; Combine 4 simultaneous linear equations with 4 unknowns (x1, x2, x3, x4).
; Solve for all 4 unknowns using the eliminate, solve, and simplify commands.

; Keep this to test simplification in Mathomatic when recursion is added to the GCD routines.
; Currently Mathomatic is unable to completely simplify all of the resulting equations.
; By using the simplify command immediately after some eliminate commands,
; equation number 4 solved for x4 is completely simplified.
;
; The rest may be easily simplifiable when polynomial GCD works recursively,
; so that it is multivariate.

clear all ; restarts Mathomatic
; The next four lines enter all of the equations into Mathomatic
b1 = a11*x1+a12*x2+a13*x3+a14*x4
b2 = a21*x1+a22*x2+a23*x3+a24*x4
b3 = a31*x1+a32*x2+a33*x3+a34*x4
b4 = a41*x1+a42*x2+a43*x3+a44*x4
2 ; select equation #2
eliminate x1 ; eliminate x1 variable from eq#2
3 ; select equation #3
eliminate x1 x2 ; eliminate x1 x2 from eq#3
4 ; select equation #4
eliminate x1 x2 x3 ; eliminate x1 x2 x3 from eq#4
simplify all
solve verifiable x4 ; solve for x4
3 ; select equation #3
eliminate x4 using 4; find x3
2 ; select equation #2
eliminate x4 using 4, x3 using 3; find x2
1 ; select equation #1
eliminate x4 using 4, x3 using 3, x2 using 2; find x1
simplify all