ele2pui SciMax Toolbox elementp

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elem

Maxima Function

Calling Sequence

elem (ele, sym, lvar)

Description

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.

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.

ele2pui SciMax Toolbox elementp