Symbolic Math Toolbox

Symbolic and Numeric Conversions

Consider the ordinary MATLAB quantity

• t = 0.1
  

The sym function has four options for returning a symbolic representation of the numeric value stored in t. The 'f' option

• sym(t,'f')
  

returns a symbolic floating-point representation

• '1.999999999999a'*2^(-4)
  

The 'r' option

• sym(t,'r')
  

returns the rational form

• 1/10
  

This is the default setting for sym. That is, calling sym without a second argument is the same as using sym with the 'r' option:

• sym(t)
   
  ans =
  1/10
  

The third option 'e' returns the rational form of t plus the difference between the theoretical rational expression for t and its actual (machine) floating-point value in terms of eps (the floating-point relative accuracy):

• sym(t,'e')
   
  ans =
  1/10+eps/40
  

The fourth option 'd' returns the decimal expansion of t up to the number of significant digits specified by digits:

• sym(t,'d')
   
  ans =
  .10000000000000000555111512312578
  

The default value of digits is 32 (hence, sym(t,'d') returns a number with 32 significant digits), but if you prefer a shorter representation, use the digits command as follows:

• digits(7)
  sym(t,'d')
   
  ans =
  .1000000
  

A particularly effective use of sym is to convert a matrix from numeric to symbolic form. The command

• A = hilb(3)
  

generates the 3-by-3 Hilbert matrix:

• A =
   
      1.0000    0.5000    0.3333
      0.5000    0.3333    0.2500
      0.3333    0.2500    0.2000
  

By applying sym to A

• A = sym(A)
  

you can obtain the symbolic (infinitely precise) form of the 3-by-3 Hilbert matrix:

• A =
   
  [   1, 1/2, 1/3]
  [ 1/2, 1/3, 1/4]
  [ 1/3, 1/4, 1/5]
  

The subs Command

Constructing Real and Complex Variables