In this section is some basic information about Maple that may help with symbolic computation and the use of Maple. One of the first things is assigning equations to variables in Maple. This is very useful because it will allow you to enter an equation once and then perform many operations on or with that equation.
To assign an equation to a variable use the := operator.
An example of this is shown below.
> f:=x^2+3*x+13;
2
f := x + 3 x + 13
> f;
2
x + 3 x + 13
> f:=0;
f := 0
> f;
0
In the above example the equation x^2+3*x+13 was
assigned to the variable f. f was then called
and Maple printed out the equation. On the third line zero was
assigned to f. This was done to clear the variable.
Maple, unlike Mathematica, does not have a Clear
function for variables. Before using a variable in an equation be
sure you know what it represents or if you are not sure assign a
constant such as 1 or 0 to it.
Another operator that is useful is the !. This performs the same function as in Mathematica. Namely it allows you to call a Unix command while still in Maple. With this you can view the contents of the directory you are presently in, change directories, clear the screen, or any other Unix command you wish to call.
When using Maple, remember to finish any line with a semicolon so Maple knows to process the command.
The first function here, simplify has a lot of
ambiguity attached to it. No one really knows how the simplest
form of an equation is represented. Maple does have a command
though that follows a wide collection of rules to obtain a result
that it believes is in a more simple form.
> f:=(a+b/x+c/x^2);
c
f := a + b/x + ----
2
x
> simplify(f);
2
a x + b x + c
--------------
2
x
In the example above the equation the was first saved to the
variable f is simplified somewhat with the
simplify command. There is also a command in
Maple called expand which performs the opposite
operation of simplify in that it will expand an
equation out into all of its parts.
> f:=(a+b/x+c/x^2);
c
f := a + b/x + ----
2
x
> g:=simplify(f);
2
a x + b x + c
g := --------------
2
x
> g;
2
a x + b x + c
--------------
2
x
> expand(g);
c
a + b/x + ----
2
x
The example starts out by assigning an equation to the variable
f and then simplifying this equation and assigning
the result to the variable g. expand
is then called with the equation in g as an argument
and the result is the same equation that was saved in f.
solve is a very useful function when dealing with
various equations. Like the Solve function in
Mathematica, it lets you solve an equation for some constant
or for some variable within the equation. By using solve
equations can be rearranged and put in terms of different
variables within them. solve can take one or two
arguments. The first argument is the equation that is to be solved.
The second argument is the variable that the equation is to solved
in terms of. Below is an example that was used with the
Solve function in Mathematica.
> f:=3*x+2*x^2+5*y+2*y^3;
2 3
f := 3 x + 2 x + 5 y + 2 y
> solve(f=100, x);
3 1/2 3 1/2
- 3/4 + 1/4 (809 - 40 y - 16 y ) , - 3/4 - 1/4 (809 - 40 y - 16 y )
In this example the equation 3*x+2*x^2+5*y+2*y^3 was
saved to the variable f. Next, f was set
equal to zero within the call to the solve function and
the equation was to be solved in terms of x. Just like in the
Mathematica example, solve returns the same two answers,
although displayed in a different manner.
Below is and example of when only one argument needs to be sent
to solve.
> solve(x^2-x+1=0,x);
1/2 1/2
1/2 + 1/2 I 3 , 1/2 - 1/2 I 3
> solve(x^2-x+1);
1/2 1/2
1/2 + 1/2 I 3 , 1/2 - 1/2 I 3
> solve(x^2-x+1+y);
2
{x = x, y = - x + x - 1}
solve will let you drop the variable, in
this case x, and the =0 if there is
no ambiguity in the equation. When solve does
encounter an ambiguity it may just return a trivial answer which
is shown in the third line of the example above.