Bug fix: Problems with unapply

The function unapply , which constructs a procedure from an expression, has three major shortcomings, listed below. To correct them, I have written the alternative procedure vnapply .

• unapply does not work with arrays (including matrices and vectors) or tables. I'm not showing the result of the unapply command below, because that result can cause Maple to crash if you click on it.

  > f:=unapply(vector([1,x,x^2]), x):

  > f(t);

  

  Here it is with vnapply :

  > readlib(vnapply):
  f:= vnapply(vector([1,x,x^2]), x);

  

  > f(t);

  

• When the expression contains derivatives with respect to the variables, we don't want unapply to return a result such as , because that wouldn't work unless x is a name of a variable. What we do want is to take the derivative of g , and then return the function that evaluates this at its argument. This can be expressed using the D operator.

  > unapply(diff(g(x),x), x);

  

  Unfortunately, unapply fails to do this in slightly more complicated circumstances.

  > unapply(2*diff(g(x),x), x);

  

  Here it is with vnapply :

  > vnapply(2*diff(g(x),x), x);

  

• unapply has a rather strange feature: if the expression is an integer power, then what is returned is the power of a procedure rather than a procedure.

  > f:= unapply((x+1)^2,x);

  

  > whattype(f);

  

  In most cases this behaviour is harmless: applying f to any argument v will result in , as it should.

  > f(q+1);

  

  However, one place it will not work is in the evalhf environment:

  > evalhf(f(3));

  Error, unable to evaluate function `f` in evalhf

  Here it is using vnapply :

  > g:= vnapply((x+1)^2,x);

  

  > evalhf(g(3));

  

Maple Advisor Database, R. Israel 1998