Changes
http://wiki.axiom-developer.org/358VariableIsApparentlyAlwaysAssumedToBePositive/diff
--
??changed:
-(1) -> f(x|x<0)==-x**2
- Type: Void
-(2) -> f(x)==x**2
- Type: Void
+\begin{axiom}
+f(x|x<0)==-x**2
+f(x)==x**2
+\end{axiom}
??changed:
Then, draw the function
-
-(3) -> draw(f(x),x=-1..1)
- Compiling function f with type Variable x -> Polynomial Integer
-Compiling /tmp/gazonk0.lsp.
-End of Pass 1.
-End of Pass 2.
-OPTIMIZE levels: Safety=0 (No runtime error checking), Space=0, Speed=3
-Finished compiling /tmp/gazonk0.lsp.
- Compiling function %F with type DoubleFloat -> DoubleFloat
- Graph data being transmitted to the viewport manager...
- AXIOM2D data being transmitted to the viewport manager...
-
- (3) TwoDimensionalViewport: "x*x"
- Type: TwoDimensionalViewport
-
+\begin{axiom}
+draw(f(x),x=-1..1)
+\end{axiom}
Note that the function is compiled with Variable x -> Polynomial Integer, and
the viewport shows the function x*x, even for x<0, where it should show -x*x.
??changed:
The same holds when you eval the function:
-
-(4) -> )clear all
- All user variables and function definitions have been cleared.
-(1) -> f(x|x<0)==-x**2
- Type: Void
-(2) -> f(x)==x**2
- Type: Void
-(3) -> eval(f(x),x=-5)
- Compiling function f with type Variable x -> Polynomial Integer
-
- (3) 25
- Type: Polynomial Integer
-
-Here, we should expect -25. And shouldn't this:
-
-(4) -> f(x)
-(4) ->
- 2
- (4) x
-[1 more lines...]
+\begin{axiom}
+eval(f(x),x=-5)
+\end{axiom}
+Here, we should expect -25. And shouldn't
+\begin{axiom}
+f(x)
+\end{axiom}
result in something similar to
??changed:
result in something similar to
-
-(5) -> )display values f
- Definition:
- 2
- f (x | x < 0) == - x
- 2
- f x == x
-
-?
+\begin{axiom}
+)display values f
+\end{axiom}
??changed:
Integration, therefore, also goes wrong,
-
-(5) -> integrate(f(x),x=-5..5)
-(5) ->
- 250
- (5) ---
- 3
- Type: Union(f1: OrderedCompletion Expression Integer,...)
-
+\begin{axiom}
+integrate(f(x),x=-5..5)
+\end{axiom}
which should of course yield 0. It would appear that in certain operations,
when performing a function on f (like draw, eval, integrate), or when x is not
specified, it is assumed to be positive. After that, the actual value is filled
in and this can therefore yield an erroneous result.
--
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