  ZX-calculus is a graphical language for quantum computing which is complete
in the sense that calculation in matrices can be done in a purely diagrammatic
way. However, all previous universally complete axiomatisations of ZX-calculus
have included at least one rule involving trigonometric functions such as sin
and cos which makes it difficult for application purpose. In this paper we give
an algebraic complete axiomatisation of ZX-calculus instead such that there are
only ring operations involved for phases. With this algebraic axiomatisation of
ZX-calculus, we are able to establish for the first time a simple translation
of diagrams from another graphical language called ZH-calculus and to derive
all the ZX-translated rules of ZH-calculus. As a consequence, we have a great
benefit that all techniques obtained in ZH-calculus can be transplanted to
ZX-calculus, which can't be obtained by just using the completeness of
ZX-calculus.
