Add missing ordering and correct some orderings.

src/Rings/mpoly.jl

@@ -377,6 +377,8 @@ function singular(o::Orderings.GenOrdering)
     return Singular.ordering_Dp(length(v))
   elseif o.ord == :revlex
     return Singular.ordering_rp(length(v))
+  elseif o.ord == :neglex
+    return Singular.ordering_ls(length(v))
   elseif o.ord == :negdegrevlex
     return Singular.ordering_ds(length(v))
   elseif o.ord == :negdeglex

src/Rings/orderings.jl

@@ -722,9 +722,9 @@ function _isless_lex(f::MPolyElem, k::Int, l::Int)
  function _isless_weightnegdeglex(f::MPolyElem, k::Int, l::Int, w::Vector{Int})
    dk = weighted_degree(f, k, w)
    dl = weighted_degree(f, l, w)
-   if dk < dl
+   if dk > dl
      return true
-   elseif dk > dl
+   elseif dk < dl
      return false
    end
    return _isless_lex(f, k, l)
@@ -738,7 +738,7 @@ function _isless_lex(f::MPolyElem, k::Int, l::Int)
    elseif dk < dl
      return false
    end
-   return _isless_negrevlex(f, k, l)
+   return _isless_revlex(f, k, l)
  end
 
  function _isless_matrix(f::MPolyElem, k::Int, l::Int, M::Union{ Matrix{T}, MatElem{T} }) where T
@@ -959,9 +959,9 @@ function _cmp_monomials(f::MPolyElem, k::Int, l::Int, o::Oscar.Orderings.GenOrde
             end
           end
       elseif o.ord == :negwdeglex
-         if dk < dl
+         if dk > dl
             return -1
-          elseif dk > dl
+          elseif dk < dl
             return 1
           end
           for i in o.vars
@@ -979,7 +979,7 @@ function _cmp_monomials(f::MPolyElem, k::Int, l::Int, o::Oscar.Orderings.GenOrde
           elseif dk < dl
             return 1
           end
-          for i in o.vars
+          for i in reverse(o.vars)
             ek = exponent(f, k, i)
             el = exponent(f, l, i)
             if ek > el

test/Rings/orderings-test.jl

@@ -89,6 +89,7 @@ end
    o = negrevlex([x1, x2])*wdegrevlex([x3, x4], [1, 2])
    @test collect(monomials(f, o)) == M
 
+   # currently fails
    M = [one(R), x3, x3^2, x4, x3^3, x3*x4, x3^2*x4, x4^2, x3*x4^2,
         x4^3, x2, x2*x3, x2*x3^2, x2*x4, x2*x3*x4, x2*x4^2, x2^2, x2^2*x3,
         x2^2*x4, x2^3, x1, x1*x3, x1*x3^2, x1*x4, x1*x3*x4, x1*x4^2, x1*x2,
@@ -98,7 +99,6 @@ end
    o = neglex([x1, x2])*negwdegrevlex([x3, x4], [1, 2])
    @test collect(monomials(f, o)) == M
 
-   # currently fails
    M = [x3^3, x3^2*x4, x3^2, x3*x4^2, x3*x4, x3, x4^3, x4^2, x4,
         one(R), x1*x3^2, x1*x3*x4, x1*x3, x1*x4^2, x1*x4, x1, x1^2*x3, x1^2*x4,
         x1^2, x2*x3^2, x2*x3*x4, x2*x3, x2*x4^2, x2*x4, x2, x1^3, x1*x2*x3,