divrem with flag complete_reduction (#681)

* divrem with flag complete_reduction

* complete_reduction for reduce (#682)

* implementation via idLift and options

src/ideal/ideal.jl

@@ -747,20 +747,24 @@ function division(I::sideal{S}, G::sideal{S}) where S <: SPolyUnion
 end
 
 @doc raw"""
-    divrem(I::sideal{S}, G::sideal{S}) where S <: SPolyUnion
+    divrem(I::sideal{S}, G::sideal{S}; complete_reduction::Bool = false) where S <: SPolyUnion
 
 Computes a division with remainder of the generators of `I` by
 the generators of `G`. Returns a tuple (Quo, Rem, U) where
-  `Matrix(I)*Matrix(U) = Matrix(G)*Matrix(Quo) + Matrix(Rem)`
+  `Matrix(I)*U = Matrix(G)*Matrix(Quo) + Matrix(Rem)`
 and `Rem = normalform(I, G)`. `U` is a diagonal matrix of units differing
 from the identity matrix only for local ring orderings.
 """
-function divrem(I::sideal{S}, G::sideal{S}) where S <: SPolyUnion
+function divrem(I::sideal{S}, G::sideal{S}; complete_reduction::Bool = false) where S <: SPolyUnion
    check_parent(I, G)
    R = base_ring(I)
-   ptr_T,ptr_Rest,ptr_U = GC.@preserve I G R libSingular.id_DivRem_Unit(I.ptr, G.ptr,
-                                                      R.ptr)
-   return (smodule{S}(R,ptr_T), sideal{S}(R,ptr_Rest), smodule{S}(R,ptr_U))
+   old_redsb=libSingular.set_option("OPT_REDSB",complete_reduction)
+   old_redtail=libSingular.set_option("OPT_REDTAIL",complete_reduction)
+   ptr_T,ptr_Rest,ptr_U = GC.@preserve I G R libSingular.id_Lift(G.ptr, I.ptr, true,
+                                                                   false, true, R.ptr)
+   libSingular.set_option("OPT_REDSB",old_redsb)
+   libSingular.set_option("OPT_REDTAIL",old_redtail)
+   return (smodule{S}(R,ptr_T), sideal{S}(R,ptr_Rest), smatrix{S}(R,ptr_U))
 end
 
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