[LON-CAPA-users] formula response and maxima floating point numbers
Lon H Mitchell
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
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?