add radical and prepare for more

deps/src/ideals.cpp

@@ -100,6 +100,54 @@ auto id_Std_helper(ideal a, ring b, bool complete_reduction = false)
     return id;
 }
 
+auto id_Radical_helper(ideal a, ring b)
+{
+    ideal id = NULL;
+    if (!idIs0(a))
+    {
+        id = ii_CallProcId2Id("primdec.lib","radical",a,b);
+    }
+    else
+        id = idInit(0, a->rank);
+    return id;
+}
+
+auto id_RadicalZ_helper(ideal a, ring b)
+{
+    ideal id = NULL;
+    if (!idIs0(a))
+    {
+        id = ii_CallProcId2Id("primdecint.lib","radicalZ",a,b);
+    }
+    else
+        id = idInit(0, a->rank);
+    return id;
+}
+
+auto id_equiRadical_helper(ideal a, ring b)
+{
+    ideal id = NULL;
+    if (!idIs0(a))
+    {
+        id = ii_CallProcId2Id("primdec.lib","equiRadical",a,b);
+    }
+    else
+        id = idInit(0, a->rank);
+    return id;
+}
+
+auto id_equidimMax_helper(ideal a, ring b)
+{
+    ideal id = NULL;
+    if (!idIs0(a))
+    {
+        id = ii_CallProcId2Id("primdec.lib","equidimMax",a,b);
+    }
+    else
+        id = idInit(0, a->rank);
+    return id;
+}
+
 void singular_define_ideals(jlcxx::Module & Singular)
 {
     Singular.method("id_Delete",
@@ -123,6 +171,10 @@ void singular_define_ideals(jlcxx::Module & Singular)
 
     Singular.method("idElem", &idElem);
 
+    Singular.method("id_equiRadical", &id_equiRadical_helper);
+
+    Singular.method("id_equidimMax", &id_equidimMax_helper);
+
     Singular.method("id_Normalize", &id_Normalize);
 
     Singular.method("id_Head", &id_Head);
@@ -174,6 +226,10 @@ void singular_define_ideals(jlcxx::Module & Singular)
 
     Singular.method("id_Std", &id_Std_helper);
 
+    Singular.method("id_Radical", &id_Radical_helper);
+
+    Singular.method("id_RadicalZ", &id_RadicalZ_helper);
+
     Singular.method("id_Eliminate", [](ideal m, poly p, ring o) {
         const ring origin = currRing;
         rChangeCurrRing(o);

docs/src/ideal.md

@@ -101,6 +101,10 @@ isvar_generated(::sideal)
 normalize!(::sideal)
 ```
 
+```@docs
+radical(::sideal)
+```
+
 **Examples**
 
 ```

src/ideal/ideal.jl

@@ -1,7 +1,7 @@
 export sideal, IdealSet, syz, lead, normalize!, isconstant, iszerodim, fres,
        highcorner, jacobi, jet, kbase, ngens, sres, intersection, quotient,
        reduce, eliminate, kernel, equal, contains, isvar_generated, saturation,
-       satstd, slimgb, std, vdim
+       satstd, slimgb, std, vdim, radical
 
 ###############################################################################
 #
@@ -335,6 +335,17 @@ function std(I::sideal; complete_reduction::Bool=false)
    return z
 end
 
+@doc Markdown.doc"""
+    radical(I::sideal)
+> Compute for thedical of an ideal $I$.
+"""
+function radical(I::sideal)
+   R = base_ring(I)
+   ptr = libSingular.id_Radical(I.ptr, R.ptr)
+   z = Ideal(R, ptr)
+   return z
+end
+
 @doc Markdown.doc"""
    satstd{T <: AbstractAlgebra.RingElem}(I::sideal{T}, J::sideal{T})
 > Given an ideal $J$ generated by variables, computes a standard basis of