Maxima 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: comp2ele
.