User Guide

Numeric computation is the manipulation of expressions in the context of
finite-precision arithmetic. Expressions involving exact numbers, for example,
, are replaced by close approximations using floating-point numbers,
for example 1.41421. These computations generally involve some error.
Understanding and controlling this error is often of as much importance as
the computed result.
In Maple, numeric computation is normally performed if you use floating-
point numbers (numbers containing a decimal point) or the evalf command.
The plot command (see Plots and Animations (page 189)) uses numeric
computation, while commands such as int, limit, and gcd (see Integer Oper-
ations (page 71) and Mathematical Computations (page 123)) generally use
only symbolic computation to achieve their results.
Exact Computations
In Maple, integers, rational numbers, mathematical constants such as π and
∞, and mathematical structures such as matrices with these as entries are
treated as exact quantities. Names, such as , , , and
mathematical functions, such as sin(x) and LambertW(k, z), are symbolic
objects. Names can be assigned exact quantities as their values, and functions
can be evaluated at symbolic or exact arguments.
>
Important: Unless requested to do otherwise (see the following section),
Maple evaluates expressions containing exact quantities to exact results, as
you would do if you were performing the calculation by hand, and not to
numeric approximations, as you normally obtain from a standard hand-held
calculator.
3.2 Symbolic and Numeric Computation • 67