Simplified: (!+/~)i.11
On Fri, Mar 28, 2014 at 9:06 AM, Pascal Jasmin <godspiral2...@yahoo.ca> wrote: > well done, > > the tacit version: > > (] !"1 +/~) i.11 > > > > ----- Original Message ----- > From: Bo Jacoby <bojac...@yahoo.dk> > To: "programm...@jsoftware.com" <programm...@jsoftware.com> > Cc: > Sent: Friday, March 28, 2014 3:23:06 AM > Subject: Re: [Jprogramming] Applied APL - How to think like an APL > programmer? > > "his table on page 105 looks interesting. I wonder what is the shortest J > expression that can reproduce it" > > This one may not be the shortest, but it works: > > n!"1 n+/n=.i.11 > > > > > > > Den 0:07 fredag den 28. marts 2014 skrev Jose Mario Quintana > <jose.mario.quint...@gmail.com>: > > Was Wallis himself the first to assume x^0 =1 even for x=0? See, >> >> >> >>http://www.maths.tcd.ie/pub/HistMath/People/Wallis/RouseBall/RB_Wallis.html >> >> >> >>Perhaps a Latin fluent member of the forum could shed some light into the >>dark: >> >> >> >>https://archive.org/details/ArithmeticaInfinitorum ? >> >> >> >>At any rate, his table on page 105 looks interesting. I wonder what is the >>shortest J expression that can reproduce it... :) >> >> >> >> >> >> >>On Fri, Jan 17, 2014 at 4:22 PM, Roger Hui <rogerhui.can...@gmail.com>wrote: >> >>> Come to think of it, the insight that 1=0^0 is required for the standard >>> statement of polynomials may have come from Ken Iverson. Knuth doesn't >>> mention this point and only mentions the binomial theorem. (Same with "Ask >>> a Mathematician".) But the polynomial argument is more convincing because >>> polynomials are ubiquitous. >>> >>> >>> >>> On Fri, Jan 17, 2014 at 12:56 PM, Roger Hui <rogerhui.can...@gmail.com >>> >wrote: >>> >>> > Found it. It is in the very same paper. >>> > http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf . >>> > >>> > On page 6, Knuth wrote: >>> > >>> > ... The debate stopped there, apparently with the conclusion that 0^0 >>> > should be undefined. >>> > >>> > But no, no, ten thousand times no! Anybody who wants the binomial >>> theorem >>> > ... to hold for at least one non-negative integer n _must_ before that >>> 0^0 >>> > = 1, ... >>> > >>> > >>> > "Ask a Mathematican" >>> > >>> > >>> http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/ >>> > has an interesting and useful discussion on this issue. In it the >>> > "Mathematician" wrote: >>> > >>> > Zero raised to the zero power is one. Why? Because mathematicians said >>> > so. No really, it's true. >>> > >>> > And then goes on to explain why 1=0^0 is a good idea. >>> > >>> > >>> > >>> > >>> > >>> > >>> > On Fri, Jan 17, 2014 at 12:30 PM, Roger Hui <rogerhui.can...@gmail.com >>> >wrote: >>> > >>> >> BTW, Knuth did something else which typifies APL thinking. In a note or >>> >> paper (I can not find it now), he argued strongly that 1=0^0, not >>> >> undefined, not 0, not anything else. The common conventional statement >>> of >>> >> a polynomial, p(x)=sigma(k=0;k<=n) a[k]*x^k, requires that x^0 be 1. >>> Some >>> >> writers are aware of this dependency and, being careful, write instead >>> the >>> >> ugly p(x)=a[0]+sigma(k=1;k<=n)a[k]*x^k. >>> >> >>> >> Attention to edge cases is typical of APL thinking. It's another way to >>> >> stay in the world of expressions and away from the world of statements. >>> >> You know: >>> >> >>> >> if k=0 then >>> >> a[0] >>> >> else >>> >> a[k]*x^k >>> >> endif >>> >> >>> >> >>> >> >>> >> >>> >> On Wed, Jan 15, 2014 at 6:20 PM, Roger Hui <rogerhui.can...@gmail.com >>> >wrote: >>> >> >>> >>> One aspect: J/APL programmers tend to stay in the nice world of >>> >>> expressions and avoid the nastier world of statements. This tendency >>> >>> pushes you towards array thinking and away from scalar thinking. >>> >>> >>> >>> For example, if b is a boolean array, and you want 4 where b is 0 and >>> 17 >>> >>> where b is 1, write: >>> >>> >>> >>> (4*0=b)+(17*1=b) >>> >>> >>> >>> And of course the signs of real numbers x are: >>> >>> >>> >>> (x>0)-(x<0) >>> >>> >>> >>> Even Knuth, an eminent mathematician and computer scientist but not an >>> >>> APL programmer, knows to <strike>steal</strike> adopt this idea. See: >>> Knuth, >>> >>> *Two Notes on Notation*< >>> http://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf>, >>> >>> 1992-05-01. In the first half of the paper he describes how "Iverson's >>> >>> convention" can be used to simplify the statement and manipulation of >>> sums. >>> >>> >>> >>> See also: >>> >>> >>> >>> http://www.jsoftware.com/papers/perlis77.htm >>> >>> http://www.jsoftware.com/papers/perlis78.htm >>> >>> http://www.jsoftware.com/papers/APLQA.htm#Perlis-foreword >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> >>> On Wed, Jan 15, 2014 at 5:32 PM, Joe Bogner <joebog...@gmail.com> >>> wrote: >>> >>> >>> >>>> I went googling for some deeper material on how to think like an APL >>> >>>> programmer. I have read/skimmed through a good set of the material on >>> >>>> http://jsoftware.com/papers/ and have skimmed through many of the >>> >>>> books listed on http://www.jsoftware.com/jwiki/Books. >>> >>>> >>> >>>> Are there any specific recommendations, free or for purchase? Or, >>> >>>> perhaps I should spend more time with the list above. >>> >>>> >>> >>>> I found this, The APL Idiom List by Perlis and Rugaber, which looks >>> >>>> similar to what I'm looking for: >>> >>>> http://archive.vector.org.uk/resource/yaleidioms.pdf. >>> >>>> >>> >>>> The review of this book looks like what I'm after, >>> >>>> >>> >>>> >>> http://www.amazon.com/Handbook-APL-programming-Clark-Wiedmann/dp/0884050262 >>> >>>> , >>> >>>> constructing useful programs and going into more depth. >>> >>>> >>> >>>> Or something of the style of The Little Schemer, >>> >>>> http://scottn.us/downloads/The_Little_Schemer.pdf >>> >>>> >>> >>>> I searched the forum and had trouble finding a relevant post >>> >>>> ---------------------------------------------------------------------- >>> >>>> 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
