[LON-CAPA-users] formula response and maxima floating point numbers

Lon H Mitchell lon-capa-users@mail.lon-capa.org
Thu, 09 Sep 2010 09:54:13 -0400

According to the Maxima manual, a shortcut to getting a floating point 
approximation to a function value is to use a decimal argument.  For 
example, sqrt(2.0) will return 1.414213562373095 while sqrt(2) will stay 
as sqrt(2).  

This shortcut can result in some seemingly incomprehensible answers.  
For example, "is(sqrt(1.5) = sqrt(3/2))" returns /false/.  Further, a 
formula response problem with answer "1+ sqrt(3/2)*x" will mark "1 + 
sqrt(1.5)*x" as incorrect and vice versa.  Since the behavior is 
inherent to Maxima,  math response problems can be similarly affected.     

Note that this behavior only seems to arise when dealing with a function 
value.  For example, "x^(1.5)" and "x^(3/2)" are considered equivalent 
by Maxima, as are "1.5" and "3/2".

While one possible solution is to use sampling rather than algebraic 
checking, my guess would be that sqrt(1.5) = sqrt(3/2) would be an 
expected equivalence on the part of most users.

The question then: is there a way to instruct Maxima to turn this 
shortcut behavior off, and, if so, is it possible to change formula 
response problems (or lonmaxima) to make use of it?


Lon Mitchell