#62 to_poly_solve in core, was: Maxima can't solve equation

[Anonymous]

Can someone tell me if this is an equation that Maxima should solve? because it solves it in terms of l1 which is the variable I'm trying to solve it for.

l1/sqrt(l1^2+22500)-(500-l1)/sqrt((500-l1)^2+2500)

[Barton Willis]

The optional package to_poly_solve solves this equation:

(%i1) load("topoly_solver.mac")$
(%i2) to_poly_solve(l1/sqrt(l1^2+22500)-(500-l1)/sqrt((500-l1)^2+2500),l1);
(%o2) [[l1=375]]

[Nobody/Anonymous]

ok, but it seems a simple enough equation that Maxima should solve without having to use an optional package, right?

[Barton Willis]

Yes, it would be good if the solve function would handle this equation. For now, this is the best
we have---we're always looking for volunteers that can help.

[Barton Willis]

Yes, it would be good if the solve function would handle this equation. For now, this is the best
we have---we're always looking for volunteers that can help.

[Robert Dodier]

Renaming this item and reclassifying it as a feature request.

[Dieter Kaiser]

An example from bug report ID: 2969546:

--------------
Maxima is not able to solve this simple equation
400-(800*(6-x))/sqrt((6-x)^2+4)=0
--------------

The package to_poly_solver can handle this equation:

(%i3) load(to_poly_solver);
(%o3) "/usr/local/share/maxima/5.20post/share/contrib/to_poly_solver.mac"

(%i4) eqn:400-(800*(6-x))/sqrt((6-x)^2+4)=0$

(%i5) to_poly_solve(eqn,x);
(%o5) %union([x = (2*3^(3/2)-2)/sqrt(3)])

Dieter Kaiser

[Dieter Kaiser]

Adding the examples of the bug report ID: 2933063 "simple equations with sqrt(x^2....) cannot be solved"

--------------------
example 1: sqrt(x^2+a^2)=x+2
example 2: sqrt(x^2+a^2)=3*x
example 3: sqrt(x^2+(a/2)^2)=x+sqrt(x^2+a^2)
--------------------

All examples can be solved with to_poly_solve:

(%i1) load(to_poly_solver);
(%o1) "/usr/local/share/maxima/5.20post/share/contrib/to_poly_solver.mac"

(%i3) to_poly_solve(sqrt(x^2+a^2)=x+2,x);
(%o3) %union([x = (a^2-4)/4])

(%i5) assume(a>0)$

(%i6) to_poly_solve(sqrt(x^2+a^2)=3*x,x);
(%o6) %union([x = a/2^(3/2)])

(%i7) to_poly_solve(sqrt(x^2+(a/2)^2)=x+sqrt(x^2+a^2),x);
(%o7) %union([x = (sqrt(13)-7)*a/(2^(3/2)*sqrt(3)*sqrt(sqrt(13)-1))])

Dieter Kaiser

[Dieter Kaiser]

Adding example from bug report ID: 2041214 "unable solve":

--------------------
solve([x+y=1,sqrt(x+1)=1],[x,y])
--------------------

(%i1) load(to_poly_solver)$

(%i2) to_poly_solve([x+y=1,sqrt(x+1)=1],[x,y]);
(%o2) %union([x = 0,y = 1])

Dieter Kaiser