source: CGBLisp/examples/billiard1.lisp@ 1

;; Triangular billiard orbits (xi,yi) reflecting off of 3 circles
;; with centers (ui,vi) and radii ri
;;(trace grobner-gcd)
(setf *colored-poly-debug* t)
(string-grobner-system
"[-Y0^2-X0^2+R0^2,-Y1^2-X1^2+2*X1+R1^2-1,-Y2^2+2*V2*Y2-X2^2+2*U2*X2-V2^2-U2^2+R2^2,-Y1^2+2*Y0*Y1-Y0^2-X1^2+2*X0*X1-X0^2+L0^2,-Y2^2+2*Y1*Y2-Y1^2-X2^2+2*X1*X2-X1^2+L1^2,-Y2^2+2*Y0*Y2-Y0^2-X2^2+2*X0*X2-X0^2+L2^2,SIN0^2+COS0^2-1,-Y0^2-X0^2+R0^2,-Y1^2+2*Y0*Y1-Y0^2-X1^2+2*X0*X1-X0^2+L0^2,Y0*Y1-Y0^2+X0*X1-X0^2+COS0*L0*R0,-X0*Y1+X1*Y0+L0*R0*SIN0,SIN1^2+COS1^2-1,-Y1^2-X1^2+2*X1+R1^2-1,-Y2^2+2*Y1*Y2-Y1^2-X2^2+2*X1*X2-X1^2+L1^2,Y1*Y2-Y1^2+X1*X2-X2-X1^2+X1+COS1*L1*R1,-X1*Y2+Y2+X2*Y1-Y1+L1*R1*SIN1,SIN2^2+COS2^2-1,-Y2^2+2*V2*Y2-X2^2+2*U2*X2-V2^2-U2^2+R2^2,-Y2^2+2*Y0*Y2-Y0^2-X2^2+2*X0*X2-X0^2+L2^2,-Y2^2+Y0*Y2+V2*Y2-V2*Y0-X2^2+X0*X2+U2*X2-U2*X0+COS2*L2*R2,X0*Y2-U2*Y2-X2*Y0+U2*Y0+V2*X2-V2*X0+L2*R2*SIN2,SIN0^2+COS0^2-1,-Y2^2+2*Y0*Y2-Y0^2-X2^2+2*X0*X2-X0^2+L2^2,-Y0^2-X0^2+R0^2,Y0*Y2-Y0^2+X0*X2-X0^2+COS0*L2*R0,X0*Y2-X2*Y0+L2*R0*SIN0,SIN1^2+COS1^2-1,-Y1^2+2*Y0*Y1-Y0^2-X1^2+2*X0*X1-X0^2+L0^2,-Y1^2-X1^2+2*X1+R1^2-1,-Y1^2+Y0*Y1-X1^2+X0*X1+X1-X0+COS1*L0*R1,-X0*Y1+Y1+X1*Y0-Y0+L0*R1*SIN1,SIN2^2+COS2^2-1,-Y2^2+2*Y1*Y2-Y1^2-X2^2+2*X1*X2-X1^2+L1^2,-Y2^2+2*V2*Y2-X2^2+2*U2*X2-V2^2-U2^2+R2^2,-Y2^2+Y1*Y2+V2*Y2-V2*Y1-X2^2+X1*X2+U2*X2-U2*X1+COS2*L1*R2,-X1*Y2+U2*Y2+X2*Y1-U2*Y1-V2*X2+V2*X1+L1*R2*SIN2]"
'(COS0 SIN0 COS1 SIN1 COS2 SIN2 X0 Y0 X1 Y1 x2 y2 L0 L1 l2) ;variables
'(r0 r1 r2 u2 v2) ;parameters
:main-order #'lex>
:parameter-order #'lex>
:cover '(("[]" "[]"))
)