Twisted de Rham complex for toric Calabi-Yau complete intersections and flat $F$-manifold structures

We describe the primitive middle-dimensional cohomology $\mathbb{H}$ of a compact simplicial toric complete intersection variety in terms of a twisted de Rham complex. Then this enables us to construct a concrete algorithm of formal flat $F$-manifold structures on $\mathbb{H}$ in the Calabi-Yau case by using the techniques of \cite{Park23}, which turn the twisted de Rham complex into a quantization dGBV (differential Gerstenhaber-Batalin-Vilkovisky) algebra and seek for an algorithmic solution to an associated \textit{weak primitive form.}