CAS-> Variable() warning msg?
10-31-2014, 09:36 AM
Post: #1
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
CAS-> Variable() warning msg?
In HOME when a variable is intended to be used as a function, for example: a:=x^2
then: a(4) => 16, etc., without further adieu.

In CAS a warning asserting that "Substitution" should be used for the expression in a. Depending on the expression, that could be a lot of extra baggage, and generates computational delay. Is there another context for a() than originally defined? (Why is the warning necessary in CAS)?

-Dale-
10-31-2014, 10:54 AM
Post: #2
 parisse Senior Member Posts: 1,179 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
You are confusing an expression and a function (HOME does not have functions). Functional notation is reserved to function (f(x):=x^2 or f:=x->x^2 then f(2)), not to expressions where subst should be used (g:=x^2, subst(g,x=2) or g|x=2). I'm currently introducing in Xcas a new notation for substitution in expressions, like this: g(x=2).
10-31-2014, 01:03 PM
Post: #3
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: CAS-> Variable() warning msg?
The example, a:=x^2, was created in the CAS environment.

Upon switching to the HOME environment, for any a(n), //where a(x) is used as a pseudonym for standard function notation f(x), but functionally the same//, is operated on according to the function's definition, just like a function machine, per the wikipedia 'function' definition.

In HOME a(n) returns the function value immediately, with no warning message.
In CAS first a warning is issued, then the same a(n) function value is returned.

I was wondering if there were some OTHER kind of operation that COULD take place using the function variables contents, different (and unintended), from the original definition a:=x^2? This could justify the CAS warning, which, perhaps, would not occur in the HOME environment.

I stumbled on this kind of variable usage (on the prime) the other day, and I'm just exploring its possible virtues.

-Dale-
10-31-2014, 02:49 PM
Post: #4
 parisse Senior Member Posts: 1,179 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
Most of the CAS commands expects expressions, not functions. As soon as you do computer algebra, you must make the distinction between both. That's why the CAS evaluates univariate_expression(something) like if univariate_expression was a function, but issues a warning.
10-31-2014, 03:42 PM (This post was last modified: 10-31-2014 03:50 PM by Han.)
Post: #5
 Han Senior Member Posts: 1,881 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
You should be careful with using functional notation on expressions as opposed to actual functions (and by functions, I mean as "defined" by the CAS).

a:=x^2;
x:={1,2,3,4};

a(1) through a(4) will behave as expected, but a(-1) will produce an error. The CAS is able to handle list processing, so that x^2 is {1,4,9,16}. The a(n) notation is now a reference to the n-th object in the list x^2. So a(-1) makes absolutely no sense in this context.

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10-31-2014, 04:39 PM (This post was last modified: 10-31-2014 05:14 PM by DrD.)
Post: #6
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: CAS-> Variable() warning msg?
EMU CAS

Testing with a:=x^2

a(-1) => 1
a(-4) => 16
a({-1,-2,-4}) => {1,4,16}
n:=7, a(n) => 49
n:=-6, a(n) => 36

So far so good. Seemed to work with complex numbers, too. Where does it fail?
10-31-2014, 05:00 PM
Post: #7
 Han Senior Member Posts: 1,881 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
It fails when you define x as a list in exactly the same manner shown my post.

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10-31-2014, 05:17 PM (This post was last modified: 10-31-2014 05:22 PM by DrD.)
Post: #8
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: CAS-> Variable() warning msg?
Yeah ... I screwed that up by re-using x as the dummy variable, thus killing my x-based defining expression. So I edited the post to use n, instead. I'm sorry about that.
10-31-2014, 11:04 PM (This post was last modified: 10-31-2014 11:09 PM by Han.)
Post: #9
 Han Senior Member Posts: 1,881 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
Try this:

restart;
a:=x^2;
x:={1,2,3,4};
a(1);
a(2);
a(3);
a(4);
a(-1);
a(5);

The last two produce an error. On the other hand, using:

restart:
a(x):=x^2;
x:={1,2,3,4};
a(1);
a(2);
a(3);
a(4);
a(-1);
a(5);

will result in no failures.

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11-01-2014, 12:48 PM
Post: #10
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: CAS-> Variable() warning msg?
(10-31-2014 11:04 PM)Han Wrote:  Try this:

restart;
a:=x^2;
x:={1,2,3,4};
a(1);
a(2);
a(3);
a(4);
a(-1);
a(5);

Restart, and restart() are cool! Learned something from that.

True, this example fails; but using variable 'x' is troublesome in the quoted example. If you use a different variable, say 'n', as the independent variable instead, the above works fine. Using 'x' in the defining expression, then using 'x' again as an independent variable, is asking for trouble. The independent 'x' became a pointer to the list 'x', in expression involving x^2. Using 'n' has no particular relationship to 'x^2'. I don't think that counts as a fail in this case.

I'm not really sure that there is a point to all of this, other than I just happened on to the prime's use of a variable to contain a function, returning the function value by containing an independent range within parentheses on it (not an index into it). Sort of a short hand way of using functions, more for the general good than anything.

Usually, when I discover something (new to me) like that, I find limitations I hadn't considered. So I hang back waiting for the recoil! This idea works pretty good, in spite of the cautions about it.

-Dale-
11-01-2014, 01:13 PM
Post: #11
 Han Senior Member Posts: 1,881 Joined: Dec 2013
RE: CAS-> Variable() warning msg?
(11-01-2014 12:48 PM)DrD Wrote:  True, this example fails; but using variable 'x' is troublesome in the quoted example. If you use a different variable, say 'n', as the independent variable instead, the above works fine. Using 'x' in the defining expression, then using 'x' again as an independent variable, is asking for trouble. The independent 'x' became a pointer to the list 'x', in expression involving x^2. Using 'n' has no particular relationship to 'x^2'. I don't think that counts as a fail in this case.

This is precisely the point of the example. That is, when you create a proper function, the 'x' in the function is just a dummy variable. So if one subsequently defines 'x' it does not affect the behavior of the function. On the other hand, creating an expression and expecting it to work like a function (even if it does work most of the time) is a bad idea of one intends to use the expression as an actual function because there will be instances when such expected behavior breaks.

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11-01-2014, 01:25 PM (This post was last modified: 11-01-2014 01:27 PM by DrD.)
Post: #12
 DrD Senior Member Posts: 1,132 Joined: Feb 2014
RE: CAS-> Variable() warning msg?
Ok ... but that is not entirely unlike crossing over HOME and CAS with "variable" consequences. Case matters, reserved variables matter, and context matters. It's a matter of remembering which variables matter, ... not to splatter the matter any badder.

-Dale-
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