Optional Arguments and Default Values

Many Maple routines accept optional arguments. This is often used to allow the user to use default values instead of having to specify all parameters. Examples are the functions plot, factor, collect, and series. Let us consider the degree function. The degree function computes the degree of a univariate polynomial in one variable, and for multivariate polynomials, the total degree. For example

=-1.00.5plus##1`##1=12=^^M=12 > p := x^3+2*x+1;

3 p := x + 2 x + 1

> degree(p);

3

> q := 3*x^2*y+2*y^2-x*z+7;

2 2 q := 3 x y + 2 y - x z + 7

> degree(q);

3

plusplus -100 plus Sometimes you will want to compute the degree in a specific variable, say . This can be done by specifying an optional second argument to the degree function, namely, the variable. For example

=-1.00.5plus##1`##1=12=^^M=12 > degree(p,x);

3

> degree(q,x);

2

plusplus -100 plus How would we code the degree function? Let us assume that the input is a formula and if an optional second argument is given, it is a name or set of names for the variables. We would write

DEGREE := proc(a:algebraic,x:{name,set(name)}) local s,t;
    if nargs = 1 then # determine the variable(s) for the user
        s := indets(a); # the set of all the variables of a
        if not type(s,set(name)) then ERROR(`input not a polynomial`) fi;
        DEGREE(a,s)
    elif type(a,constant) then 0
    elif type(a,name) then
        if type(x,name) then if a = x then 1 else 0 fi
        else if member(a,x) then 1 else 0 fi
        fi
    elif type(a,`+`) then max( seq( DEGREE(t,x), t=a ) )
    elif type(a,`*`) then
        s := 0;
        for t in a do s := s + DEGREE(t,x) od;
        s
    elif type(a,algebraic^integer) then DEGREE(op(1,a),x) * op(2,a)
    else ERROR(`cannot compute degree`)
    fi
end;