Add is_known_to_be_radical.

src/Rings/mpoly-ideals.jl

@@ -573,6 +573,7 @@ Ideal generated by
 ```
 """
 @attr MPolyIdeal{T} function radical(I::MPolyIdeal{T}) where {T <: MPolyRingElem}
+  is_known_to_be_radical(I) && return I
   # Calling `elimpart` (within `simplify`) turns out to significantly speed things up in many cases.
   R = base_ring(I)
   Q, pr = quo(R, I)
@@ -611,6 +612,7 @@ function radical(
     I::MPolyIdeal{T};
     factor_generators::Bool=true
   ) where {U<:Union{AbsSimpleNumFieldElem, <:Hecke.RelSimpleNumFieldElem}, T<:MPolyRingElem{U}}
+  is_known_to_be_radical(I) && return I
   get_attribute!(I, :radical) do
     is_one(I) && return I
     R = base_ring(I)
@@ -660,6 +662,13 @@ Computes the radical.
   return is_subset(radical(I), I)
 end
 
+function is_known_to_be_radical(I::Ideal)
+  has_attribute(I, :is_radical) && get_attribute(I, :is_radical) === true && return true
+  has_attribute(I, :is_prime) && get_attribute(I, :is_prime) === true && return true
+  return false
+end
+
+
 #######################################################
 @doc raw"""
     primary_decomposition(I::MPolyIdeal; algorithm = :GTZ, cache=true)