plucker L
plucker p
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More generally, if the input is the ideal of a subvariety $Y\subset\mathbb{G}(k,\mathbb{P}^n)$, then the method returns the ideal of the variety $W\subset\mathbb{P}^n$ swept out by the linear spaces corresponding to points of $Y$. As an example, we now compute a surface scroll $W\subset\mathbb{P}^4$ over an elliptic curve $Y\subset\mathbb{G}(1,\mathbb{P}^4)$.
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In this example, we can recover the subvariety $Y\subset\mathbb{G}(k,\mathbb{P}^n)$ by computing the Fano variety of $k$-planes contained in $W$.
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Warning: Notice that, by default, the computation is done on a randomly chosen affine chart on the Grassmannian. To change this behavior, you can use the AffineChartGrass option.
The object plucker is a method function with options.