  ZX-calculus is a strict mathematical formalism for graphical quantum
computing which is based on the field of complex numbers. In this paper, we
extend its power by generalising ZX-calculus to such an extent that it is
universal both in an arbitrary commutative ring and in an arbitrary commutative
semiring. Furthermore, we follow the framework of arXiv:2007.13739 to prove
respectively that the proposed ZX-calculus over an arbitrary commutative ring
(semiring) is complete for matrices over the same ring (semiring), via a normal
form inspired from matrix elementary operations such as row addition and row
multiplication. This work could lead to various applications including doing
elementary number theory in string diagrams.
