Dealing with more than one Optional parameter

Question

I have a procedure

f:=proc(x,option1,option2) ... end proc;

In my case option1 is always an integer and option2 is either a list or something else (including integer). Both options are optional, so these commands work as expected:

f(x);
f(x,3);
f(x,4,[1,2]);
f(x,5,3);
f(x,6,expand);

But if option1 isn't specified then I don't know an easy way to deal with it since Maple doesn't allow the usage like

f(x,,3);
f(x,,[1,2]);

I can make it understand

f(x,[1,2]);

but I still have a problem with

f(x,3);

since it's not clear if 3 is option1 or option2. I can rewrite the code to understand function calls in this format

f(x,[1,option1],[2,option2]);
f(x,[1,option1]);
f(x,[2,option2]);

but I'm curious if there is a simpler way to achieve that since for some Maple functions (like plot) the order of most options doesn't matter.

Answer 1

Most of the plotting commands use Maple's more modern argument-processing to manage procedure options.

In particular most options to plotting commands are provided as so-called keyword options. That automatically provides the functionlity in which the location (of such options) doesn't matter.

For example,

f:=proc(v, 
        {ord::{integer,NoUserValue}:=':-NoUserValue'},
        {special::{integer,list,NoUserValue}:=':-NoUserValue'});

  print(':-ord'=ord, ':-special'=special);

end proc:

f(x);

    ord = NoUserValue, special = NoUserValue

f(x,ord=3);

         ord = 3, special = NoUserValue

f(x,special=5);

         ord = NoUserValue, special = 5

f(x,special=5,ord=3);

               ord = 3, special = 5

f(x,ord=3,special=5);

               ord = 3, special = 5

As you've noticed, you [logically] cannot use multiple *positional/ordered" parameters if both have the same type and some earlier ones are missing.

If you really wanted you could make one of those options into a positional parameter, although naturally that would lose its flexibility of arbitrary placement. For example,

restart;
f2:=proc(v, 
        ord::{integer,NoUserValue}:=':-NoUserValue',
        {special::{integer,list,NoUserValue}:=':-NoUserValue'});

  print(':-ord'=ord, ':-special'=special);

end proc:
f2(x);
f2(x,3);
f2(x,special=5);
f2(x,special=5,3);
f2(x,3,special=5);

restart;
f3:=proc(v, 
         special::{integer,list,NoUserValue}:=':-NoUserValue',
         {ord::{integer,NoUserValue}:=':-NoUserValue'});

  print(':-ord'=ord, ':-special'=special);

end proc:
f3(x);
f3(x,5);
f3(x,ord=3);
f3(x,ord=3,5);
f3(x,5,ord=3);

There are too many variants to show them all here, sensibly.

You don't have to use the name "NoUserValue" as the default values.