# Chapter 15: Software # # The file "SymmetricPolynomials" has a function which implements the # algorithm in Theorem 15.1. # It requires that you list the variables in your symmetric polynomial. # first load the file: # > read SymmetricPolynomials; # # Here is p3 in terms of s1, s2 and s3: # > symmetric( u^3 + v^3 + w^3, [u,v,w] ); 3 s[1] - 3 s[1] s[2] + 3 s[3] # # Here is the discriminant Delta in four variables x1, x2, x3, x4 # written in terms of the elementary # symmetric polynomials: # > Delta := expand( (x1 - x2)^2*(x1 - x3)^2*(x1 - x4)^2*(x2 - x3)^2*(x2 - > x4)^2*(x3 - x4)^2 ): > symmetric( Delta, [x1,x2,x3,x4] ); 2 2 2 2 3 3 3 s[1] s[2] s[3] - 4 s[1] s[2] s[4] - 4 s[1] s[3] 3 4 2 3 2 + 18 s[1] s[2] s[3] s[4] - 27 s[1] s[4] - 4 s[2] s[3] 4 3 + 16 s[2] s[4] + 18 s[1] s[2] s[3] 2 2 2 - 80 s[1] s[2] s[3] s[4] - 6 s[1] s[3] s[4] 2 2 4 2 + 144 s[1] s[2] s[4] - 27 s[3] + 144 s[2] s[3] s[4] 2 2 2 3 - 128 s[2] s[4] - 192 s[1] s[3] s[4] + 256 s[4]