symmetric polynomial of multi-variables

I understood Power sum symmetric polynomial and Fundamental theorem of symmetric polynomials

Here the symmetric function would be of the form F(x1,x2,x3,….) and thus using those theorems we can decompose into power sum symmetric polynomial or Elementary symmetric polynomials

But now here i have symmetric function of F( (x1,y1,z1) ,(x2,y2,z2),(x3,y3,z3),….)

F is symmetric here it means tuples can interchanged but not xi,yi,zi to zi,xi,yi

How can i apply the above theorems for functions of above type?

submitted by /u/_sathya
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Nevin Manimala

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