Add quo for LaurentMPolyWrapRing

src/Rings/Laurent.jl

@@ -61,7 +61,8 @@ function _polyringquo(R::LaurentMPolyWrapRing)
   get_attribute!(R, :polyring) do
     n = nvars(R)
     C = base_ring(R)
-    Cx, x, xinv = polynomial_ring(C,"x#" => 1:n, "x#^-1" => 1:n; cached = false)
+    var_names = symbols(R.mpolyring)
+    Cx, x, xinv = polynomial_ring(C, var_names, [Symbol("inv(", name, ")")  for name in var_names]; cached = false)
     I = ideal(Cx, [x[i]*xinv[i] - 1 for i in 1:n])
     Q, = quo(Cx, I)
     return _LaurentMPolyBackend(R, Q)
@@ -241,3 +242,13 @@ end
 
 
 
+function quo(R::Oscar.LaurentMPolyWrapRing, I::Oscar.LaurentMPolyIdeal)
+  @req R === base_ring(I) "ring and ideal do not match"
+  poly_repr = Oscar._polyringquo(R)
+  underlying_poly_ring_quo = codomain(poly_repr)
+  II = ideal(underlying_poly_ring_quo, poly_repr.(gens(I)))
+  Q,phi = quo(underlying_poly_ring_quo, II)
+  map_down(f::AbstractAlgebra.Generic.LaurentMPolyWrap) = phi(poly_repr(f))
+  lift_up(f::MPolyQuoRingElem) = poly_repr.inv(preimage(phi,f))
+  return Q, MapFromFunc(R,Q, map_down, lift_up)
+end

test/Rings/Laurent.jl

@@ -32,3 +32,45 @@
     end
   end
 end
+
+
+@testset "Laurent quotient" begin
+  # Quick test
+
+  # Taken from issue 4814 (suggested by thofman)
+
+  R, (x, y) = laurent_polynomial_ring(GF(2), [:x, :y]);
+  f1 = x^2*y^3 + x*y^3 + 1;
+  f2 = y + y^2 + x^3;
+  f3 = x^9 * y^6 - 1;
+  f4 = y^15 - 1;
+  I = ideal(R, [f1, f2, f3, f4]);
+
+  Q,phi = quo(R, I); # same as R/ideal(x^2+x+1, y^2+y+1)
+
+  @test parent(phi(x)) == Q;
+  @test parent(phi(y)) == Q;
+  @test is_one(phi(x^3));
+  @test is_one(phi(x)^3);
+  @test is_one(phi(y^3));
+  @test is_one(phi(y)^3);
+  @test in(preimage(phi,phi(x)) - x, I);
+  @test preimage(phi,phi(x)) == 1+x^(-1); # would be "more natural" if underlying ring had elim order for the inverses
+
+
+  # Ideal generated by non-polynomials
+  R, (x, y) = laurent_polynomial_ring(QQ, [:x, :y]);
+  C10 = x^2 -x +1 -x^(-1) +x^(-2);
+  C28 = y^6 -y^4 +y^2 -1 +y^(-2) -y^(-4) +y^(-6);
+  J = ideal(R, [C10,C28]);
+  Q,phi = quo(R,J);
+  u = phi(x^(-1)*y^3);
+  @test is_unit(u)
+  @test is_unit(u^(-1))
+  @test is_one(u^140)
+  @test !is_one(u^70)
+  @test !is_one(u^28)
+  @test !is_one(u^20)
+  @test is_one(u*inv(u))
+  @test 1/u == inv(u)
+end