CAS simplifying non-zero expressions to 0

[Nigel (UK)]

(10-06-2014 12:06 PM)parisse Wrote:  When I learned physics, I was always told not to use numbers in equations, but always symbols, and replace them only at the end (when all computations are done) by their numeric values. If you follow this rule, you will never have these kind of problems with CAS instructions like simplify, expand, etc.
A CAS can not work properly with approx data, it has to replace them by exact data, and it can not guess if 1e-34 or any other value is near 0 because of the dimension of the quantity (I mean unit choice, since dimensionless number are rarely close to 0) and should not be replaced by 0 (but should be replaced by a nonzero symbolic constant), or if it's a rounding error and should be replaced by 0.

The questions my students are set often involve a series of calculations, with numerical answers required at each stage and with earlier answers feeding into the later calculations. It is possible to define a symbol for each intermediate answer but it slows things down. It is quicker simply to work with the numerical values.

At the moment I'm teaching circular motion in my lessons. Some of the questions are about cars and trains; some of them are about elementary particles in magnetic fields. For the former type of question I can enter equations with approximate numbers and find solutions; for the latter I must define symbols or everything is simplified to zero, even though both questions are essentially of the same type. This is unnecessarily confusing.

In pure maths I imagine that small numbers are usually the result of rounding errors; in physics small numbers are completely normal and no such judgement should be made. Xcas is perfectly able and willing to work with approximate numbers - it solves 6.63 x f = E for f and raises no objection. All I would like is the option to solve 6.63e-34 x f = E for f in the same way.

In case I'm coming across as miserable, I love the Prime and I think it is tremendous to have something as powerful as Xcas in portable form. But this "feature" is annoying!

Nigel (UK)