Can the star of a ray of a fan be computed in sage?

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Let p be a ray of a fan F in a lattice N. Let Np be the quotient lattice N / N.span(p). The star of p is the fan in Np defined by

Star(p) = {bar(sigma) | p <= sigma}

(This definition is taken from Definition 4.4 on page 55 of this paper. Is there an algorithm to compute Star(p) in sage? If so, what about the embedding morphism Star(p) --> F?