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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:

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