Symbolic Math Toolbox

Simple Example

As an example, you can use the Maple function gcd to calculate the greatest common divisor of two integers or two polynomials. For example, to calculate the greatest common divisor of 14 and 21, enter

• maple('gcd(14, 21)')
  ans =
  7
  

To calculate the greatest common divisor of x^2-y^2 and x^3-y^3 enter

• maple('gcd(x^2-y^2,x^3-y^3)')
  ans =
  -y+x
  

To learn more about the function gcd, you can bring up its reference page by entering

• doc gcd
  

As an alternative to typing the maple command every time you want to access gcd, you can write a simple M-file that does this for you. To do so, first create the M-file gcd in the subdirectory toolbox/symbolic/@sym of the directory where MATLAB is installed, and include the following commands in the M-file:

• function g = gcd(a, b)
  g = maple('gcd',a, b);
  

If you run this file

• syms x y
  z = gcd(x^2-y^2,x^3-y^3)
  w = gcd(6, 24)
  

you get

• z = 
  -y+x
  
  w = 
  6
  

Now, extend the function so that you can take the gcd of two matrices in a pointwise fashion:

• function g = gcd(a,b)
  
  if any(size(a) ~= size(b))
    error('Inputs must have the same size.')
  end
  
  for k = 1: prod(size(a))
    g(k) = maple('gcd',a(k), b(k));
  end
  
  g = reshape(g,size(a));
  

Running this on some test data

• A = sym([2 4 6; 3 5 6; 3 6 4]);
  B = sym([40 30 8; 17 60 20; 6 3 20]);
  gcd(A,B)
  

you get the result

• ans =
  [ 2, 2, 2 ]
  [ 1, 5, 2 ]
  [ 3, 3, 4 ]
  

Using Maple Functions

Vectorized Example