adds cyclic.jl

Author: ederc

src/examples/cyclic.jl

@@ -0,0 +1,23 @@
+@doc Markdown.doc"""
+    cyclic(R::MPolyRing)
+
+Return the Cyclic ideal in the variables of `R`.
+
+# Example
+```jldoctest
+julia> using AlgebraicSolving
+
+julia> R, vars = PolynomialRing(QQ, ["x$i" for i in 1:4])
+(Multivariate polynomial ring in 4 variables over QQ, Nemo.QQMPolyRingElem[x1, x2, x3, x4])
+
+julia> cyclic(R)
+Nemo.QQMPolyRingElem[x1 + x2 + x3 + x4, x1*x2 + x1*x4 + x2*x3 + x3*x4, x1*x2*x3 + x1*x2*x4 + x1*x3*x4 + x2*x3*x4, x1*x2*x3*x4 - 1]
+```
+"""
+function cyclic(R::MPolyRing)
+    vars = gens(R)
+    n = length(vars)
+    pols = [sum(prod(vars[j%n+1] for j in k:k+i) for k in 1:n) for i in 0:n-2]
+    push!(pols, prod(vars[i] for i in 1:n)-1)
+    return Ideal(pols)
+end