How to read a polynomial?

Polynomial are sums of monomial expression. Such a monomial expression is given by a coefficient and a vector. The length of the vector is the number of different indeterminates in this monomial; the first entry is the exponent of the first indeterminate, the second enrtry is the exponent of the second indeterminate and so on.
For example the polynomial p(x)= x5+3x2-5x+1 is written as 1 [5] 3 [2] -5 [1] 1[0]

The polynomial p(x,y,z)=x+ 1/4 x2 y -5 z will be written as 1 [1,0,0] 1/4 [2,1] -5 [0,0,1]

You see the '+', with which the monomial summands are connected, will be ommitted.