Kip, you don't need to define log because ^. works for complex argunent.
>________________________________ > Fra: km <k...@math.uh.edu> >Til: "programm...@jsoftware.com" <programm...@jsoftware.com> >Sendt: 16:16 fredag den 18. januar 2013 >Emne: Re: [Jprogramming] Hermitian from triangular > >Linda, you can define > > log =: 13 : '(^. y) % ^. x' > >which I bet is the way dyadic ^. is defined. > > 10 log 10^i:2 >_2 _1 0 1 2 > 1j2 log 1j2^i:2 >_2j_1.45289e_16 _1j_7.26445e_17 0 1 2j1.45289e_16 > 1j2 ^. 1j2^i:2 >_2j_1.45289e_16 _1j_7.26445e_17 0 1 2j1.45289e_16 > >I suppose it would take special code to get rid of the tiny imaginary parts >here. > >Kip > >Sent from my iPad > > >On Jan 18, 2013, at 4:33 AM, "Linda Alvord" <lindaalv...@verizon.net> 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: programming-boun...@forums.jsoftware.com >> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of km >> Sent: Thursday, January 17, 2013 9:31 AM >> To: programm...@jsoftware.com >> 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" <lindaalv...@verizon.net> 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: programming-boun...@forums.jsoftware.com >>> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo >>> Jacoby >>> Sennt: Thursday, January 17, 2013 3:37 AM >>> To: programm...@jsoftware.com >>> 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 <henryhr...@nc.rr.com> >>>> Til: programm...@jsoftware.com >>>> 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 <henryhr...@nc.rr.com> >> 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