On Fri, Nov 12, 2004 at 05:34:49PM +0200, Alexander Vidybida wrote:
> On Wed, Nov 10, 2004 at 10:06:42AM -0600, Barton Willis wrote:
> > Illustration of what I mean by "work too hard to try to apply the
> > even / odd function simplifications"
> >
> > (%i1) assume(x<0);
> > (%o1) [x < 0]
> > (%i2) sin(x);
> > (%o2) - SIN(- x)
> >
> > It seems gratuitous to apply the odd function rule in this case. We need
> > a reasonable heuristic for deciding when to apply the even / odd
> ...
>
> The above transformation seems methodologically wrong.
> In a symbolic system, the '-' sign presence should trigger simplification,
> but not the argument's positivity/negativity. Thus, after the odd function rule
> application, we should have:
>
> sin(-x) goes to -sin(x) independently of what is known about the x sign,
> and, of course,
> sin(x) goes to sin(x), again independently of what is known about the x sign.
Just have observed more unnecessary work:
(%i20) ieq2;
1 - x
q - q x /
%E f(x) [ - q x - q
(%o20) -------------- - I f(y) dy = %E - %E
q ]
/
0
(%i21) ieq3:subst(1-x,x,%);
0
/ q - q (1 - x)
[ f(1 - x) %E - q (1 - x) - q
(%o21) I f(y) dy + ------------------------ = %E - %E
] q
/
x
Here, swapping of neither terms, nor integration limits was expected.
I would prefer to have both unswapped.
(%i23) SOLVE(ieq3,f(1-x)),expand;
0
/
- q x [ - q x - q - q
(%o23) [f(1 - x) = - q %E I f(y) dy - q %E + q %E ]
]
/
x
If the integration limits were swapped in order to hide the 'minus' sighn,
than it would be normal to swap them back here.
Best wishes,
--
Alexander