Symbolic Math Toolbox

Vectorized Example

Suppose we want to calculate the sine of a symbolic matrix. One way to do this is

• function y = sin1(x)
  
  for k = 1: prod(size(x))
     y(k) = maple('sin',x(k));
  end
  
  y = reshape(y,size(x));
  

So the statements

• syms x y
  A = [0 x; y pi/4]
  sin1(A)
  

return

• A =
  [    0,    x ]
  [    y, pi/4 ]
   
  ans =
  [           0,      sin(x) ]
  [      sin(y), 1/2*2^(1/2) ]
  

A more efficient way to do this is to call Maple just once, using the Maple map function. The map function applies a Maple function to each element of an array. In our sine calculation example, this looks like

• function y = sin2(x)
  
  if  prod(size(x)) == 1
  % scalar case
     y = maple('sin',x);
  
  else
  % array case
     y = maple('map','sin',x);
  
  end
  

Note that our sin2 function treats scalar and array cases differently. It applies the map function to arrays but not to scalars. This is because map applies a function to each operand of a scalar.

Because our sin2 function calls Maple only once, it is considerably faster than our sin1 function, which calls Maple prod(size(A)) number of times.

The map function can also be used for Maple functions that require multiple input arguments. In this case, the syntax is

• maple('map', Maple function, sym array, arg2, arg3, ..., argn)
  

For example, one way to call the collect M-file is collect(S,x). In this case, the collect function collects all the coefficients with the same power of x for each element in S. The core section of the implementation is shown below.

• r = maple('map','collect',sym(s),sym(x));
  

For additional information on the Maple map function, type

• mhelp map
  

Simple Example

Debugging