Introduction Functions  Environments:-  J  Matlab Mathematica Maple APL HP48G TI85 TI89
Function definitions in J
sample =: list of ((first of right) + h*/ indices)
d =: behead - curtail
mids =: half of (behead + curtail)
S =: 0: , + / \
sum =: + /
 
where 
 
first =:  {. 
of =:  @ 
right =:  ] 
left =:  [ 
h =:  %~ d 
indices =:  i. of (1: + left)
half =:  -
behead =:  }. 
curtail =:  }: 
list =:  ,
A typical sequence to demonstrate that the derivative of the integral returns the original function might consist of 

           x =: 100 sample 0 3 
          =:  exp - x ^ 2
          Iy  =: S (mids y) * d x 
         DIy =: (d Iy)  %  d x 
     plot  (y  vs  x) and (DIy vs mids x)

vs is a function that delivers the lists y and x to the plot function in the required form; while function and delivers several tables to plot
i. is the index generator :  i.5 gives  0,1,2,3,4 
* gives (term-by-term) multiplication 
% gives (term-by-term) division 
/  applies an operation over a list 
 

File jmm.ijs is a script to run in J to define the functions
Introduction Functions Environments:-  J  Matlab Mathematica Maple APL HP48G TI85 TI89