Or:
(ic2 -: ic)"1 ,.1 2 1j2 0j2
1 1 1 1
Linda
-----Original Message-----
From: [email protected]
[mailto:[email protected]] On Behalf Of km
Sent: Saturday, January 19, 2013 7:27 PM
To: [email protected]
Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
Dan, your ic2 is very nice. I remember trying to use +. and coming up with
something much more complicated.
About your closing question, consider
(ic2"0 -: ic"0) 1 2 1j2 0j2
1
Monadic i: has rank 0 and for reasonable behavior I think ic and ic2 should
be used with rank 0 on vector arguments.
Kip Murray
Sent from my iPad
On Jan 19, 2013, at 1:05 PM, "Dan Bron" <[email protected]> wrote:
>
> PS: It's always good to test our theories, so:
>
> ic =. [: , ([: i: 9&o.) j./ ([: i: 11&o.)
> ic2 =. [: , j./&i:/@+.
>
> ic 1 NB. Kip example #1
> _1 0 1
> ic2 1
> _1 0 1
>
> ic 2 NB. Kip example #2
> _2 _1 0 1 2
> ic2 2
> _2 _1 0 1 2
>
> ic 1j2 NB. Kip example #3
> _1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
> ic2 1j2
> _1j_2 _1j_1 _1 _1j1 _1j2 0j_2 0j_1 0 0j1 0j2 1j_2 1j_1 1 1j1 1j2
>
> ic 0j2 NB. Kip example #4
> 0j_2 0j_1 0 0j1 0j2
> ic2 0j2
> 0j_2 0j_1 0 0j1 0j2
>
> (ic2 -: ic)&> 1 2 1j2 0j2
> 1 1 1 1
>
> NB. But...
>
> (ic2 -: ic) 1 2 1j2 0j2
> 0
>
> NB. When we move beyond the original scope of a single, scalar input
> NB. the answers differ. What gives? Left as an exercise for the reader.
>
>
>
> -----Original Message-----
> From: [email protected]
> [mailto:[email protected]] On Behalf Of km
> Sent: Saturday, January 19, 2013 6:21 AM
> To: [email protected]
> Subject: Re: [Jprogramming] [Jprogrammingou Hermitian from triangular
>
> 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.
>>>>>> -----------------------------------------------------------------
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