Renaming of revlex, negrevlex, introduction of deginvlex

Project.toml

@@ -42,7 +42,7 @@ Random = "1.6"
 RandomExtensions = "0.4.3"
 RecipesBase = "1.2.1"
 Serialization = "1.6"
-Singular = "0.19.0"
+Singular = "0.20.0"
 TOPCOM_jll = "0.17.8"
 UUIDs = "1.6"
 cohomCalg_jll = "0.32.0"

docs/src/CommutativeAlgebra/GroebnerBases/orderings.md

@@ -153,27 +153,37 @@ lex(R::MPolyRing)
 
 The *degree lexicographical ordering* `deglex` is defined by setting $\;\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n\;$ and
 
-$x^\alpha > x^\beta \;  \Leftrightarrow \;  \deg(x^\alpha) > \deg(x^\beta)  \;\text{ or }\; \exists \; 1 \leq i \leq n: \alpha_1 = \beta_1, \dots, \alpha_{i-1} = \beta_{i-1}, \alpha_i > \beta_i.$
+$x^\alpha > x^\beta \;  \Leftrightarrow \;  \deg(x^\alpha) > \deg(x^\beta)  \;\text{ or }\; (\deg(x^\alpha) = \deg(x^\beta) \;\text{ and }\; \exists \; 1 \leq i \leq n: \alpha_1 = \beta_1, \dots, \alpha_{i-1} = \beta_{i-1}, \alpha_i > \beta_i).$
 
 ```@docs
 deglex(R::MPolyRing)
 ```
 
-#### The Reverse Lexicographical Ordering
+#### The Inverse Lexicographical Ordering
 
-The *reverse lexicographical ordering* `revlex` is defined by setting
+The *inverse lexicographical ordering* `invlex` is defined by setting
 
 $x^\alpha > x^\beta \;  \Leftrightarrow \;\exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i  > \beta_i.$
 
 ```@docs
-revlex(R::MPolyRing)
+invlex(R::MPolyRing)
+```
+
+#### The Degree Inverse Lexicographical Ordering
+
+The *degree inverse lexicographical ordering* `deginvlex` is defined by setting
+
+$x^\alpha > x^\beta \;  \Leftrightarrow \deg(x^\alpha) > \deg(x^\beta)  \;\text{ or }\;(\deg(x^\alpha) = \deg(x^\beta) \;\text{ and }\; \;\exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i  > \beta_i).$
+
+```@docs
+deginvlex(R::MPolyRing)
 ```
 
 #### The Degree Reverse Lexicographical Ordering
 
 The *degree reverse lexicographical ordering* `degrevlex` is defined by setting $\;\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n\;$ and
 
-$x^\alpha > x^\beta \;  \Leftrightarrow \; \deg(x^\alpha) > \deg(x^\beta)  \;\text{ or }\;\exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i < \beta_i.$
+$x^\alpha > x^\beta \;  \Leftrightarrow \; \deg(x^\alpha) > \deg(x^\beta)  \;\text{ or }\;(\deg(x^\alpha) = \deg(x^\beta) \;\text{ and }\; \exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i < \beta_i).$
 
 ```@docs
 degrevlex(R::MPolyRing)
@@ -219,27 +229,27 @@ neglex(R::MPolyRing)
 
 The *negative degree lexicographical ordering* `negdeglex` is defined by setting $\;\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n\;$ and
 
-$x^\alpha > x^\beta \;  \Leftrightarrow \;  \deg(x^\alpha) < \deg(x^\beta)  \;\text{ or }\; \exists \; 1 \leq i \leq n: \alpha_1 = \beta_1, \dots, \alpha_{i-1} = \beta_{i-1}, \alpha_i > \beta_i.$
+$x^\alpha > x^\beta \;  \Leftrightarrow \;  \deg(x^\alpha) < \deg(x^\beta)  \;\text{ or }\; (\deg(x^\alpha) = \deg(x^\beta) \;\text{ and }\;  \exists \; 1 \leq i \leq n: \alpha_1 = \beta_1, \dots, \alpha_{i-1} = \beta_{i-1}, \alpha_i > \beta_i).$
 
 ```@docs
 negdeglex(R::MPolyRing)
 ```
 
-#### The Negative Reverse Lexicographical Ordering
+#### The Negative Inverse Lexicographical Ordering
 
-The *negative reverse lexicographical ordering* `negrevlex` is defined by setting
+The *negative inverse lexicographical ordering* `neginvlex` is defined by setting
 
 $x^\alpha > x^\beta \;  \Leftrightarrow \;\exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i  < \beta_i.$
 
 ```@docs
-negrevlex(R::MPolyRing)
+neginvlex(R::MPolyRing)
 ```
 
 #### The Negative Degree Reverse Lexicographical Ordering
 
 The *negative degree reverse lexicographical ordering* `negdegrevlex` is defined by setting $\;\deg(x^\alpha) = \alpha_1 + \cdots + \alpha_n\;$ and
 
-$x^\alpha > x^\beta \;  \Leftrightarrow \; \deg(x^\alpha) < \deg(x^\beta)  \;\text{ or }\;\exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i < \beta_i.$
+$x^\alpha > x^\beta \;  \Leftrightarrow \; \deg(x^\alpha) < \deg(x^\beta)  \;\text{ or }\;(\deg(x^\alpha) = \deg(x^\beta) \;\text{ and }\; \exists \; 1 \leq i \leq n: \alpha_n = \beta_n, \dots, \alpha_{i+1} = \beta_{i+1}, \alpha_i < \beta_i).$
 
 ```@docs
 negdegrevlex(R::MPolyRing)
@@ -392,7 +402,7 @@ Alternatively, we may wish to use $i < j$ instead of $i > j$ in this definition.
 
 In other words, these orderings are obtained by concatenating a monomial ordering on the monomials of $R$
 with a way of ordering the basis vectors of $F$ or vice versa. In OSCAR, we refer to the $i < j$ ordering on the
-basis vectors as *lex*, and to the $i > j$ ordering as *revlex*. And, we use the `*` operator for concatenation. 
+basis vectors as *lex*, and to the $i > j$ ordering as *invlex*. And, we use the `*` operator for concatenation. 
 
 ##### Examples
 
@@ -402,11 +412,11 @@ julia> R, (w, x, y, z) = polynomial_ring(QQ, ["w", "x", "y", "z"]);
 julia> F = free_module(R, 3)
 Free module of rank 3 over Multivariate polynomial ring in 4 variables over QQ
 
-julia> o1 = degrevlex(R)*revlex(gens(F))
-degrevlex([w, x, y, z])*revlex([gen(1), gen(2), gen(3)])
+julia> o1 = degrevlex(R)*invlex(gens(F))
+degrevlex([w, x, y, z])*invlex([gen(1), gen(2), gen(3)])
 
-julia> o2 = revlex(gens(F))*degrevlex(R)
-revlex([gen(1), gen(2), gen(3)])*degrevlex([w, x, y, z])
+julia> o2 = invlex(gens(F))*degrevlex(R)
+invlex([gen(1), gen(2), gen(3)])*degrevlex([w, x, y, z])
 
 ```
 

experimental/BasisLieHighestWeight/test/MainAlgorithm-test.jl

@@ -553,7 +553,7 @@ end
 
   @testset "Check dimension" begin
     @testset "Monomial order $monomial_ordering" for monomial_ordering in
-                                                     (:lex, :revlex, :degrevlex)
+                                                     (:lex, :invlex, :degrevlex)
       check_dimension(:A, 3, [1, 1, 1], monomial_ordering)
       #check_dimension(:B, 3, [2,1,0], monomial_ordering)
       #check_dimension(:C, 3, [1,1,1], monomial_ordering)

src/Modules/FreeModElem-orderings.jl

@@ -6,8 +6,8 @@ function Orderings.lex(F::ModuleFP)
    return Orderings.ModuleOrdering(F, Orderings.ModOrdering(1:ngens(F), :lex))
 end
 
-function Orderings.revlex(F::ModuleFP)
-   return Orderings.ModuleOrdering(F, Orderings.ModOrdering(1:ngens(F), :revlex))
+function Orderings.invlex(F::ModuleFP)
+   return Orderings.ModuleOrdering(F, Orderings.ModOrdering(1:ngens(F), :invlex))
 end
 
 @doc raw"""

src/Rings/mpoly-graded.jl

@@ -1912,7 +1912,7 @@ function homogenization(I::MPolyIdeal{T}, W::Union{ZZMatrix, Matrix{<:IntegerUni
   N = ngens(Ph)
   num_x = ngens(P)
   num_h = ngens(Ph) - num_x
-  # Build ordering matrix: weights matrix followed by identity mat, underneath is a revlex matrix
+  # Build ordering matrix: weights matrix followed by identity mat, underneath is a invlex matrix
   Id = reduce(hcat, [[kronecker_delta(i,j)  for i in 1:num_h]  for j in 1:num_h])
   RevLexMat = reduce(hcat, [[-kronecker_delta(i+j, 1+ngens(Ph))  for i in 1:ngens(Ph)]  for j in 1:ngens(Ph)])
   M = hcat(W, Id)

src/Rings/mpolyquo-localizations.jl

@@ -2197,7 +2197,7 @@ Note: This is only available for localizations at rational points.
   F = free_module(R, length(Jlist))
   Imax = ideal(R,gens(R))
   M = sub(F,[F(syz_mod[i]) for i=1:Singular.ngens(syz_mod)])[1] + (Imax*F)[1]
-  oF =  negdegrevlex(R)*revlex(F)
+  oF =  negdegrevlex(R)*invlex(F)
   res_vec = typeof(gen(I,1))[]
 
   ## select by Nakayama