detect sqrt in expression?

Looks good!

Here are some test cases you may find interesting -- I'm not sure what your
intended behavior is in these cases:

multival(x^(1/2+a),x) => false
multival(x^(a/2),x) => false
    (what if a=1?)
multival(x^a,x) => false
    (what if a=1/2?)

multival((-1)^(1/3),x), domain:'complex => false

multival(x^%i,x) => false

Up to you....

          -s


On Sat, Nov 19, 2011 at 19:07, Edwin Woollett <woollett at charter.net> wrote:

> On Nov. 17, Stavros Macrakis wrote:
> -----------------
>
>  Really?  It seems pretty straightforward to me, something like
>>
>> hasmultival(ex,var) := if mapatom(ex) then false
>>
>> else if member(inop(ex), '[log, asin, acos, asinh, etc. etc.] ) and
>> member(var,listofvars(ex)) then true
>>
>> else if inop(ex) = "^" and ...
>>
>> else ...recursive case...
>>
> ------------------------------**----
> Thanks for the suggested framework.
> So far, the code seems to be meeting my
> goal, but bugs will probably show up
> when I make it part of nint.
>
> ------------------------------**----------------
> (%i1) load(hasmultv);
>
> (%o1) "c:/work2/hasmultv.mac"
> (%i2) multival(a,x);
>
> (%o2) false
> (%i3) multival(sqrt(x),x);
>
> (%o3) true
> (%i4) multival(x*sqrt(x),x);
>
> (%o4) true
> (%i5) multival(x*sqrt(x^2),x);
>
> (%o5) false
> (%i6) multival(a^x,x);
>
> (%o6) false
> (%i7) multival(a^(%i*x),x);
>
> (%o7) false
> (%i8) multival(a^(2/3),x);
>
> (%o8) false
> (%i9) multival(x^(2/3),x);
>
> (%o9) true
> (%i10) multival(x^x,x);
>
> (%o10) false
> (%i11) multival(x^(%i*x),x);
>
> (%o11) true
> (%i12) multival(x^(%i*sin(x)),x);
>
> (%o12) true
> (%i13) multival(log(x),x);
>
> (%o13) true
>
> (%i14) multival(sqrt(x)*log(x),x);
>
> (%o14) true
> (%i15) multival(acos(x),x);
>
> (%o15) true
> (%i16) multival(x^acos(x),x);
>
> (%o16) true
> ------------------------------**-------
> with the code:
>
> any_of(list) := member(true,list)$
>
> /* multival(e,x) returns true if a potentially multiple valued
>    function of x is detected in expression e */
>
>
> multival(ex,var) := block([inflag:true,**listconstvars:true],
>
>     if mapatom(ex) then false
>
>     else if member(op(ex), '[log, acos,acosh,acot,acoth,acsc,**acsch,
>                           asec,asech,asin,asinh,atan,**atan2,atanh] ) and
>                     member(var,listofvars(ex)) then true
>
>     else if op(ex) = "^" and mvp(ex,var) then true
>
>     else any_of(maplist(lambda ([u],multival(u,var)),ex)))$
>
>
>
>  /* complexvar(ee,vv) returns true if
>    ee contains both variable vv and %i  */
>
>
> complexvar(ee,vv) := block([listconstvars:true],
>
>       if mapatom(ee) then false
>
>       else if member (vv,listofvars(ee)) and member(%i,listofvars(ee))
> then true
>
>       else any_of(maplist(lambda ([u],complexvar(u,vv)),ee)))$
>
>
>
> /* mvp(e,v) returns true if  e = f^g has either the
>     form f(x)^g(x,%i) or f(x)^(p/q)    */
>
>  mvp (e,v) := block([inflag:true],
>
>      /* disp("mvp"),
>        display (e,v),
>        */
>
>      if mapatom(e) then false
>
>      else if length(e) = 1 then false
>
>      else if atom(part(e,2)) then false
>
>      else if member(v,listofvars(part(e,1))**) and
>                       op(part(e,2)) = "/" then true
>
>      else if member(v,listofvars(part(e,1))**) and
> complexvar(part(e,2),v) then true
>
>
>      else any_of(maplist(lambda ([u],mvp(u,v)),e)))$
>
>      ------------------------------**-----
> Ted
>
>
>