Noun forms of elementry arithmetic functions

There are a variety of other approaches possible.
One is to do this
simp:off;

and then x+1+x   remains unchanged.

Another is to not use Maxima, but just write in Lisp.

Another is to forget the nary and prefix stuff and use
functional notation, e.g.

myPlus(x,1,x);
You can then consider modifying the display program
to show x+1+x.

I think you should look first at  simp:off
though.

Good luck
RJF


Chris Sangwin wrote:

> 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