I would like to produce detailed worked solutions for students
automatically in Maxima as part of computer aided assessment
questions. To do this I would like much finer control over the
simplifications which Maxima performs to very elementary
expressions. For example, I would like to manipulate expressions
such as
x + 1 + x,
without these automatically being simplified to 2*x+1.
To do this I have defined noun forms of the elementry
arithmetic operators, eg
nary("n+",100);
prefix("n-",100);
nary("n*",120);
infix("n/",122,123);
infix("n^",140,139);
It is then possible to have expressions such as
x n+ 1 n+ x
or
x n+ n- x
I have started to write functions which manipulate them, such as
one to convert all operators in an expression to noun form, eg
noun_arith(ex) := block(
ex:subst("N+","+",ex),
ex:subst("N*","*",ex),
ex:subst("N-","-",ex),
ex:subst("N/","//",ex),
ex:subst("N^","^",ex),
ev(ex));
I expect this will develop into a library of related functions and
so before I start on this in ernest I'd like to discuss this with
the list. I think such noun forms would be more generally useful
for many other applications.
(1) Do such noun forms already exist?
(2) Is using the function nary, etc to define these noun forms the
correct way to proceed in Maxima? If not, what else should I do?
(3) Where can I find information on the binding levels of +, -
etc? (Those used above were stolen from the mactex.lisp file.)
(4) using factor(2^6-1) returns
((MTIMES SIMP FACTORED) ((MEXPT SIMP) 3 2) 7)
How does this relate to the proposed noun forms?
(5) I've modified the tex() function to display the noun forms
exactly as their verb counterparts through lisp code such as
(defprop $n+ tex-mplus tex)
(defprop $n+ ("+") texsym)
(defprop $n+ 100. tex-lbp)
(defprop $n+ 100. tex-rbp)
This works surprisingly well, but I'm (not surprisingly) having
great difficulty with the unary minus. How can I tell tex() to
display these noun forms in an identical way to their namesakes?
I've attached two files to give an idea of what progress I have
made.
Any advice would be very welcome.
Chris
Attached file: noun_arith.lisp
Attached file: na.mac