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.
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:
There are also some inexact matches for
?? elem to see them.
(%o1) true (%i2)