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The Maxima on-line user's manual

Algebra Calculator

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Elem Calculator

Elem

Function: elem (<ele>, <sym>, <lvar>) decomposes the symmetric polynomial <sym>, in the variables contained in the list <lvar>, in terms of the elementary symmetric functions given in the list <ele>. If the first element of <ele> 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 <ele>, formal values of the type <e1>, <e2>, 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.

elem ([], y, [x, y]);

On an alphabet of size 3 with <e1>, the first elementary symmetric function, with value 7, the symmetric polynomial in 3 variables whose contracted form (which here depends on only two of its variables) is <x^4-2*x*y> decomposes as follows in elementary symmetric functions:

          (%i1) elem ([3, 7], x^4 - 2*x*y, [x, y]);
          (%o1) 7 (e3 - 7 e2 + 7 (49 - e2)) + 21 e3

                                                   + (- 2 (49 - e2) - 2) e2
          (%i2) ratsimp (%);
                                        2
          (%o2)             28 e3 + 2 e2  - 198 e2 + 2401

Other functions for changing bases: comp2ele.

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

(%o1)                                true
(%i2) 

Elem Example

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elem-ratsimp

elem ([x,1/x,1-x,x/(x...

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elem-multi_elem

elem ([2,a,b], x*y+x+...

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elem ([], x, [x, y]);

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elem ([3], x*y*z, [x,...

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elem ([], x, [x, y]);

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elem ([a, b, c], (1+x...

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elem

elem ([a, b, c], (1+x...

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elem-ratsimp

elem ([2, x,1/x],e1, ...

ratsimp (%);

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