Minimal associated primes

src/Rings/mpoly-ideals.jl

@@ -1172,6 +1172,24 @@ function minimal_primes(I::MPolyIdeal; algorithm::Symbol = :GTZ, cache::Bool=tru
   return V
 end
 
+@doc raw"""
+    function minimal_primes_zero_dim(I::MPolyIdeal{QQPolyRingElem})
+
+Return a vector containing the minimal associated prime ideals of `I`.
+
+Calls a modular variant of `minimal_primes` for zero dimensional ideals over a polynomial ring
+with coefficient ring over the rationals.
+
+No input checks. It is unclear if there exists input where this variant is 
+faster than just calling `minimal_primes` directly.
+"""
+function minimal_primes_zero_dim(I::MPolyIdeal{QQMPolyRingElem})
+  R = base_ring(I)
+  L = Singular.LibAssprimeszerodim.assPrimes(singular_generators(I))
+  result = typeof(I)[ideal(R, q) for q in L]
+  return result
+end
+
 # rerouting the procedure for minimal primes this way leads to 
 # much longer computations compared to the flattening of the coefficient
 # field implemented above.

test/Rings/mpoly.jl

@@ -159,6 +159,12 @@ end
   l = minimal_primes(i, algorithm=:charSets)
   @test length(l) == 2
   @test l[1] == i1 && l[2] == i2 || l[1] == i2 && l[2] == i1
+
+  I1 = ideal(R,[x-1,y-1,z-1])
+  I2 = ideal(R,[x^2+1,y^2+1,z])
+  J = intersect(I1,I2)
+  @test length(Oscar.minimal_primes_zero_dim(J))==3
+
   R, (a, b, c, d) = polynomial_ring(ZZ, [:a, :b, :c, :d])
   i = ideal(R, [R(9), (a+3)*(b+3)])
   i1 = ideal(R, [R(3), a])