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  3  -5  1
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