Actually _ stands for positive infinity 1%0 _ _1%0 __
when Roger Hui and Ken Iverson designed J, their mathematical perspective built upon previous APL experiences. For example, 0%0 became 0 in J whereas it is 1 in APL. E. E. McDonnell wrote a thorough article documenting this choice: http://www.jsoftware.com/papers/zero.htm In APL 1 divided by zero is a domain error and it halts your program. J has a more sensible and pragmatic way of dealing with division by zero. On Wed, Aug 16, 2017 at 10:08 AM, Linda Alvord <[email protected]> wrote: > Thanks Jimmy. When I translated you answer into J, I got the same result. > But, if the csc of a number isundefined, should the signum be 1? > > > > load 'plot' > do=: 13 : '({.y) +(i.{:y)*(--/ 2{.y)%<:{:y' > A=:do 0 2p1 17 > ]csc=:*1%1 o. A > 1 1 1 1 1 1 1 1 1 _1 _1 _1 _1 _1 _1 _1 _1 > > ]sec=:*1%2 o. A > 1 1 1 1 1 _1 _1 _1 _1 _1 _1 _1 _1 1 1 1 1 > > > ]csc=:1%3 o. 0{A > _ > ]csc=:*1%3 o. 0{A > 1 > > Linda > > -----Original Message----- > From: Programming [mailto:[email protected]] On > Behalf Of Jimmy Gauvin > Sent: Tuesday, August 15, 2017 10:57 PM > To: [email protected] > Subject: Re: [Jprogramming] Fwd: FW: why are there no negative signs for > cot, sec and csc? > > No zeroes for sec or csc, from the definition: > > csc A = 1 / (sin A) > sec A = 1 / (cos A) > cot A = 1 / (tan A) > > sin and cos vary from 1 to -1 passing by zero so there is no way of > getting a zero from 1/sin or 1/cos > > tan on the other hand varies from plus infinity to minus infinity so you > obtain zeroes from 1/tan when tan is at the limits of its domain > > On Tue, Aug 15, 2017 at 8:13 PM, Linda Alvord <[email protected]> > wrote: > > > Thanks Raul. It shows that I haven't used J for any trig in aboug 20 > > years. Here is almost what I want. > > > > > > Hoever the cot looks good. Shouldn't there be some 0's in the sec and > csc? > > > > *(%"0)3 2 1 (o."0 1) t > > 1 1 1 1 0 _1 _1 _1 _1 1 1 1 0 _1 _1 _1 _1 > > 1 1 1 1 1 _1 _1 _1 _1 _1 _1 _1 _1 1 1 1 1 > > 1 1 1 1 1 1 1 1 1 _1 _1 _1 _1 _1 _1 _1 _1 > > > > > > > > Linda > > > > > > -----Original Message----- > > From: Programming [mailto:[email protected]] On > > Behalf Of Raul Miller > > Sent: Tuesday, August 15, 2017 1:50 PM > > To: Programming forum <[email protected]> > > Subject: Re: [Jprogramming] Fwd: FW: why are there no negative signs > > for cot, sec and csc? > > > > Or you could do: > > > > cot=: %@(tan=: 3&o.) > > sec=: %@(cos=: 2&o.) > > csc=: %@(sin=: 1&o.) > > > > Thanks, > > > > -- > > Raul > > > > > > On Tue, Aug 15, 2017 at 1:11 PM, Jimmy Gauvin <[email protected]> > > wrote: > > > Hi, > > > > > > problem is with 4 5 6 which denote the following: > > > > > > coh=: 4&o. NB. sqrt (1+(y^2)) > > > sinh=: 5&o. NB. hyperbolic sine of y > > > cosh=: 6&o. NB. hyperbolic cosine of y > > > > > > see: http://code.jsoftware.com/wiki/Vocabulary/odot#dyadic > > > > > > There dosen't seem to be specific numbers for cot, sec and csc. > > > You have to go by their definition: > > > > > > [image: \cot \theta ={\frac {\cos \theta }{\sin \theta }}=\tan > > \left({\frac > > > {\pi }{2}}-\theta \right)={\frac {1}{\tan \theta }}] > > > > > > [image: \sec \theta =\csc \left({\frac {\pi }{2}}-\theta > > > \right)={\frac {1}{\cos \theta }}] > > > > > > [image: \csc \theta =\sec \left({\frac {\pi }{2}}-\theta > > > \right)={\frac {1}{\sin \theta }}] > > > > > > > > > > > > On Tue, Aug 15, 2017 at 12:41 PM, Linda Alvord > > > <[email protected]> > > > wrote: > > > > > >> > > >> > > >> Sent from AOL Mobile Mail > > >> > > >> > > >> From: Linda Alvord <[email protected]> > > >> Date: Tuesday, August 15, 2017 > > >> Subject: FW: why are there no negative signs for cot,sec and csc? > > >> Cc: lindaalvord <[email protected]> > > >> > > >> > > >> > > >> > > >> > > >> > > >> > > >> > > >> > > >> From: Linda Alvord [mailto:[email protected]] > > >> Sent: Tuesday, August 15, 2017 11:22 AM > > >> To: '[email protected]' <[email protected]> > > >> Subject: why are there no negative signs for cot,sec and csc? > > >> > > >> > > >> > > >> do=: 13 : '({.y) +(i.{:y)*(--/ 2{.y)%<:{:y' > > >> > > >> t=:do 0 2p1 17 > > >> > > >> all=:1 2 3 4 5 6 (o."0 1) t > > >> > > >> *all > > >> > > >> 0 1 1 1 1 1 1 1 0 _1 _1 _1 _1 _1 _1 _1 0 > > >> > > >> 1 1 1 1 0 _1 _1 _1 _1 _1 _1 _1 0 1 1 1 1 > > >> > > >> 0 1 1 1 1 _1 _1 _1 0 1 1 1 1 _1 _1 _1 0 > > >> > > >> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > > >> > > >> 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > > >> > > >> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 > > >> > > >> > > >> > > >> Linda > > >> > > >> ------------------------------------------------------------------- > > >> --- 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
