add quotient_ideal

docs/make.jl

@@ -20,6 +20,7 @@ makedocs(
             "polynomial.md",
             "noncommutative.md",
             "ideal.md",
+            "qring.md",
             "Modules" => [
                   "module.md",
                   "vector.md"

docs/src/ideal.md

@@ -90,7 +90,7 @@ iszero(::sideal)
 ```
 
 ```@docs
-is_zerodim(::sideal)
+is_zerodim(I::sideal)
 ```
 
 ```@docs

docs/src/polynomial.md

@@ -253,10 +253,6 @@ has_local_ordering(R::PolyRing)
 degree_bound(R::PolyRing)
 ```
 
-```@docs
-leading_exponent_vector(p::spoly)
-```
-
 ```@docs
 total_degree(p::spoly)
 ```

docs/src/qring.md

@@ -0,0 +1,39 @@
+```@meta
+CurrentModule = Singular
+```
+
+# Quotient Rings
+
+Quotient rings $Q = R/I$ in Singular.jl are constructed with the constructor
+`QuotientRing(R, I)`. The input ideal $I$ to the constructor must be a Groebner
+basis. The $R$-ideal $I$ may be recovered as `quotient_ideal(Q)`.
+
+```@docs
+is_quotient_ring(R::PolyRingUnion)
+quotient_ideal(Q::PolyRing{T}) where T <: Nemo.RingElem
+```
+
+**Examples**
+
+```julia
+julia> R, (x, y) = PolynomialRing(QQ, ["x", "y"]);
+
+julia> is_quotient_ring(R)
+false
+
+julia> Q1, (x, y) = QuotientRing(R, Ideal(R, x^2+y^2));
+
+julia> is_quotient_ring(Q1)
+true
+
+julia> quotient_ideal(Q1)
+Singular ideal over Singular Polynomial Ring (QQ),(x,y),(dp(2),C) with generators (x^2 + y^2)
+
+julia> Q2, (x, y) = QuotientRing(Q1, std(Ideal(Q1, x*y)));
+
+julia> quotient_ideal(Q2)
+Singular ideal over Singular Polynomial Ring (QQ),(x,y),(dp(2),C) with generators (x*y, y^3, x^2 + y^2)
+
+julia> base_ring(quotient_ideal(Q1)) == base_ring(quotient_ideal(Q2))
+true
+```

src/ideal/ideal.jl

@@ -82,7 +82,6 @@ end
 Return `true` if the given ideal is zero dimensional, i.e. the Krull dimension of
 $R/I$ is zero, where $R$ is the polynomial ring over which $I$ is an ideal..
 """
-
 function is_zerodim(I::sideal)
    I.isGB || error("Not a Groebner basis")
    R = base_ring(I)

src/ideal/quotient.jl

@@ -1,7 +1,7 @@
-export is_quotient_ring, QuotientRing
+export is_quotient_ring, QuotientRing, quotient_ideal
 
 @doc Markdown.doc"""
-    is_quotient_ring(R::PolyRing)
+    is_quotient_ring(R::PolyRingUnion)
 
 Return `true` if the given ring is the quotient of a polynomial ring with
 a non - zero ideal.
@@ -10,6 +10,20 @@ function is_quotient_ring(R::PolyRingUnion)
    GC.@preserve R return Bool(Singular.libSingular.rIsQuotientRing(R.ptr))
 end
 
+@doc Markdown.doc"""
+    quotient_ideal(Q::PolyRing{T}) where T <: Nemo.RingElem
+
+Return `I` for a given quotient ring `Q = R/I`.
+"""
+function quotient_ideal(Q::PolyRing{T}) where T <: Nemo.RingElem
+   is_quotient_ring(Q) || ArgumentError("input ring is not a quotient ring")
+   R = PolyRing{T}(base_ring(Q), symbols(Q), ordering(Q), true, degree_bound(Q))
+   GC.@preserve Q begin
+      iptr = libSingular.r_get_qideal(Q.ptr)
+      return sideal{spoly{T}}(R, libSingular.id_Copy(iptr, R.ptr), true)
+   end
+end
+
 ###############################################################################
 #
 #   Quotient ring construction

test/ideal/quotient-test.jl

@@ -3,6 +3,7 @@
    Q, (x, y, z) = @inferred QuotientRing(R, Ideal(R, x^2 - y*z))
 
    @test is_quotient_ring(Q)
+   @test isequal(quotient_ideal(Q), Ideal(R, x^2 - y*z))
 
    I = Ideal(Q, x)
    @test !I.isGB