extractImageEquations(F, I, d)
extractImageEquations T
This method finds (approximate) implicit degree $d$ equations for the image of a variety, by numerical interpolation. The option AttemptZZ specifies whether to use the LLL algorithm to compute "short" equations over ZZ. The default value is false.
If a numerical interpolation table has already been computed, then to avoid repetitive calculation one may run this function with the interpolation table as input.
For example, we determine the defining quadrics of the twisted cubic, as follows.
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Here is how to do the same computation symbolically.
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We determine the $5$ Plücker quadrics defining the Grassmannian $Gr(3,5)$ of $P^2$'s in $P^4$, in the ambient space $P^9$.
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The option Threshold sets the threshold for rounding the interpolation matrix. If this option has value $n$, then the interpolation matrix will be rounded to $n$ decimal digits, after which LLL will be performed. The default value is $5$.
The object extractImageEquations is a method function with options.