Actual Mathomatic output from the demo 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—> clear all
1—> ; Some symbolic differentiation examples follow.
1—> 
1—> ; Take the derivative of the absolute value function:
1—> |x|

          1
#1: (x^2)^-
          2

1—> derivative
Differentiating with respect to (x) and simplifying...

        x
#2: ---------
           1
    ((x^2)^-)
           2

2—> 
2—> ; Take the derivative of an algebraic fraction:
2—> (2+3x)/(4+5x)

    (2 + (3·x))
#3: -----------
    (4 + (5·x))

3—> derivative
Differentiating with respect to (x) and simplifying...

           2
#4: ---------------
    ((4 + (5·x))^2)

4—> 
4—> ; A Taylor series demonstration:
4—> y=x_new^n

#5: y = x_new^n

5—> taylor x_new 1 x_old ; build the (nth root of y) iterative approximation formula
Computing the Taylor series of the RHS and simplifying...
1 derivative applied.

#6: y = (x_old^n) + (n·(x_old^(n − 1))·x_new) − (n·(x_old^n))

6—> solve verify x_new ; solve for the output variable, verifying the result

             (y − (x_old^n))
#6: x_new = (--------------- + 1)·x_old
              ((x_old^n)·n)

Solution verified.
6—> simplify ; convergent nth root approximation formula:

                        y
                   (--------- − 1)
                    (x_old^n)
#6: x_new = x_old·(--------------- + 1)
                          n

6—> replace x_old x_new with x ; make x_old (input) and x_new (output) the same

              y
           (----- − 1)
            (x^n)
#6: x = x·(----------- + 1)
                n

6—> x ; make sure the formula was correct by solving for x
Removing possible solution: "x = 0".

          1
#6: x = y^-
          n

6—> 
6—> ; Another Taylor series demo:
6—> e^x ; enter the exponential function

#7: e#^x

7—> taylor x 10 0 ; generate a 10th order taylor series of the exponential function
Computing the Taylor series and simplifying...
10 derivatives applied.

            (x^2)   (x^3)   (x^4)   (x^5)   (x^6)   (x^7)   (x^8)   (x^9)    (x^10)
#8: 1 + x + ----- + ----- + ----- + ----- + ----- + ----- + ----- + ------ + -------
              2       6      24      120     720    5040    40320   362880   3628800

8—> laplace x ; do a Laplace transform on it

    1     1       1       1       1       1       1       1       1       1        1
#9: - + ----- + ----- + ----- + ----- + ----- + ----- + ----- + ----- + ------ + ------
    x   (x^2)   (x^3)   (x^4)   (x^5)   (x^6)   (x^7)   (x^8)   (x^9)   (x^10)   (x^11)

9—> simplify ; show the structure of the result

                                                      1
                                                 (1 + -)
                                                      x
                                            (1 + -------)
                                                    x
                                       (1 + -------------)
                                                  x
                                  (1 + -------------------)
                                                x
                             (1 + -------------------------)
                                              x
                        (1 + -------------------------------)
                                            x
                   (1 + -------------------------------------)
                                          x
              (1 + -------------------------------------------)
                                        x
         (1 + -------------------------------------------------)
                                      x
    (1 + -------------------------------------------------------)
                                    x
#9: -------------------------------------------------------------
                                  x

9—> laplace inverse x ; undo the Laplace transform

             (x^2)   (x^3)   (x^4)   (x^5)   (x^6)   (x^7)   (x^8)   (x^9)    (x^10)
#10: 1 + x + ----- + ----- + ----- + ----- + ----- + ----- + ----- + ------ + -------
               2       6      24      120     720    5040    40320   362880   3628800

10—> compare with 8 ; check the result
Comparing #8 with #10...
Expressions are identical.
Finished reading file "demo.in".
10—> 
End of input.