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Computer Algebra System (CAS) 14-1
14
Computer Algebra System (CAS)
What is a CAS?
A computer algebra system (hereafter CAS) enables you
to perform symbolic calculations. With a CAS you
manipulate mathematical equations and expressions in
symbolic form, rather than manipulating approximations
of the numerical quantities represented by those symbols.
In other words, a CAS works in exact mode, giving you
infinite precision. On the other hand, non-CAS
calculations, such as those performed in HOME view or
by an aplet, are numerical calculations and are limited by
the precision of the calculator (to 10
–12
in the case of the
HP 40gs).
For example, with Standard as your numerical format,
1/2 + 1/6 returns 0.6666666666667 if you are
working in the HOME screen; however, 1/2 + 1/6
returns 2/3 if you are working with CAS. HOME
calculations are restricted to approximate (or numeric)
mode, while CAS calculations always work in exact
mode (unless you specifically change the default CAS
modes).
Each mode has advantages and disadvantages. For
example, in exact mode there is no rounding error, but
some calculations will take much longer to complete and
require more memory than equivalent calculations in
numeric mode.
Performing symbolic calculations
You perform CAS calculations with a special tool known
as the Equation Writer. Some computer algebra
operations can also be done in the HOME screen, as
long as you take certain precautions (see “Using CAS
functions in HOME” on page 14-7). Moreover, some
computer algebra operations can only be done in the
HOME screen; for example, symbolic linear algebra
hp40g+.book Page 1 Friday, December 9, 2005 1:03 AM