Using SLOPE function in Function APP with CAS defined function

[Han]

(12-09-2014 02:46 PM)cdecastro Wrote:  I understand many of the issues related to the "culture clash" between the HOME environment and the CAS environment but find it unfortunate that there is not better integration. Students working in the CAS will certainly have occasion to work with the graphical representations of expressions derived within the CAS. When options for finding slope, zeros, etc, present themselves to the user, one expects they will operate correctly. I like the Prime but hope future developments will include a more seamless integration.

Thank you for the replies!

Regards,
Chris

For me, a lot of it was due to unfamiliarity with the CAS itself. After I spent some time reading up on xcas/giac I felt a bit more comfortable with using CAS and Home together. One of the most important things I learned was how the CAS handles functions.

A function can be created several ways:

f(x):=x^2;
OR
f:=(x)->(x^2); // like in Maple

Functions can be "copied":

F1:=f;

and there is also functional algebra:

g(x):=x^2;
h(t):=3*t+1;
f:=g+h;

f(s); // -> s^2 + 3*s + 1

There is also a difference between a mathematical function vs a CAS function. When we read \( f(x) = x^2 \) in a textbook, then \( f(x) \) is both a (mathematical) function _and_ the evaluation of the function \( f \) at an input of \( x \). In the CAS (and most CAS) typing f(x) results in the evaluation of a function at x -- which is an expression in terms of x, and typing f alone actually produces a (CAS) function.

Hope that helps.

Edit: The command f:=g+h; is the same as f(x):=g(x)+h(x). If you had wanted to create \( f(x) = x^2 + 3t+1 \) so that the \( t \) is a constant with respect to \( x \), then type: f(x):=g(x)+h(t); as the right hand side is an expression in terms of x and t, and the := operator creates a function with only x as the variable as specified by the (x) after f.