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.
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