### The Maxima on-line user's manual

Algebra Calculator

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Function: radcan (<expr>) Simplifies <expr>, which can contain logs, exponentials, and radicals, by converting it into a form which is canonical over a large class of expressions and a given ordering of variables; that is, all functionally equivalent forms are mapped into a unique form. For a somewhat larger class of expressions, `radcan` produces a regular form. Two equivalent expressions in this class do not necessarily have the same appearance, but their difference can be simplified by `radcan` to zero.

For some expressions `radcan` is quite time consuming. This is the cost of exploring certain relationships among the components of the expression for simplifications based on factoring and partial-fraction expansions of exponents.

Examples:

```          (%i1) radcan((log(x+x^2)-log(x))^a/log(1+x)^(a/2));
a/2
(%o1)                            log(x + 1)```

```          (%i2) radcan((log(1+2*a^x+a^(2*x))/log(1+a^x)));
(%o2)                                  2```

```          (%i3) radcan((%e^x-1)/(1+%e^(x/2)));
x/2
(%o3)                              %e    - 1```

There are also some inexact matches for `radcan`. Try `?? radcan` to see them.

```(%o1)                                true
(%i2) ```

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