[Maxima-discuss] Returning vector [0, 0, 0] instead of scalar 0 for cross product in vect.mac

[Robert D. <rob...@gm...>]

Hi,

some time ago a bug was reported for vect.mac. The cross product of a
vector with itself is supposed to be zero. Now in vect.mac, a vector
is represented as a list of three elements, so the question is whether
the zero vector result for the cross product should be 0 or [0, 0, 0].
For the original report and some discussion see:
https://sourceforge.net/p/maxima/bugs/3287/

The current behavior is that x ~ x (i.e. cross product of x with
itself) returns 0, I propose it's changed to x*0 which is going to be
a list when x is a list. What does anyone say about that? (Yes, x*0
simplifies to 0 when x is not a list. I agree that's an unsolved
problem.)

I was thinking at first that the result should be zero since 0 is a
perfectly good symbol for the additive identity for vectors. However,
[0, 0, 0] is just as good, just a little more verbose, and [0, 0, 0]
helps Maxima keep track of what's going on. As it stands, the cross
product yields some unexpected results, see the bug report for
examples.

The general approach of using a list to represent a vector has some
unhappy consequences, since Maxima has a lot of ideas about lists and
that stuff doesn't always square with what vectors are supposed to do.
But short of reworking the vector stuff from the ground up (which,
indeed, I have experimented with in the past), I am just trying to fix
up the existing vect.mac package.

best,

Robert Dodier