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

Algebra Calculator

#### Pui

Function: pui (<L>, <sym>, <lvar>) decomposes the symmetric polynomial <sym>, in the variables in the list <lvar>, in terms of the power functions in the list <L>. If the first element of <L> is given, it will be the size of the alphabet, otherwise the size will be the degree of the polynomial <sym>. If values are missing in the list <L>, formal values of the type <p1>, <p2> , etc. will be added. The polynomial <sym> may be given in three different forms: contracted (`elem` should then be 1, its default value), partitioned (`elem` should be 3), or extended (i.e. the entire polynomial, and `elem` should then be 2). The function `pui` is used in the same way.

```          (%i1) pui;
(%o1)                           1
(%i2) pui ([3, a, b], u*x*y*z, [x, y, z]);
2
a (a  - b) u   (a b - p3) u
(%o2)              ------------ - ------------
6              3
(%i3) ratsimp (%);
3
(2 p3 - 3 a b + a ) u
(%o3)                 ---------------------
6
Other functions for changing bases: `comp2ele`.```

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

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

### Related Examples

? pui;

Calculate

##### pui-ratsimp

pui;

pui ([3, a, b], u*x*...

ratsimp (%);

Calculate

? pui;

Calculate

##### pui-ratsimp

pui;

pui ([3, a, b], u*x*...

ratsimp (%);

Calculate