Sollya User's Manual

Name:

_x_ universal name for the mathematical free variable.

Library names:

sollya_obj_t sollya_lib_free_variable() sollya_obj_t sollya_lib_build_function_free_variable() #define SOLLYA_X_ (sollya_lib_build_function_free_variable())

Description:

_x_ is an identifier that always denotes the mathematical free variable. It cannot be assigned.
Sollya manipulates mathematical functions of a single variable. The first time that a variable name is used without having been assigned before, this variable name is automatically considered by Sollya as the name of the free variable. Subsequently, any other unassigned variable name will be considered as the free variable with a warning making this conversion explicit. This is convenient for an every-day use of the interactive tool, but it has the drawback that the free variable name can change from a session to another. There are contexts (e.g., within a procedure, or for doing pattern matching) when one might want to refer to the free variable regardless of its name in the current session. For this purpose _x_ is a universal identifier, always available and always denoting the free variable, whatever its name is in the current context.

Example 1:

   > verbosity=1!;
   > sin(a);
   sin(a)
   > b;
   Warning: the identifier "b" is neither assigned to, nor bound to a library function nor external procedure, nor equal to the current free variable.
   Will interpret "b" as "a".
   a
   > _x_;
   a

Example 2:

   > verbosity=1!;
   > sin(y);
   sin(y)
   > f = proc(a) {
       return sin(a + _x_);
     };
   > rename(y,z);
   Information: the free variable has been renamed from "y" to "z".
   > f(1);
   sin(1 + z)

Example 3:

   > f = sin(y);
   > match f with
       sin(a) : { print("sin of a with a =", a);
                  match a with
                    _x_ : { print("a turns out to be the free variable"); }
            default : { print("a is some expression"); };
                }
       _x_ : { print("Free variable") ; }
       default: { print("Something else"); };
   sin of a with a = y
   a turns out to be the free variable