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11.3 Arbeiten mit Maple
11.3.1 Simplification
For the most part, Maple leaves expressions the way you entered them or the way they were created
from some computation. However, there are some obvious simplifications that it automatically
performs. An example of this would be turning 0 * x into the simpler 0.
The simplify command provides typical expression simplifications. By using simplify(expr, property)
you can control what simplifications are performed:
> 4^(1/2) + 3;
1/2
4 + 3
> simplify (%); (Anmerkung: das % ist ein Platzhalter für den zuletzt berechneten Wert;
5 in Maple Version 4 ist es statt dessen ein " )
The expand command forces distribution of multiplication over addition. For instance:
> f := (x + y) * (x - y);
f := (x + y) (x - y)
> expand(f);
2 2
x - y
Since expand turns f into x^2 + y * x - x * y - y^2, the automatic simplifications turn the expression into
x^2 - y^2.
For more information on simplification, see ?simplify, ?expand, ?factor, ?normal.
11.3.2 Some Predefined Symbols (Vordefinierte Symbole)
There are four kinds of symbols that have some form of predefined meaning within Maple:
Syntactic parts of the Maple command and programming language. The meanings of these cannot be
redefined. ("if" and "quit" are typical examples.)
System-supplied functions. These may be redefined, but you will lose the functionality of the systemsupplied
function. ("solve" and "trace" are typical examples.)
Predefined constants and names. Library functions assume that these symbols exist with no assigned
value, so errors or incorrect results will usually result if they are redefined. ("I", the complex square
root of -1, and "true" are typical examples. See ?constants for the complete list.)
System programming variables. These are used to control computational effects, so they can
(cautiously!) be assigned new values. ("Digits" and "printlevel" are typical examples.)
The global variable "printlevel" is a particularly handy one to know. By setting "printlevel := 0;" you turn
off the automatic printing of your commands; setting "printlevel := 1;" is the default behaviour. See
?printlevel for the effect of other settings.
11.3.3 Summation
Maple allows you to specify both definite and indefinite symbolic summations using the sum
command:
> # Be sure that the index variable is a mathematical variable.
> # If i had a value (say, 3), it would be meaningless to say
> # something like "sum 3 squared for 3 from 1 to n" when you
> # meant to say "sum i squared for i from 1 to n":
> i;
i
> # This is an example of a sum over an indefinite (non-negative)
> # index range:
> x; # Just to be sure, we want to see if x is a mathematical variable.
x
> sum(x^i, i);
109