Actual Mathomatic output from the poly script

Mathomatic version 15.1.4 (www.mathomatic.org)
Copyright (C) 1987-2010 George Gesslein II.
100 equation spaces available, 1920 kilobytes per equation space.
HTML color mode enabled; disable with the -c option or "set no color".
1—> ; Combine 3 quadratic polynomial equations with 3 unknown coefficients (a, b, c).
1—> ; Solve for variables (a), (b), and (c).
1—> 
1—> clear all ; restart Mathomatic
1—> ; enter all 3 equations:
1—> y1=a+b*x1+c*x1^2

#1: y1 = a + (b·x1) + (c·(x1^2))

1—> y2=a+b*x2+c*x2^2

#2: y2 = a + (b·x2) + (c·(x2^2))

2—> y3=a+b*x3+c*x3^2

#3: y3 = a + (b·x3) + (c·(x3^2))

3—> 2 ; select equation number 2 as the current equation

#2: y2 = a + (b·x2) + (c·(x2^2))

2—> eliminate a ; eliminate variable (a) from the current equation
Solving equation #1 for (a) and substituting into the current equation...

#2: y2 = (b·x2) − (x1·(b + (c·x1))) + y1 + (c·(x2^2))

2—> 3 ; select equation number 3

#3: y3 = a + (b·x3) + (c·(x3^2))

3—> eliminate a b ; eliminate variables (a) and then (b) from the current equation
Substituting the RHS of equation #1 into the current equation for variable (a)...
Solving equation #2 for (b) and substituting into the current equation...

         (y1 − y2 + (c·((x2^2) − (x1^2))))·x3        (y1 − y2 + (c·((x2^2) − (x1^2))))
#3: y3 = ------------------------------------ − (x1·(--------------------------------- + (c·x1))) + y1 + (c·(x3^2))
                      (x1 − x2)                                  (x1 − x2)

3—> c ; solve and find (c)

               ((y2·(x1 − x3)) + (y1·(x3 − x2)) − (y3·(x1 − x2)))
#3: c = -----------------------------------------------------------------
        ((x1·((x2^2) + (x1·(x3 − x2)))) − (x3·((x2^2) + (x3·(x1 − x2)))))

3—> simplify

         (y1 − y2)   (y3 − y2)
        (--------- + ---------)
         (x2 − x1)   (x3 − x2)
#3: c = -----------------------
               (x3 − x1)

3—> 2 ; select equation number 2 again

        (y1 − y2 + (c·((x2^2) − (x1^2))))
#2: b = ---------------------------------
                    (x1 − x2)

2—> eliminate c using 3 ; find (b) by combining equation numbers 2 and 3
Substituting the RHS of equation #3 into the current equation for variable (c)...

                    (y1 − y2)   (y3 − y2)
                   (--------- + ---------)·((x2^2) − (x1^2))
                    (x2 − x1)   (x3 − x2)
        (y1 − y2 + -----------------------------------------)
                                   (x3 − x1)
#2: b = -----------------------------------------------------
                              (x1 − x2)

2—> simplify

        (((x3^2)·(y1 − y2)) + ((x1^2)·(y2 − y3)) + ((x2^2)·(y3 − y1)))
#2: b = --------------------------------------------------------------
                       ((x2 − x1)·(x3 − x1)·(x2 − x3))

2—> 1 ; select equation number 1

#1: a = -((x1·(b + (c·x1))) − y1)

1—> eliminate c using 3 b using 2 ; find (a)
Substituting the RHS of equation #3 into the current equation for variable (c)...
Substituting the RHS of equation #2 into the current equation for variable (b)...

                                                                                 (y1 − y2)   (y3 − y2)
                                                                                (--------- + ---------)·x1
               (((x3^2)·(y1 − y2)) + ((x1^2)·(y2 − y3)) + ((x2^2)·(y3 − y1)))    (x2 − x1)   (x3 − x2)
#1: a = -((x1·(-------------------------------------------------------------- + --------------------------)) − y1)
                              ((x2 − x1)·(x3 − x1)·(x2 − x3))                           (x3 − x1)

1—> 
1—> simplify fraction all ; list all solutions, converting to simple fractions

        (((x1^2)·((y2·x3) − (y3·x2))) + (x1·(((x2^2)·y3) − ((x3^2)·y2))) + (y1·(((x3^2)·x2) − (x3·(x2^2)))))
#1: a = ----------------------------------------------------------------------------------------------------
                                          ((x2 − x1)·(x3 − x1)·(x3 − x2))


        (((x3^2)·(y1 − y2)) + ((x1^2)·(y2 − y3)) + ((x2^2)·(y3 − y1)))
#2: b = --------------------------------------------------------------
                       ((x2 − x1)·(x3 − x1)·(x2 − x3))


        ((x3·(y1 − y2)) + (x2·(y3 − y1)) + (x1·(y2 − y3)))
#3: c = --------------------------------------------------
                 ((x2 − x1)·(x3 − x1)·(x3 − x2))

Finished reading file "poly.in".
1—> 
End of input.