(1) The user documentation for to_poly_solve is in Maxima (version 5.25.1 or 5.25.0).
If you want more examples, locate the file rtest_to_poly_solver.mac (.../share/contrib)
(2) In your work, solve indicates that the solution set is empty. Maybe it is.
Try a special case:
(%i93) eqs : subst([a=1,mu=1,W=2,r=1,f=2],[eq1,eq2])$
Possibly make solution set larger
(%i94) eqs : map(lambda([s],s^2),eqs)$
Algsys finds solutions (notice tau[r] --> tau[1], tau[f] --> tau[2])
(%i95) sol : algsys(%,[tau[1],tau[2]])$
Test each putative solution:
(%i96) map(lambda([s], expand(rectform(subst(s, eqs)))),sol)$
(%i97) float(%);
(%o97) [[-0.8*%i-0.6=1.0,0.0=0.0],[-0.8*%i-0.6=1.0,0.0=0.0],[0.8*%i-0.6=1.0,0.0=0.0],[0.8*%i-0.6=1.0,0.0=0.0]]
Apparently, the solution set is empty.
(3) Although tau[f] prints as a lovely subscripted variable, tau[f] is a nounform for a hashtable.
Using tau[f] to mean a subscripted variable can lead to trouble. I suggest switching to tau_f.
--Barton
-----maxima-bounces at math.utexas.edu wrote: -----
I'm still struggling with how to manipulate equations
so that Maxima can solve them.? See example below.
Is there a document somewhere that gives general
guidance, and examples, how to use to_poly_solve?
Maxima script without output:
(%i1)kill(all)$ display2d: false$
(%i2) s: (1/r)*f*(tau[f]+tau[r])/2;
(%i3) F[f]:sqrt((tau[f]/r)^2+s^2);
(%i4) eq1: F[f]=mu*a*W/2;
(%i5) F[r]:sqrt((tau[r]/r)^2+s^2);
(%i6) eq2: F[r]=mu*(1-a)*W/2;
(%i7) solve([eq1,eq2],[tau[f],tau[r]]);
Same script, with output:
(%i1) kill(all)$ display2d: false;
(%o1) false
(%i2) s: (1/r)*f*(tau[f]+tau[r])/2;
(%o2) f*(tau[r]+tau[f])/(2*r)
(%i3) F[f]:sqrt((tau[f]/r)^2+s^2);
(%o3) sqrt(f^2*(tau[r]+tau[f])^2/(4*r^2)+tau[f]^2/r^2)
(%i4) eq1: F[f]=mu*a*W/2;
(%o4) sqrt(f^2*(tau[r]+tau[f])^2/(4*r^2)+tau[f]^2/r^2) = a*mu*W/2
(%i5) F[r]:sqrt((tau[r]/r)^2+s^2);
(%o5) sqrt(f^2*(tau[r]+tau[f])^2/(4*r^2)+tau[r]^2/r^2)
(%i6) eq2: F[r]=mu*(1-a)*W/2;
(%o6) sqrt(f^2*(tau[r]+tau[f])^2/(4*r^2)+tau[r]^2/r^2) = (1-a)*mu*W/2
(%i7) solve([eq1,eq2],[tau[f],tau[r]]);
(%o7) []_______________________________________________
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