Page 31 - A Guide to MATLAB for Beginners and Experienced Users

12 Chapter 2: MATLAB Basics

to about 15 digits, not its exact value. To compute an exact answer, instead
of an approximate answer, we must create an exact symbolic representation
of π/2 by typing sym(’pi/2’). Now let’s take the cosine of the symbolic
representation of π/2:

>> cos(sym(’pi/2’))

ans =
0
This is the expected answer.
The quotes around pi/2 in sym(’pi/2’) create a string consisting of the
characters pi/2 and prevent MATLAB from evaluating pi/2 as a floating
point number. The command sym converts the string to a symbolic expression.
The commands sym and syms are closely related. In fact, syms x is equiv-
alent to x = sym(’x’). The command syms has a lasting effect on its argu-
ment (it declares it to be symbolic from now on), while sym has only a tempo-
rary effect unless you assign the output to a variable, as in x = sym(’x’).
Here is how to add 1/2 and 1/3 symbolically:

>> sym(’1/2’) + sym(’1/3’)

ans =
5/6
Finally, you can also do variable-precision arithmetic with vpa. For example,
√
to print 50 digits of 2, type
>> vpa(’sqrt(2)’, 50)

ans =
1.4142135623730950488016887242096980785696718753769
➱ You should be wary of using sym or vpa on an expression that
MATLAB must evaluate before applying variable-precision
arithmetic. To illustrate, enter the expressions 3ˆ45, vpa(3ˆ45),
and vpa(’3ˆ45’). The first gives a floating point approximation to
the answer, the second — because MATLAB only carries 16-digit
precision in its floating point evaluation of the exponentiation —
gives an answer that is correct only in its first 16 digits, and the
third gives the exact answer.
See the section Symbolic and Floating Point Numbers in Chapter 4 for details
about how MATLABconverts between symbolic and floating point numbers.