"trigrat" caught in infinite loop - depending on how you call it

On 2012-11-07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:

> Well, it looks as though it's not an issue in the assume database,
> anyway....  All we need to do is wrap $trigrat with (let ((varlist)) ...).

Looks like binding VARLIST does indeed fix the problem with trigrat, but
it turns out trigrat is a Maxima function, so the problem is not in
trigrat but in one of the functions it calls.

Here's the existing trigrat function (from share/trigonometry/trigrat.lisp):

#$trigrat(exp):=
    if matrixp (exp) or listp (exp) or setp (exp) or trigrat_equationp
(exp)
    then map (trigrat, exp)
    else block([e,n,d,lg,f,lexp,ls,d2,l2,alg,gcd1],
		alg:algebraic,gcd1:gcd,
		algebraic:true,gcd:subres,
		e: rat(ratsimp(expand(exponentialize(exp)))),
		n:num(e),d:denom(e),
		listofei(d),
		l2:map(lambda([u,v],u^((hipow(d2,v)+lopow(d2,v))/2)),
				lexp,lg),
		f:if length(lexp)=0 then 1
		  else if length(lexp)=1 then part(l2,1)
		  else apply("*",l2),
  		n:rectform(ratexpand(n/f)),
	        d:rectform(ratexpand(d/f)),
		e:ratsimp(n/d,%i),
		algebraic:alg,gcd:gcd1,
		e)$

Adding ?varlist:false to the list of variables in the block fixes the bug. 

I guess at this point we need to figure out which of the built-in
functions is not restoring VARLIST ....

best

Robert Dodier