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Domain of set of vectors that are images of sets under mappings
solvelib::VectorImageSet()
solvelib::VectorImageSet(v, x, S)
Dom::ImageSet(v, [x1, …], [S1, …])
solvelib::VectorImageSet is the domain of all sets of vectors of complex numbers that can be written as the set of all values taken on by some mapping, i.e., sets of the form for some complex-valued functions f_{j} and some sets S_{1}, …, S_{n} of complex numbers.
Sets of this type are used by solve to express solutions of systems of equations like .
solvelib::VectorImageSet(v, x, S) represents the set of all vectors that can be obtained by substituting some element of S for x in the vector v.
solvelib::VectorImageSet(v, [x1, ...], [S1, ...]) represents the set of all values that can be obtained by substituting, for each i, the identifier x_{i} by some element of S_{i} in the vector v.
The user never needs to call solvelib::VectorImageSet directly. Instead, Dom::ImageSet should be used; it will automatically create a vector image set if its first argument is a list or matrix. The entries and methods of the domain solvelib::VectorImageSet are the same as those of Dom::ImageSet, and may be found on that help page.
We create a set of two-dimensional vectors:
S:= Dom::ImageSet([k*PI, k*I*PI], k, Z_)
Since this is a set of vectors, a solvelib::VectorImageSet is created automatically:
type(S)
Set-theoretic operations (union, intersection, set difference) may be applied to S:
S intersect {[0, 0], [1, 1]}, S minus S
delete S: