In maxima I have calculated a complicated 2x2 matrix, let's call it "HUGE" and it has 8 variables in it:
a, b, c, d, tr11, tr12, tr21, tr22
This is not correct syntax, but just to illustrate:
Given
HUGE(a,b,c,d,tr11,tr12,tr21,tr22)=matrix([0,0],[0,0])
I want to factorize/transform it into
HUGE_NEW(a,b,c,d)=matrix([tr11,tr21],[tr12,tr22])
By writing things like HUGE_NEW(a,b,c,d) I mean a new matrix that contains variables a,b,c,d only.
In other words I want to say something like
solve (HUGE - matrix([tr11,tr21],[tr12,tr22]) = matrix([0,0],[0,0]), [a, b, c, d], [tr11, tr12, tr21, tr22])
How can I go about it? My matrix is really complicated, so doing it with pen and paper is not an option.
In case someone asks for the actual value of my HUGE-matrix to try it out:
HUGE: matrix([−(sqrt(d^2−2*a*d+4*b*c+a^2)*((b*d+a*b)*tr12*tr22+(−d^2−a*d)*tr12*tr21+(−b*d−a*b)*tr11*tr12+(d^2+a*d)*tr11^2)+(b*d^2+2*b^2*c+a^2*b)*tr12*tr22+((−2*b*c−a^2)*d−d^3)*tr12*tr21+(b*d^2+2*b^2*c+a^2*b)*tr11*tr12+((−2*b*c−a^2)*d−d^3)*tr11^2)/(2*a*d−2*b*c),−(sqrt(d^2−2*a*d+4*b*c+a^2)*((b*d+a*b)*tr22^2+(−d^2−a*d)*tr21*tr22+((−b*d−a*b)*tr12+(d^2+a*d)*tr11)*tr21)+(b*d^2+2*b^2*c+a^2*b)*tr22^2+((−2*b*c−a^2)*d−d^3)*tr21*tr22+((b*d^2+2*b^2*c+a^2*b)*tr12+((−2*b*c−a^2)*d−d^3)*tr11)*tr21)/(2*a*d−2*b*c)],[(sqrt(d^2−2*a*d+4*b*c+a^2)*((a*d+a^2)*tr12*tr22+(−c*d−a*c)*tr12*tr21+(−a*d−a^2)*tr11*tr12+(c*d+a*c)*tr11^2)+(a*d^2+2*a*b*c+a^3)*tr12*tr22+(−c*d^2−2*b*c^2−a^2*c)*tr12*tr21+(a*d^2+2*a*b*c+a^3)*tr11*tr12+(−c*d^2−2*b*c^2−a^2*c)*tr11^2)/(2*a*d−2*b*c),(sqrt(d^2−2*a*d+4*b*c+a^2)*((a*d+a^2)*tr22^2+(−c*d−a*c)*tr21*tr22+((−a*d−a^2)*tr12+(c*d+a*c)*tr11)*tr21)+(a*d^2+2*a*b*c+a^3)*tr22^2+(−c*d^2−2*b*c^2−a^2*c)*tr21*tr22+((a*d^2+2*a*b*c+a^3)*tr12+(−c*d^2−2*b*c^2−a^2*c)*tr11)*tr21)/(2*a*d−2*b*c)])
Edit:
When I do this:
solve(HUGE = matrix([0,0],[0,0]),[tr11,tr12,tr21,tr11]);
maxima returns:
[]
I also tried:
solve([
−(sqrt(d^2−2*a*d+4*b*c+a^2)*((b*d+a*b)*tr12*tr22+(−d^2−a*d)*tr12*tr21+(−b*d−a*b)*tr11*tr12+(d^2+a*d)*tr11^2)+(b*d^2+2*b^2*c+a^2*b)*tr12*tr22+((−2*b*c−a^2)*d−d^3)*tr12*tr21+(b*d^2+2*b^2*c+a^2*b)*tr11*tr12+((−2*b*c−a^2)*d−d^3)*tr11^2+2*a^2*d−2*a*b*c)/(2*a*d−2*b*c)=0,
−(sqrt(d^2−2*a*d+4*b*c+a^2)*((b*d+a*b)*tr22^2+(−d^2−a*d)*tr21*tr22+((−b*d−a*b)*tr12+(d^2+a*d)*tr11)*tr21)+(b*d^2+2*b^2*c+a^2*b)*tr22^2+((−2*b*c−a^2)*d−d^3)*tr21*tr22+((b*d^2+2*b^2*c+a^2*b)*tr12+((−2*b*c−a^2)*d−d^3)*tr11)*tr21+2*a*c*d−2*b*c^2)/(2*a*d−2*b*c)=0,
(sqrt(d^2−2*a*d+4*b*c+a^2)*((a*d+a^2)*tr12*tr22+(−c*d−a*c)*tr12*tr21+(−a*d−a^2)*tr11*tr12+(c*d+a*c)*tr11^2)+(a*d^2+2*a*b*c+a^3)*tr12*tr22+(−c*d^2−2*b*c^2−a^2*c)*tr12*tr21+(a*d^2+2*a*b*c+a^3)*tr11*tr12+(−c*d^2−2*b*c^2−a^2*c)*tr11^2−2*a*b*d+2*b^2*c)/(2*a*d−2*b*c)=0,
(sqrt(d^2−2*a*d+4*b*c+a^2)*((a*d+a^2)*tr22^2+(−c*d−a*c)*tr21*tr22+((−a*d−a^2)*tr12+(c*d+a*c)*tr11)*tr21)+(a*d^2+2*a*b*c+a^3)*tr22^2+(−c*d^2−2*b*c^2−a^2*c)*tr21*tr22+((a*d^2+2*a*b*c+a^3)*tr12+(−c*d^2−2*b*c^2−a^2*c)*tr11)*tr21−2*a*d^2+2*b*c*d)/(2*a*d−2*b*c)=0
],[tr11,tr12,tr21,tr22]);
which results in an error:
Polynomial quotient is not exact
-- an error. To debug this try: debugmode(true);
I see your equations have sqrt in them. Try the to_poly_solve package for that. i.e. load(to_poly_solve); and then to_poly_solve([HUGE[1,1] = 0, HUGE[1,2] = 0, HUGE[2,1] = 0, HUGE[2,2] = 0], [tr11, tr12, tr21, tr22]);
When I try that, I get several messy expressions as a result. I didn't check to see if they are correct solutions. Good luck, have fun, let us know how it goes.