  In 1982 V\'{i}ctor Neumann-Lara introduced the dichromatic number of a
digraph $D$ as the smallest integer $k$ such that the vertices $V$ of $D$ can
be colored with $k$ colors and each color class induces an acyclic digraph.
Later a flow theory for the dichromatic number transferring Tutte's theory of
nowhere-zero flows (NZ-flows) from classic graph colorings has been developed
by Hochst\"attler. The purpose of this paper is to pursue this analogy by
introducing a new definition of algebraic Neumann-Lara-flows (NL-flows) and a
closed formula for their polynomial. Furthermore we generalize the Equivalence
Theorem for nowhere-zero flows to NL-flows in the setting of regular oriented
matroids. Finally we discuss computational aspects of computing the NL-flow
polynomial for orientations of complete digraphs and obtain a closed formula in
the acyclic case.
