Re: [Reduce-algebra-developers] Real solutions of solve

[Arthur N. <ac...@ca...>]

On Wed, 27 Jul 2011, Simon Weitzhofer wrote:

> Hi there,
>
> is it possible to get only the real solutions of an equation from solve? (Such
> that solve(x^4=1,x) returns only {x=1, x=-1})
>
> Thank you,
> Simon
>

You may wish to investigate
    realroots(x^2 + 1)         {}
    realroots(x^2 - 1)         {x = -1 , x = 1}
for cases where you KNOW that you will be getting numeric roots...?

In terms of an objection to "i", I note that at present the simplification 
of sqrt reads

symbolic procedure simpsqrt u;
    if u=0 then nil ./ 1 else
    if null !*keepsqrts
      then simpexpt1(car u, simpexpon '(quotient 1 2), nil)
     else begin scalar x,y;
        x := xsimp car u;
        return if null numr x then nil ./ 1
                else if denr x=1 and domainp numr x and !:minusp numr x
                 then if numr x=-1 then simp 'i
                       else multsq(simp 'i,
                                   simpsqrt list prepd !:minus numr x)
                else if y := domainvalchk('sqrt,list x) then y
                else simprad(x,2)
      end;

so "sqrt(-1)" is turned into "i" at a fairly low level.

Arthur