define

define

define a function

Syntax

Define F(X_1, .., X_n)   C   EndDefine
Define F(X_1, .., opt X_n)   C   EndDefine
Define F(...)   C   EndDefine
  return FUNCTION

Description

1. INTRODUCTION. This command adds the user-defined function F to the library. The function F can be called in the following way:

    F(E_1,...,E_n)

where the E_i 's are expressions. The result of the evaluation of each expression E_i is assigned to the respective formal parameter X_i , and the command sequence C is executed. If, during the execution of C , a statement Return E is executed, then the result of the evaluation of E is the return-value of the function F . If no Return command is executed, or Return is executed without argument, then the return-value is Null .

Example

/**/  Define square(X)
/**/    Return X^2;
/**/  EndDefine;

/**/  square(5);
25

or a variable number of arguments

Example

/**/  define strange(...)  --> all args are in the list ARGV
/**/    if len(ARGV) = 0 then return 1234; endif;
/**/    if len(ARGV) > 4 then return last(ARGV)^2; endif;
/**/    error("Wrong number for arguments for \"strange\"!");
/**/  enddefine;

/**/ strange();
1234
/**/ strange(1, 4, "a", 5, 10);
100
/**/ -- strange(1,2); --> ERROR

2. SCOPE. Every variable defined or modified by the command sequence C is considered local to the function unless the variable is global or relative to a ref parameter. See TopLevel for the use of global variables. See ref to learn about calling a function by reference, i.e. so that the function can change the value of an existing variable.

Example

/**/  Define Example_1(L)
/**/    L := L + 5;
/**/    Return L;
/**/  EndDefine;

/**/  L := 0;
/**/  Example_1(L);
5
/**/  L;  -- L is unchanged despite the function call.
0

3. VARIABLE NUMBER OF PARAMETERS. It is also possible to have some optional arguments or a variable number of arguments:

Example

-- OPTIONAL ARGUMENTS must be in the last positions

/**/  define deg0(f, opt x)
/**/    if f=0 then return 0; endif;
/**/    if IsDefined(x) then return deg(f,x); endif;
/**/    return deg(f);
/**/  enddefine;

/**/  use P ::= QQ[x,y,z];
/**/  deg0(zero(P));
0
/**/  deg0(x^2+y);
2
/**/  deg0(x^2+y, y);
1

-- VARIABLE number of ARGUMENTS

/**/   Define MySum(...)  -->  arguments are in the LIST "ARGV"
/**/     If len(ARGV) = 0 Then Return 12345;
/**/     Else
/**/       ans := 0;
/**/       Foreach N In ARGV Do ans := ans+N; EndForeach;
/**/     EndIf;
/**/     Return ans;
/**/   EndDefine;

/**/  MySum(1,2,3,4,5);
15
/**/  MySum();
12345

The old statement, Help S; is OBSOLETE!

See Also