Hello James,
funny to find this letter in the morning, because I've spent last night
teaching Maxima to solve irrational equations :)) I attach the code I
have so far.
Maxima has the ability to solve systems of polinomial equations (do
describe(solve)) only.
The procedure goes thru the expr from leaves to top, substituting all
irrational subexpressions containing vars with new variables and adds
rational equations to define these new variables. Finally it gets the
system of polynoimial equations and algsys tries to solve it. then all
the solutiona are substed into initial equations to check which are the
proper solutions.
The problems I've faced so far: 1)Algsys is slooooow 2) substituting
even correct solution into initial equations doesn't always simplify to
true 3) Usually Algsys gives approximate solutions (I know, I can alter
it adjusting algexact, but it leads to 'quotient is not exact' errors,
like in algsys([S1-3*S2=2,(x+3)*S1^6=(x-5),(x-5)*S2^6=(x+3)],[S1,S2,x])).
Can somebody give advice concerning the problems mentioned above?
Example session:
(C21) solve\-irrat(sqrt(1+x)=2,[x]);
[x]
G22262 = 2
2
[G22262 = x + 1]
[[G22262 = 2, x = 3]]
(D21) [[x = 3]]
--
Andrei Zorine
James Frye wrote:
> ...something like this?
>
> C1: f1(x):= x - 2 * sqrt (x);
> C2: solve (f(x) = 10, x);
>
> gives back
>
> D2: [x = 2 SQRT(x) + 10]
>
> which IMHO isn't much of a solution :-) But when I substitute y = sqrt
> (x) to get an equivalent function
>
> C3: f3(y):= y^2 - 2 * y;
> C4: float (solve (f2(y) = 10, y);
>
> I get two answers [y = -2.316, y = 4.316], and if I square the second, I
> get a solution to f1?
>
> I'm puzzled.
>
> James
>
Attached file: irratsolve.mac