Revision history [back]

Use the method expand with a specific alphabet. (If the default alphabet is not wanted.) For instance:

e = SymmetricFunctions( QQ ).e()
alphabet = 'a,b,c,d'

print "The elementary symmetric functions in the alphabet %s are:" % alphabet
for k in [0,1,2,3,4]:
    print e( [k] ).expand( 4, alphabet=alphabet )

print "\ne(3,2,2,1) is:\n%s" % e( [3,2,2,1] ).expand( 4, alphabet=alphabet ).factor()

And we get:

The elementary symmetric functions in the alphabet a,b,c,d are:
1
a + b + c + d
a*b + a*c + b*c + a*d + b*d + c*d
a*b*c + a*b*d + a*c*d + b*c*d
a*b*c*d

e(3,2,2,1) is:
(a + b + c + d) * (a*b + a*c + b*c + a*d + b*d + c*d)^2 * (a*b*c + a*b*d + a*c*d + b*c*d)