Symbolic Math Toolbox

Constructing Real and Complex Variables

The sym command allows you to specify the mathematical properties of symbolic variables by using the 'real' option. That is, the statements

• x = sym('x','real'); y = sym('y','real');
  

or more efficiently

• syms x y real
  z = x + i*y
  

create symbolic variables x and y that have the added mathematical property of being real variables. Specifically this means that the expression

• f = x^2 + y^2
  

is strictly nonnegative. Hence, z is a complex variable and can be manipulated as such. Thus, the commands

• conj(x), conj(z), expand(z*conj(z))
  

return

• x, x-i*y, x^2+y^2 
  

respectively. The conj command is the complex conjugate operator for the toolbox. If conj(x) == x returns 1, then x is a real variable.

Clearing Variables in the Maple Workspace

When you declare x to be real with the command

• syms x real
  

a becomes a symbolic object in the MATLAB workspace and a positive real variable in the Maple kernel workspace. If you later want to remove the real property from x, enter

• syms a unreal
  

Note that entering

• clear x
  

only clears x in the MATLAB workspace. If you then enter syms x, MATLAB still treats x as a positive real number.

Symbolic and Numeric Conversions

Creating Abstract Functions