Open rtoy opened 2 weeks ago
rtoy
commented
2 weeks ago Imported from SourceForge on 2024-07-01 17:02:04 Created by sueyllam on 2009-04-12 06:57:48 Original: https://sourceforge.net/p/maxima/bugs/1643/#32e3
file with system 0f Solvable 4 algebraic equations
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rtoy
commented
2 weeks ago Imported from SourceForge on 2024-07-01 17:02:06 Created by robert_dodier on 2009-04-12 17:29:19 Original: https://sourceforge.net/p/maxima/bugs/1643/#4882
For the record, the system of equations is the following:
algsys([a^2-y^2-(h+l/2)^2=0, r^2-(r-y)^2-(h+l/2)^2=0, r^2-a^2/4-a^2*r^2/(4*h^2)=0, h+l-a=0], [h,l,r,y]);
rtoy
commented
2 weeks ago Imported from SourceForge on 2024-07-01 17:02:08 Created by andrejv on 2009-04-12 22:13:31 Original: https://sourceforge.net/p/maxima/bugs/1643/#1050
A workaround is to use grobner bases to modify the equations:
(%i1) load(grobner)$ Loading maxima-grobner $Revision: 1.5 $ $Date: 2008/05/05 08:47:28 $ (%i2) eqs: [a^2-y^2-(h+l/2)^2, r^2-(r-y)^2-(h+l/2)^2, r^2-a^2/4-a^2*r^2/(4*h^2), h+l-a]$ vars: [h,l,r,y]$ (%i4) poly_reduced_grobner(eqs, vars)$ (%i5) algsys(%, vars)$ (%i6) length(%); (%o6) 8
Imported from SourceForge on 2024-07-01 17:02:03 Created by sueyllam on 2009-04-12 06:57:47 Original: https://sourceforge.net/p/maxima/bugs/1643
Maxima returned an empty solution set for the algebraic system of 4 equations shown in the attached file. The system has 8 solutions (real and complex) and MAPLE was able to find them (through MATLAB).