This work describes an algorithm identifying the local coordinates of the Drinfel’d series and then proving that the algebra of polyzetas, denoted by \({\mathscr {Z}}\) , is graded. It uses equations bridging algebraic structures of polyzetas and yields two shuffle and quasi-shuffle ideals as kernels of the zeta polymorphism. These ideals are totally lexicographically ordered and are constituted by homogenous in weight polynomials. These are considered as confluent rewriting systems in which, the left side of each rewriting rule is the leading term of the associated homogenous polynomial and the right side is the irreducible terms form algebraic generators of \({\mathscr {Z}}\) .