数式処理

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  GiNaC
  • 
    C++ library だが ginsh を使えばすぐに使える
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    行列演算を記号的に出来る (lsolve で線形方程式の解法、 determinant で行列式、 inverse で逆行列、 etc.)

    
    
    $ ginsh
    
    ginsh - GiNaC Interactive Shell (GiNaC V1.0.3)
    
      __,  _______  Copyright (C) 1999-2001 Johannes Gutenberg University Mainz,
    
     (__) *       | Germany.  This is free software with ABSOLUTELY NO WARRANTY.
    
      ._) i N a C | You are welcome to redistribute it under certain conditions.<ーーーーーーーーーーーー-' For details type `warranty;'.
    Type ?? for a list of help topics.
    
    > lsolve ({a*x＋b*y == c, d*x＋e*y == f}, {x, y});
    
    {x==(-c*e＋f*b)*(d*b-a*e)^(-1),y==(c*d-f*a)*(d*b-a*e)^(-1)}
    
    > M = [ [a, b, c], [d, e, f], [g, h, i]];
    
    [[a,b,c],[d,e,f],[g,h,i]]
    
    > determinant(M);
    
    a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e
    
    > inverse(M);
    
    [[(e*i-f*h)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1),
    
    (a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1)*(-b*i＋c*h),
    
    (-c*e＋b*f)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1)],
    
    [(-d*i＋f*g)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1),
    
    (-c*g＋a*i)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1),
    
    (-f*a＋c*d)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1)],
    
    [(d*h-g*e)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1),
    
    (-h*a＋b*g)*(a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1),
    
    (a*e*i-b*d*i-f*h*a＋b*f*g＋c*d*h-c*g*e)^(-1)*(a*e-b*d)]]