Dear Stefan:
When you input "x < 10" into a symbolic computation
program, the meaning is at first ambiguous. In the context
of a function such as test1, a meaning can be obtained by
assuming x is of the same type as 10 (or at least numeric)
and the usual ordering of numbers is used for the "<"
operation. However, if the input x is not numeric, such as
the symbol y you use, then it does not make sense to
compare a symbol y with a number, except in the context of
polynomials (y and 10 both treated as polynomials in y).
There, the usual ordering is an extension of a
term-ordering and y > 10, as polynomials, and that is why
you get 5y^2. (BTW, you have a typo in your definition of
test1.)
To implement what you expect for "test1 y" would require a
whole new setup, treating "y < 10" as an unevaluated
expression (hold the evaluation until more information is
known about y). But even if that is the setup, "test1 y"
could only return "test1 y", unless there is an
instruction from the user to "expand" the definition of
test1.
So the answer to your question "How is it possible ..."
is, "It is not possible, in the context of piecewise
functions." because no matter what the system does, you
gain no new information other than what you inputted,
until you let the system know what y is, numerically.
At a higher level of symbolic computation, it is possible
to simplify a boolean expression of inequalities (in
Axiom, as far as I know, there is no such domain yet;
Mathematica has a function called "Reduce" that does
simplifications involving inequalities and equations).
However, that would not be in the simple context of a
piecewise function.
Tim Daly has done some experiments with a proviso domain
in Axiom. He may be able to tell you more.
William
On Sat, 30 Apr 2011 20:40:28 +0200
Stefan Karrmann <[email protected]> wrote:
Dear all,
I'm new to axiom and have a problem with piecewise
functions.
test1 (x | x < 10) == 2*x
test1 (x | x < 10) == 5*x^2
test1
->
test1 (x | x < 10) == 2x
test1 (x | ^ x < 10) == 5x
Type:
FunctionCalled
test1 y
->
2
5y
I expected something like (if y < 10 then 2*y else
5*y**2).
How is it possible to pass a Variable to a piecewise
function respecting
the pieces?
PS: Using a block and => or explicit if-then-else does
not help.
--
Kind regards,
Stefan
_______________________________________________
Axiom-math mailing list
[email protected]
https://lists.nongnu.org/mailman/listinfo/axiom-math
William Sit, Professor Emeritus
Mathematics, City College of New York
Office: R6/291D Tel: 212-650-5179
Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/
_______________________________________________
Axiom-math mailing list
[email protected]
https://lists.nongnu.org/mailman/listinfo/axiom-math
