MaplePrimes - answers and comments on Question, what is maple doing?

Comparing Vectors

Robert Israel — Thu, 20 Nov 2008 20:31:03 Z

I think the problem is that, unlike most mathematical objects, Maple can have two identical Vectors in memory, and "=" will not consider them to be the same.
The recommended way to compare them would be with Equal in the LinearAlgebra package.

LinearAlgebra:-Equal

Thomas Richard — Thu, 20 Nov 2008 20:32:57 Z

Think of x as a pointer to a certain Vector. For the the actual comparison, you will need the Equal command (see ?Equal for more info):

if Equal(x,Vector(2,[1,0])) then 7 else 3 end if;

By the way, if you merely want to check if x is of type Vector, then this will do:

if type(x,Vector) then 7 else 3 end if;

minus vs equal

jakubi — Thu, 20 Nov 2008 21:08:48 Z

What I find strange is the difference in implementation. While in:

x-Vector(2, [1, 0]);

after the arguments to `-` are checked as vectors, the operation is dispatched to 'LinearAlgebra'/rtable routines (LinearAlgebra:-Multiply, LinearAlgebra:-LA_Main:-VectorAdd, etc), but for

x=Vector(2, [1, 0]);

'LinearAlgebra:-Equal' or something like that is not called.

another way to look at it

acer — Thu, 20 Nov 2008 21:39:50 Z

Suppose we make the two assignments,

> x := Vector[row]([1,2]);
                                  x := [1, 2]
 
> y := Vector[row]([1,2]);
                                  y := [1, 2]

And now we assign to an entry of x,

> x[1]:=17:

> x;
                                    [17, 2]

Most people will usually want that the corresponding entry of y to not get assigned by the above assignment to x. So, Maple has two separate and distinct Vectors [1,2] when x and y are created.

The comparison,

  if foo = bar then

will do a comparison for identity, ie. are they the same object in memory. But as just seen, they are not. They are distinct, so that their respective elements may be changed independently.

So, what's been noticed is that mutable objects (objects whose elements may be changed or altered) are generally distinct in Maple.

The routine is() can do some mathematical inference that evalb(..=..) does not do. Originally, is() was a mechanism for query properties, but perhaps it's been becoming mathematically smarter. It's not an unreasonable expectation for is() to be able to handle this query. But, as it happens, it hasn't (yet) been taught to do that.

One might ask, why does if foo=bar then.. make the "object identity" query evalb(foo=bar) rather that the LinearAlgebra:-Equal(foo,bar) query? Well, it's consistent with how most all other objects are treated in that operation. And if the implementation were reversed then someone would complain about that, and an alterntive syntax would have to be used in order to force the specific identity query on Matrices/Vectors, etc.

The Maple help system doesn't really make it easy to figure out what the `=` means in if foo=bar then..

acer

if

Robert Israel — Fri, 21 Nov 2008 14:09:36 Z

Speaking of possible changes to if:

The failure of the construction

if a < b then ... end if

when a and b evaluate to real constants that are not of type numeric is a very common cause of grief, and not just to Maple novices. Always checking conditionals using is instead of evalb might, I suppose, cause performance to suffer. But using is when Maple would otherwise return the dreaded "cannot determine if this expression is true or false" error shouldn't affect performance when the is is not necessary, and I can't see it breaking much existing code. So this is one case that I think it would be useful to change.

interesting idea

Dave L — Fri, 21 Nov 2008 18:00:38 Z

It might even be possible for that error to be caught (followed by a pass-off to is) without the usual overhead of a try..catch.

Thanks for suggesting it (AJ and RI).

Dave Linder
Mathematical Software, Maplesoft