含有章节索引的中文 文章模板

::-- hoxide [2005-07-30 12:36:55]

1. Mathomatic

1.1. 简介

• 是 Mathomatic 不是 Mathematica , 公元2005年7月30日, 在更新 cygwin 的时候偶然发现的. Mathematica 是一个轻便的通用计算机代数系统 CAS (Computer Algebra System), 它是用C写成的, 使用 GNU LGPL license.

1.2. 官方页面

http://mathomatic.orgserve.de/math/

1.3. 文档

1.4. 例子

1.4.1. 一些简单的例子

Mathomatic Version 12.3.2 (www.mathomatic.com)
Copyright (C) 1987-2005 George Gesslein II.
40 equation spaces allocated (total size is 9600 KBytes).

1-> ; Simplification tests.
1-> 
1-> clear all
1-> t=2*(x^2 - y^2)^6 - (x^2 - y^2)^5*(2 x^2 - 3)

#1: t = (2*(((x^2) - (y^2))^6)) - ((((x^2) - (y^2))^5)*((2*(x^2)) - 3))

1-> simplify

#1: t = (((y^2) - (x^2))^5)*((2*(y^2)) - 3)

1-> t=a^3/((a-b)*(a-c)) + b^3/((b-c)*(b-a)) + c^3/((c-a)*(c-b))

              (a^3)               (b^3)               (c^3)
#2: t = ----------------- + ----------------- + -----------------
        ((a - b)*(a - c))   ((b - c)*(b - a))   ((c - a)*(c - b))

2-> simplify

#2: t = a + b + c

2-> t=(x^6+a^6)*(x+1)/((x^6+a^6)*(x^2-a^2)+a^2*x^2*(x^4-a^4))+a^2*x^2*(x+1)/(x^6-a^6-a^2*x^2*(x^2-a^2))

                              ((x^6) + (a^6))*(x + 1)                                       (a^2)*(x^2)*(x + 1)
#3: t = ------------------------------------------------------------------- + -----------------------------------------------
        ((((x^6) + (a^6))*((x^2) - (a^2))) + ((a^2)*(x^2)*((x^4) - (a^4))))   ((x^6) - (a^6) - ((a^2)*(x^2)*((x^2) - (a^2))))

3-> simplify
Found polynomial Greatest Common Divisor.  Division simplified.
Found polynomial Greatest Common Divisor.  Division simplified.

            (x + 1)
#3: t = ---------------
        ((x^2) - (a^2))

3-> t=((a*n + b*m)^2 + (a*m - b*n)^2) / ((a*p + b*q)^2 + (a*q - b*p)^2)

        ((((a*n) + (b*m))^2) + (((a*m) - (b*n))^2))
#4: t = -------------------------------------------
        ((((a*p) + (b*q))^2) + (((a*q) - (b*p))^2))

4-> simplify

        ((n^2) + (m^2))
#4: t = ---------------
        ((p^2) + (q^2))

4-> y=((p*x^2+(k-s)*x+r)^2-(p*x^2+(k+s)*x+r)^2)/((p*x^2+(k+t)*x+r)^2-(p*x^2+(k-t)*x+r)^2)

        ((((p*(x^2)) + ((k - s)*x) + r)^2) - (((p*(x^2)) + ((k + s)*x) + r)^2))
#5: y = -----------------------------------------------------------------------
        ((((p*(x^2)) + ((k + t)*x) + r)^2) - (((p*(x^2)) + ((k - t)*x) + r)^2))

5-> simplify

        -1*s
#5: y = ----
         t

5-> t=(1 - (1-(y+1)/(x+y+1)) / (1-x/(x+y+1))) / ((y+1)^2 - x / (1+x/(y-x+1))*(x*(y+1)/(y-x+1) - x))

                          (y + 1)
                   (1 - -----------)
                        (x + y + 1)
              (1 - -----------------)
                             x
                   (1 - -----------)
                        (x + y + 1)
#6: t = -----------------------------------
                           x*(y + 1)
                       x*(----------- - x)
                          (y - x + 1)
        (((y + 1)^2) - -------------------)
                                  x
                        (1 + -----------)
                             (y - x + 1)

6-> simplify
Found polynomial Greatest Common Divisor.  Division simplified.

                            1
#6: t = -----------------------------------------
        (1 + (y^2) + (2*y) + (x*(y + 1)) + (x^2))

6-> y=((2*((x*(x + (((x^2) - 1)^(1/2)))) - 1)) + 1)/((2*x*((x^2) - 1)) + ((((x^2) - 1)^(1/2))*((2*(x^2)) - 1)))

                                         1
               ((2*((x*(x + (((x^2) - 1)^-))) - 1)) + 1)
                                         2
#7: y = -------------------------------------------------------
                                           1
        ((2*x*((x^2) - 1)) + ((((x^2) - 1)^-)*((2*(x^2)) - 1)))
                                           2

7-> simplify

               1
#7: y = ---------------
                     1
        (((x^2) - 1)^-)
                     2


Thank you for using Mathomatic!

1.5. 讨论

• 个人感觉非常好用, 比 Maxima 简单. --- Hoxide