Well, here's a somewhat better (though still pretty simple-minded) approach.
It takes something like
if X then A elseif Y then B else C
and simplifies it to
if X then (simplify A assuming X)
elseif Y then (simplify A assuming not X and Y)
else (simplify C assuming not X and not Y)
(%i1) load("if_simp");
(%o1) "if_simp.mac"
(%i2) resimp_if(if a>0 then abs(a) else abs(a));
(%o2) if a>0 then a else -a
(%i3) resimp_if(if a>0 then (if b>0 then abs(a*b) else abs(a*b)) else (if
b>0 then abs(a*b) else abs(a*b)));
(%o3) if a>0 then if b>0 then a*b else -a*b else if b>0 then -a*b else a*b
There is also a variant, reeval_if, which evaluates the 'then' clauses
rather than resimplifying them. This can obviously be hazardous -- *caveat
emptor.*
(%i17) if equal(a,-1) then integrate(x^a,x) else integrate(x^a,x)$
(%i18) reeval_if(%);
(%o18) if equal(a,-1) then log(x) else x^(a+1)/(a+1)
Some limitations:
It does not yet handle and's and or's in "if" clauses. (The naive approach
of just passing them along to 'assume' doesn't work.)
Since it depends on the existing assume/simplify system, it does not know
that
if equal(a,b) then a-b
can be simplified to
if equal(a,b) then 0
I'll be interested in feedback / bug reports....
-s
On Sun, Jan 20, 2013 at 9:43 PM, Robert Dodier <robert.dodier at gmail.com>wrote:
> On 2013-01-20, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
>
> > (%i1) expr: if cond then print(3) else print(4);
> > (%o1) if cond then print(3) else print(4)
> > (%i2) map(ev,%);
> > 3 << note evaluation of both branches
> > 4
> > (%o2) if cond then 3 else 4 << evaluated values in 'if' expression
>
> Hmm, yes, that's a good idea (despite the limitations which you pointed
> out).
>
> best
>
> Robert Dodier
>
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