>>>> [mailto:[email protected]] On Behalf Of Bo
>>>> Jacoby
>>>> Sennt: Thursday, January 17, 2013 3:37 AM
>>>> To: [email protected]
>>>> Subject: Re: [Jprogramming] Hermitian from triangular
>>>>
>>>> Henry, How is negative zero different from positive zero when taking
>>>> the log?
>>>> ^.%__ NB. log -0
>>>> __
>>>> ^.%_ NB. log +0
>>>> __
>>>>
>>>>
>>>> - Bo
>>>>
>>>>
>>>>> ________________________________
>>>>> Fra: Henry Rich <[email protected]>
>>>>> Til: [email protected]
>>>>> Sendt: 0:38 torsdag den 17. januar 2013
>>>>> Emne: Re: [Jprogramming] Hermitian from triangular
>>>>>
>>>>> Negative zero makes sense as a last vestige of gradual underflow;
>>>>> and
>>>> anyway, it's well-behaved: it looks like 0 except when you take the
>>>> log, reciprocal, or square root. In any normal computation, it goes
>>>> away. In contrast, NaN messes up anything it touches.
>>>>>
>>>>> I think we've had negative 0 in J forever. If NaN is a data virus,
>>>>> -0 is a
>>>> virus that has been inserted into our DNA.
>>>>>
>>>>> Henry Rich
>>>>>
>>>>> On 1/16/2013 4:45 PM, Raul Miller wrote:
>>>>>> On Wed, Jan 16, 2013 at 4:35 PM, Henry Rich <[email protected]>
>>> wrote:
>>>>>>> Negative zero isn't a bug, it's a feature that numerical types,
>>>>>>> especially William Kahan, wanted to get into IEEE-754 to help out
>>>>>>> some things. I'm not expert enough to explain.
>>>>>>
>>>>>> Something similar could be said about NaN.
>>>>> -------------------------------------------------------------------
>>>>> -
>>>>> -
>>>>> - For information about J forums see
>>>>> http://www.jsoftware.com/forums.htm
>>>> --------------------------------------------------------------------
>>>> -
>>>> - For information about J forums see
>>>> http://www.jsoftware.com/forums.htm
>>>>
>>>> --------------------------------------------------------------------
>>>> -
>>>> - For information about J forums see
>>>> http://www.jsoftware.com/forums.htm
>>> ---------------------------------------------------------------------
>>> - For information about J forums see
>>> http://www.jsoftware.com/forums.htm
>>>
>>> ---------------------------------------------------------------------
>>> - For information about J forums see
>>> http://www.jsoftware.com/forums.htm
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
>
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
