Symbolic Math Toolbox

Creating Symbolic Variables and Expressions

The sym command lets you construct symbolic variables and expressions. For example, the commands

• x = sym('x')
  a = sym('alpha')
  

create a symbolic variable x that prints as x and a symbolic variable a that prints as alpha.

Suppose you want to use a symbolic variable to represent the golden ratio

The command

• rho = sym('(1 + sqrt(5))/2')
  

achieves this goal. Now you can perform various mathematical operations on rho. For example,

• f = rho^2 - rho - 1
  

returns

• f =
   
  (1/2+1/2*5^(1/2))^2-3/2-1/2*5^(1/2)
  

Then

• simplify(f)
  

returns

• 0
  

Now suppose you want to study the quadratic function . The statement

• f = sym('a*x^2 + b*x + c')
  

assigns the symbolic expression to the variable f. Observe that in this case, the Symbolic Math Toolbox does not create variables corresponding to the terms of the expression, , , , and . To perform symbolic math operations (e.g., integration, differentiation, substitution, etc.) on f, you need to create the variables explicitly. You can do this by typing

• a = sym('a')
  b = sym('b')
  c = sym('c')
  x = sym('x')
  

or simply

• syms a b c x
  

In general, you can use sym or syms to create symbolic variables. We recommend you use syms because it requires less typing.

Symbolic Objects

Symbolic and Numeric Conversions