maxima fails to simplify one of two simmetric solutions
Subject: maxima fails to simplify one of two simmetric solutions
From: Alberto LUSIANI
Date: Thu, 12 Aug 2004 16:24:00 +0200
Hello,
I am using maxima 5.9.0.9beta2 and am surprised to see that it
simplifies in a different way two solutions that are of the same form.
(%i4) display2d:false;
(%o4) FALSE
(%i5) eqEcm:2*SQRT((-Ep)*Em);
(%o5) 2*SQRT(-Em*Ep)
(%i6) eqBoost:(Ep+Em)/My;
(%o6) (Ep+Em)/My
(%i7) SOLVE([(eqEcm = My)^2,eqBoost = BETA],[Ep,Em]);
(%o7) [[Ep = -(SQRT(BETA^2+1)*My-BETA*My)/2,Em = (SQRT(BETA^2+1)+BETA)*My/2],
[Ep = (SQRT(BETA^2+1)*My+BETA*My)/2,Em = -(SQRT(BETA^2+1)-BETA)*My/2]]
As you can see, maxima could factorize My on the Ep expressions
exactly like it does for the Em expressions, but it does
not. Elaborating on the solution expressions, maxima correctly
gets rid of the My variable for Em, while it fails do do so for Ep.
I consinder this a bug, or at least an inconsistency.
(%i8) PICKAPART(%o7[1],2);
(%i9) Ep:%t8;
(%o9) -(SQRT(BETA^2+1)*My-BETA*My)/2
(%i10) Em:%t9;
(%o10) (SQRT(BETA^2+1)+BETA)*My/2
(%i11) diff(Em,Beta)*Beta/Em;
(%o11) BETA*(BETA/SQRT(BETA^2+1)+1)/(SQRT(BETA^2+1)+BETA)
(%i12) diff(Ep,Beta)*Beta/Ep;
(%o12) BETA*(BETA*My/SQRT(BETA^2+1)-My)/(SQRT(BETA^2+1)*My-BETA*My)
(%i13) Em/My;
(%o13) (SQRT(BETA^2+1)+BETA)/2
(%i14) Ep/My;
(%o14) -(SQRT(BETA^2+1)*My-BETA*My)/(2*My)
(%i15)
Greetings,
--
Alberto