Extend ideal interface (#1731)

* Extend ideal interface

* Update src/Ideal.jl

Co-authored-by: Max Horn <[email protected]>

* Update according to comment by Max

Before, it might have happened that the command `R * ZZRingElem(2)` fails while `R * big(2)` succeeds.

* Apply suggestions from code review

Max: "the advantage is that if some ring type wants to implement say ideal(R::MyRing, n::Int) in a special optimized fashion that avoids constructing R(n), then R*2 would benefit from that"

Co-authored-by: Max Horn <[email protected]>

* Use `RingElem` instead of `Any`

Previously, there was a possibility of an infinite recursion if the base functions were not implemented. Also, writing `R(x)` when `x` is a vector is problematic, it might have unexpected results.

* Change API / base method

* Update src/Ideal.jl

* Allow ideal(R, x, y, z)

This is already allowed for Hecke ideals.
For consistency, we allow this already in AbstractAlgebra.

* Forbid ideal(R) for creating empty ideal

---------

Co-authored-by: Max Horn <[email protected]>

src/Ideal.jl

@@ -4,17 +4,40 @@
 #
 ###############################################################################
 
-function ideal
+# We assume that the function
+#   ideal(R::T, xs::Vector{U})
+# with U === elem_type(T) is implemented by anyone implementing ideals
+# for AbstractAlgebra rings.
+# The functions in this file extend the interface for `ideal`.
+
+# the following helper enables things like `ideal(R, [])` or `ideal(R, [1])`
+# the type check ensures we don't run into an infinite recursion
+function ideal(R::Ring, xs::AbstractVector{T}) where T<:RingElement
+  xs isa Vector{elem_type(R)} && error("ideals unsupported for ring $R")
+  return ideal(R, elem_type(R)[R(x) for x in xs])
 end
 
-function *(x::RingElement, R::Ring)
-  return ideal(R, x)
+function ideal(R::Ring, x, y...)
+  return ideal(R, elem_type(R)[R(z) for z in [x, y...]])
 end
 
 function *(R::Ring, x::RingElement)
   return ideal(R, x)
 end
 
+function *(x::RingElement, R::Ring)
+  return ideal(R, x)
+end
+
+function ideal(x::RingElement)
+  return ideal(parent(x), x)
+end
+
+function ideal(xs::AbstractVector{T}) where T<:RingElement
+  !is_empty(xs) || throw(ArgumentError("Empty collection, cannot determine parent ring. Try ideal(ring, xs) instead of ideal(xs)"))
+  return ideal(parent(xs[1]), xs)
+end
+
 iszero(I::Ideal) = all(iszero, gens(I))
 
 base_ring_type(::Type{<:IdealSet{T}}) where T <: RingElement = parent_type(T)