Speed up polynomial mappings

experimental/AlgebraicStatistics/src/CI.jl

@@ -137,7 +137,11 @@ julia> ci_statements(["A", "B", "X", "Y"])
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- ⋮
+ [X _||_ Y | B]
+ [X _||_ Y | {A, B}]
+ [A _||_ X | {}]
+ [A _||_ X | B]
+ [A _||_ X | Y]
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]

experimental/AlgebraicStatistics/src/Markov.jl

@@ -124,7 +124,11 @@ julia> ci_statements(R)
  [B _||_ Y | {A, X}]
  [X _||_ Y | {}]
  [X _||_ Y | A]
- ⋮
+ [X _||_ Y | B]
+ [X _||_ Y | {A, B}]
+ [A _||_ X | {}]
+ [A _||_ X | B]
+ [A _||_ X | Y]
  [A _||_ X | {B, Y}]
  [B _||_ X | {}]
  [B _||_ X | A]

experimental/AlgebraicStatistics/src/PhylogeneticParametrization.jl

@@ -62,22 +62,64 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (3, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 1, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
-  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (3, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 1, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 2, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
-  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 3, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (2, 2, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 3, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (2, 2, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
   (4, 4, 4) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
-  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (4, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (3, 3, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 4, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (2, 2, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (4, 4, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 3, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (1, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 3, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 1, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 3, 1) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (4, 1, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (3, 1, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 3, 3) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
+  (4, 1, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 2, 4) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (3, 4, 3) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (4, 2, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (3, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (2, 3, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (4, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 3, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (2, 4, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (1, 1, 4) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (2, 1, 2) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 1) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
+  (2, 3, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
+  (2, 4, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
+  (1, 1, 3) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
+  (1, 2, 4) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   ⋮         => ⋮
 ```
 """
@@ -155,6 +197,48 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 64 entries:
   (4, 4, 4) => 0
   (4, 3, 1) => 0
   (3, 3, 2) => 0
+  (4, 1, 2) => 0
+  (4, 4, 1) => x[3, 1]*x[1, 2]*x[2, 2]
+  (2, 2, 3) => 0
+  (3, 4, 2) => x[1, 2]*x[2, 2]*x[3, 2]
+  (4, 3, 3) => 0
+  (4, 4, 3) => 0
+  (4, 2, 2) => 0
+  (1, 3, 4) => 0
+  (2, 3, 2) => 0
+  (1, 4, 4) => x[1, 1]*x[2, 2]*x[3, 2]
+  (1, 3, 1) => 0
+  (2, 4, 2) => 0
+  (1, 1, 2) => 0
+  (1, 4, 1) => 0
+  (1, 3, 3) => x[1, 1]*x[2, 2]*x[3, 2]
+  (3, 3, 4) => 0
+  (1, 4, 3) => 0
+  (4, 1, 4) => x[2, 1]*x[1, 2]*x[3, 2]
+  (3, 4, 4) => 0
+  (3, 3, 1) => x[3, 1]*x[1, 2]*x[2, 2]
+  (4, 1, 1) => 0
+  (1, 2, 2) => x[1, 1]*x[2, 2]*x[3, 2]
+  (3, 1, 2) => 0
+  (3, 4, 1) => 0
+  (3, 3, 3) => 0
+  (4, 1, 3) => 0
+  (4, 2, 4) => 0
+  (3, 4, 3) => 0
+  (4, 2, 1) => 0
+  (3, 2, 2) => 0
+  (2, 3, 4) => x[1, 2]*x[2, 2]*x[3, 2]
+  (4, 2, 3) => x[1, 2]*x[2, 2]*x[3, 2]
+  (2, 3, 1) => 0
+  (2, 4, 4) => 0
+  (1, 1, 4) => 0
+  (2, 1, 2) => x[2, 1]*x[1, 2]*x[3, 2]
+  (2, 4, 1) => 0
+  (1, 1, 1) => x[1, 1]*x[2, 1]*x[3, 1]
+  (2, 3, 3) => 0
+  (2, 4, 3) => x[1, 2]*x[2, 2]*x[3, 2]
+  (1, 1, 3) => 0
+  (1, 2, 4) => 0
   ⋮         => ⋮
 ```
 """
@@ -192,16 +276,16 @@ Dict{Tuple{Vararg{Int64}}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 1//4*a[1]*a[3]*b[2] + 1//4*a[2]*b[1]*b[3] + 1//2*b[1]*b[2]*b[3]
   (1, 1, 1) => 1//4*a[1]*a[2]*a[3] + 3//4*b[1]*b[2]*b[3]
   (1, 2, 2) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*a[3]*b[1] + 1//2*b[1]*b[2]*b[3]
-  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] …
+  (1, 2, 3) => 1//4*a[1]*b[2]*b[3] + 1//4*a[2]*b[1]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//4*b[1]*b[2]*b[3]
   (1, 1, 2) => 1//4*a[1]*a[2]*b[3] + 1//4*a[3]*b[1]*b[2] + 1//2*b[1]*b[2]*b[3]
 
 julia> p_equivclasses.classes
 Dict{Tuple{Vararg{Int64}}, Vector{Tuple{Vararg{Int64}}}} with 5 entries:
-  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2…
+  (1, 2, 1) => [(1, 2, 1), (1, 3, 1), (1, 4, 1), (2, 1, 2), (2, 3, 2), (2, 4, 2), (3, 1, 3), (3, 2, 3), (3, 4, 3), (4, 1, 4), (4, 2, 4), (4, 3, 4)]
   (1, 1, 1) => [(1, 1, 1), (2, 2, 2), (3, 3, 3), (4, 4, 4)]
-  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4…
-  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3…
-  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4…
+  (1, 2, 2) => [(1, 2, 2), (1, 3, 3), (1, 4, 4), (2, 1, 1), (2, 3, 3), (2, 4, 4), (3, 1, 1), (3, 2, 2), (3, 4, 4), (4, 1, 1), (4, 2, 2), (4, 3, 3)]
+  (1, 2, 3) => [(1, 2, 3), (1, 2, 4), (1, 3, 2), (1, 3, 4), (1, 4, 2), (1, 4, 3), (2, 1, 3), (2, 1, 4), (2, 3, 1), (2, 3, 4)  …  (3, 2, 1), (3, 2, 4), (3, 4, 1), (3, 4, 2), (4, 1, 2), (4, 1, 3), (4, 2, 1), (4, …
+  (1, 1, 2) => [(1, 1, 2), (1, 1, 3), (1, 1, 4), (2, 2, 1), (2, 2, 3), (2, 2, 4), (3, 3, 1), (3, 3, 2), (3, 3, 4), (4, 4, 1), (4, 4, 2), (4, 4, 3)]
 
 julia> q_equivclasses = compute_equivalent_classes(q);
 
@@ -251,7 +335,7 @@ Dict{Tuple{Int64, Int64, Int64}, QQMPolyRingElem} with 5 entries:
   (1, 2, 1) => 3*a[1]*a[3]*b[2] + 3*a[2]*b[1]*b[3] + 6*b[1]*b[2]*b[3]
   (1, 1, 1) => a[1]*a[2]*a[3] + 3*b[1]*b[2]*b[3]
   (1, 2, 2) => 3*a[1]*b[2]*b[3] + 3*a[2]*a[3]*b[1] + 6*b[1]*b[2]*b[3]
-  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*…
+  (1, 2, 3) => 6*a[1]*b[2]*b[3] + 6*a[2]*b[1]*b[3] + 6*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
   (1, 1, 2) => 3*a[1]*a[2]*b[3] + 3*a[3]*b[1]*b[2] + 6*b[1]*b[2]*b[3]
 ```
 """

experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl

@@ -1677,7 +1677,8 @@ julia> components_of_dual_graph(qsm_model)
  "C7"
  "C8"
  "C9"
- ⋮
+ "C13"
+ "C14"
  "C16"
  "C17"
  "C21"

src/AlgebraicGeometry/Schemes/AffineSchemeOpenSubscheme/Rings/Methods.jl

@@ -506,3 +506,7 @@ function Base.show(io::IO, ::MIME"text/plain", a::AffineSchemeOpenSubschemeRingE
   end
 end
 
+# overwrite a method for mapping of rings which would throw otherwise
+function _allunique(lst::Vector{T}) where {T<:MPolyQuoRingElem{<:MPolyRingElem{<:AffineSchemeOpenSubschemeRingElem}}}
+  return false
+end

src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Attributes.jl

@@ -46,7 +46,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -95,7 +95,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -143,7 +143,7 @@ Ring homomorphism
   from multivariate polynomial ring in 3 variables over QQ
   to quotient of multivariate polynomial ring by ideal (x1)
 defined by
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 ```
@@ -254,7 +254,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 

src/AlgebraicGeometry/Schemes/AffineSchemes/Morphisms/Constructors.jl

@@ -132,7 +132,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 
@@ -181,7 +181,7 @@ Affine scheme morphism
   from [x1, x2, x3]  scheme(x1)
   to   [x1, x2, x3]  affine 3-space over QQ
 given by the pullback function
-  x1 -> 0
+  x1 -> x1
   x2 -> x2
   x3 -> x3
 

src/AlgebraicGeometry/Schemes/AffineSchemes/Objects/Attributes.jl

@@ -234,7 +234,7 @@ Affine scheme morphism
   from [x, y]  scheme(x)
   to   [x, y]  affine 2-space over QQ
 given by the pullback function
-  x -> 0
+  x -> x
   y -> y
 
 julia> inc == inclusion_morphism(Y, X)

src/Rings/MPolyMap/MPolyAnyMap.jl

@@ -42,17 +42,38 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
   coeff_map::U
   img_gens::Vector{V}
   temp_ring           # temporary ring used when evaluating maps
+  variable_indices::Vector{Int} # a table where the i-th entry contains the 
+                                # index of the variable where it is mapped to
+                                # in case the mapping takes such a particularly
+                                # simple form.
 
   function MPolyAnyMap{D, C, U, V}(domain::D,
-                                codomain::C,
-                                coeff_map::U,
-                                img_gens::Vector{V}) where {D, C, U, V}
-      @assert V === elem_type(C)
-      for g in img_gens
-        @assert parent(g) === codomain "elements does not have the correct parent"
-      end
+                                   codomain::C,
+                                   coeff_map::U,
+                                   img_gens::Vector{V}) where {D, C, U, V}
+    @assert V === elem_type(C)
+    for g in img_gens
+      @assert parent(g) === codomain "elements does not have the correct parent"
+    end
     return new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
   end
+  function MPolyAnyMap{D, C, U, V}(domain::D,
+                                   codomain::C,
+                                   coeff_map::U,
+                                   img_gens::Vector{V};
+                                   check_for_mapping_of_vars::Bool=true
+                                  ) where {D <: Union{<:MPolyRing, <:MPolyQuoRing}, 
+                                           C, U, V}
+    @assert V === elem_type(C)
+    for g in img_gens
+      @assert parent(g) === codomain "elements does not have the correct parent"
+    end
+    result = new{D, C, U, V}(domain, codomain, coeff_map, img_gens)
+    if check_for_mapping_of_vars && all(_is_gen, img_gens) && _allunique(img_gens)
+      result.variable_indices = [findfirst(==(x), gens(codomain)) for x in img_gens]
+    end
+    return result
+  end
 end
 
 function MPolyAnyMap(d::D, c::C, cm::U, ig::Vector{V}) where {D, C, U, V}