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The Maxima on-line user's manual

Algebra Calculator

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Ratexpand Calculator

Ratexpand

Function: ratexpand (<expr>) -- Option variable: ratexpand Expands <expr> by multiplying out products of sums and exponentiated sums, combining fractions over a common denominator, cancelling the greatest common divisor of the numerator and denominator, then splitting the numerator (if a sum) into its respective terms divided by the denominator.

The return value of ratexpand is a general expression, even if <expr> is a canonical rational expression (CRE).

The switch ratexpand if true will cause CRE expressions to be fully expanded when they are converted back to general form or displayed, while if it is false then they will be put into a recursive form. See also ratsimp.

When ratdenomdivide is true, ratexpand expands a ratio in which the numerator is a sum into a sum of ratios, all having a common denominator. Otherwise, ratexpand collapses a sum of ratios into a single ratio, the numerator of which is the sum of the numerators of each ratio.

When keepfloat is true, prevents floating point numbers from being rationalized when expressions which contain them are converted to canonical rational expression (CRE) form.

Examples:

          (%i1) ratexpand ((2*x - 3*y)^3);
                               3         2       2        3
          (%o1)          - 27 y  + 54 x y  - 36 x  y + 8 x
          (%i2) expr: (x - 1)/(x + 1)^2 + 1/(x - 1);
                                   x - 1       1
          (%o2)                   -------- + -----
                                         2   x - 1
                                  (x + 1)
          (%i3) expand (expr);
                              x              1           1
          (%o3)          ------------ - ------------ + -----
                          2              2             x - 1
                         x  + 2 x + 1   x  + 2 x + 1
          (%i4) ratexpand (expr);
                                  2
                               2 x                 2
          (%o4)           --------------- + ---------------
                           3    2            3    2
                          x  + x  - x - 1   x  + x  - x - 1

(%o1)                                true
(%i2) 

Ratexpand Example

Related Examples

ratexpand-ratsimp-solve

eq1: k = N*(1+z+s)^-T...

solve(eq1,N);

N=-(k*(z+1)^T * (z+s+...

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ratexpand

f: (x+y+z)^5;

ratexpand(f);

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ratexpand

eq1:(a+b)^3;

ratexpand(eq1);

Calculate

ratexpand

ratexpand ((2*x - 3*y...

expr: (x - 1)/(x + 1...

expand (expr);

Calculate

ratexpand

ratexpand((x+1)/(x**2...

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ratexpand((1-x**4)**3...

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ratexpand-ratsimp-solve

eq1: k = N*(1+z+s)^-T...

solve(eq1,N);

N=-(k*(z+1)^T * (z+s+...

Calculate

ratexpand-ratsimp

f:ratexpand((a+y1+x)^6);

ratsimp(f,a);

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((x1-v*t1)*(x2-v*t2)-...

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p : 5*(x+1)*(x+2)*(x+...

ratexpand((p/5)/(x^3));

p2(x) := (x+1)*(x+2)*...

Calculate