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The Maxima on-line user's manual

Algebra Calculator

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Fullratsimp Calculator

Fullratsimp

Function: fullratsimp (<expr>) fullratsimp repeatedly applies ratsimp followed by non-rational simplification to an expression until no further change occurs, and returns the result.

m: 4;
e0: ((m+1)*x+(m-1)*y)/(2*m);
e1: ((m-1)*x+(m+1)*y)/(2*m);
fullratsimp(subst(e0, y, e1));
 solve((a-r)*(d-r)-b*c,r);
a0: 0;
a1: 1;
a: 49/64;
b: 15/64;
c: 3/8;
d: 5/8;
sqrt(a^2+d^2-2*a*d+4*b*c);
a1*b/sqrt(a^2+d^2-2*a*d+4*b*c);

When non-rational expressions are involved, one call to ratsimp followed as is usual by non-rational ("general") simplification may not be sufficient to return a simplified result. Sometimes, more than one such call may be necessary. fullratsimp makes this process convenient.

fullratsimp (<expr>, <x_1>, ..., <x_n>) takes one or more arguments similar to ratsimp and rat.

Example:

          (%i1) expr: (x^(a/2) + 1)^2*(x^(a/2) - 1)^2/(x^a - 1);
                                 a/2     2   a/2     2
                               (x    - 1)  (x    + 1)
          (%o1)                -----------------------
                                        a
                                       x  - 1
          (%i2) ratsimp (expr);
                                    2 a      a
                                   x    - 2 x  + 1
          (%o2)                    ---------------
                                        a
                                       x  - 1
          (%i3) fullratsimp (expr);
                                        a
          (%o3)                        x  - 1
          (%i4) rat (expr);
                                 a/2 4       a/2 2
                               (x   )  - 2 (x   )  + 1
          (%o4)/R/             -----------------------
                                        a
                                       x  - 1

(%o1)                                true
(%i2) 

Fullratsimp Example

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