polynomial_ring cached=false for combinatorics (#3856)

* sets poly ring caching to false for combinatorics

* Provide `parent` keywords and fix tests

* `Int` -> `ZZRingElem`

* Document optional polynomial ring

---------

Co-authored-by: Johannes Schmitt <jschmitt@posteo.eu>

src/Combinatorics/Matroids/ChowRings.jl

@@ -60,9 +60,9 @@ function chow_ring(M::Matroid; ring::Union{MPolyRing,Nothing}=nothing, extended:
 
         @req length(var_names) > 0 "Chow ring is empty"
         if graded
-            ring, vars = graded_polynomial_ring(QQ, var_names, cached=false)
+            ring, vars = graded_polynomial_ring(QQ, var_names; cached=false)
         else
-            ring, vars = polynomial_ring(QQ, var_names, cached=false)
+            ring, vars = polynomial_ring(QQ, var_names; cached=false)
         end
     else
         if extended
@@ -166,7 +166,7 @@ function augmented_chow_ring(M::Matroid)
     var_names = vcat(element_var_names, flat_var_names)
     s = length(var_names)
 
-    ring, vars = polynomial_ring(QQ, var_names)
+    ring, vars = polynomial_ring(QQ, var_names; cached=false)
     element_vars = vars[1:n]
     flat_vars = vars[n+1:s]
 

src/Combinatorics/Matroids/matroid_strata_grassmannian.jl

@@ -142,7 +142,7 @@ function make_polynomial_ring(Bs::Vector{Vector{Int}}, B::Vector{Int},
                               F::AbstractAlgebra.Ring)
 
     MC = bases_matrix_coordinates(Bs, B)
-    R, x = polynomial_ring(F, :"x"=>MC)
+    R, x = polynomial_ring(F, :"x"=>MC; cached=false)
     xdict = Dict{Vector{Int}, MPolyRingElem}([MC[i] => x[i] for i in 1:length(MC)])
     return R, x, xdict
 end
@@ -330,7 +330,7 @@ function realization_polynomial_ring(Bs::Vector{Vector{Int}}, A::Vector{Int},
     MC = realization_bases_coordinates(Bs, A)
     D = partial_matrix_max_rows(MC)
     MR = [x for x in MC if x[1] != D[x[2]]]
-    R, x = polynomial_ring(F, :"x"=>MR)
+    R, x = polynomial_ring(F, :"x"=>MR; cached=false)
     xdict = Dict{Vector{Int}, MPolyRingElem}(MR[i] => x[i] for i in 1:length(MR))
     return R, x, xdict
 end

src/Combinatorics/Matroids/properties.jl

@@ -885,6 +885,8 @@ end
 
 @doc raw"""
     tutte_polynomial(M::Matroid)
+    tutte_polynomial(M::Matroid; parent::ZZMPolyRing)
+    tutte_polynomial(parent::ZZMPolyRing, M::Matroid)
 
 Return the Tutte polynomial of `M`. This is polynomial in the variables x and y with integral coefficients.
 See Section 15.3 in [Oxl11](@cite).
@@ -896,15 +898,20 @@ x^3 + 4*x^2 + 7*x*y + 3*x + y^4 + 3*y^3 + 6*y^2 + 3*y
 
 ```
 """
-function tutte_polynomial(M::Matroid)
-    R, (x, y) = polynomial_ring(ZZ, ["x", "y"])
-    poly = pm_object(M).TUTTE_POLYNOMIAL
-    exp = Polymake.monomials_as_matrix(poly)
-    return R(Vector{Int}(Polymake.coefficients_as_vector(poly)),[[exp[i,1],exp[i,2]] for i in 1:size(exp)[1]])
+function tutte_polynomial(M::Matroid;
+           parent::ZZMPolyRing = polynomial_ring(ZZ, [:x, :y]; cached = false)[1])
+  @assert ngens(parent) >= 2
+  poly = pm_object(M).TUTTE_POLYNOMIAL
+  exp = Polymake.monomials_as_matrix(poly)
+  return parent(Vector{ZZRingElem}(Polymake.coefficients_as_vector(poly)), [[exp[i, 1],exp[i, 2]] for i in 1:size(exp)[1]])
 end
 
+tutte_polynomial(R::ZZMPolyRing, M::Matroid) = tutte_polynomial(M, parent = R)
+
 @doc raw"""
     characteristic_polynomial(M::Matroid)
+    characteristic_polynomial(M::Matroid; parent::ZZPolyRing)
+    characteristic_polynomial(parent::ZZPolyRing, M::Matroid)
 
 Return the characteristic polynomial of `M`. This is polynomial in the variable q with integral coefficients.
 It is computed as an evaluation of the Tutte polynmomial.
@@ -917,13 +924,17 @@ q^3 - 7*q^2 + 14*q - 8
 
 ```
 """
-function characteristic_polynomial(M::Matroid)
-    R, q = polynomial_ring(ZZ, 'q')
-    return (-1)^rank(M)*tutte_polynomial(M)(1-q,0)
+function characteristic_polynomial(M::Matroid;
+           parent::ZZPolyRing = polynomial_ring(ZZ, :q; cached = false)[1])
+  return (-1)^rank(M) * tutte_polynomial(M)(1 - gen(parent), 0)
 end
 
+characteristic_polynomial(R::ZZPolyRing, M::Matroid) = characteristic_polynomial(M, parent = R)
+
 @doc raw"""
     reduced_characteristic_polynomial(M::Matroid)
+    reduced_characteristic_polynomial(M::Matroid; parent::ZZPolyRing)
+    reduced_characteristic_polynomial(parent::ZZPolyRing, M::Matroid)
 
 Return the reduced characteristic polynomial of `M`. This is the quotient of the characteristic polynomial by (q-1).
 See Section 15.2 in [Oxl11](@cite).
@@ -935,18 +946,20 @@ q^2 - 6*q + 8
 
 ```
 """
-function reduced_characteristic_polynomial(M::Matroid)
-    R, q = polynomial_ring(ZZ, 'q')
-    p = characteristic_polynomial(M)
-    c = Vector{Int}(undef,degree(p))
-    s = 0
-    for i in 1:degree(p)
-        s-= coeff(p,i-1)
-        c[i] = s
-    end
-    return R(c)
+function reduced_characteristic_polynomial(M::Matroid;
+           parent::ZZPolyRing = polynomial_ring(ZZ, :q; cached = false)[1])
+  p = characteristic_polynomial(M, parent = parent)
+  c = Vector{ZZRingElem}(undef, degree(p))
+  s = ZZ(0)
+  for i in 1:degree(p)
+    s -= coeff(p, i - 1)
+    c[i] = s
+  end
+  return parent(c)
 end
 
+reduced_characteristic_polynomial(R::ZZPolyRing, M::Matroid) = reduced_characteristic_polynomial(M, parent = R)
+
 # This function compares two sets A and B in reverse lexicographic order.
 # It assumes that both sets are of the same length and ordered.
 # It returns true if A is less than B in this order

test/Combinatorics/Matroids/Matroids.jl

@@ -249,7 +249,7 @@
             @test vertical_connectivity(M) == values[4]
             @test girth(M) == values[5]
             @test tutte_connectivity(M) == values[6]
-            @test characteristic_polynomial(M) == values[7]
+            @test characteristic_polynomial(R, M) == values[7]
             @test length(cobases(M)) == length(bases(M))
             @test cohyperplanes(M) == [setdiff(matroid_groundset(M),set) for set in circuits(M)]
             @test is_regular(M) == values[8]
@@ -288,7 +288,7 @@
 
         @test cobases(N) == [['i','j'], [2,'j'], [2,'i'], [1,'j'], [1,'i']]
 
-        @test charpoly(N) == R(q^2-3q+2)
+        @test charpoly(R, N) == R(q^2-3q+2)
 
         @test is_clutter(bases(N)) == true
         @test is_clutter(circuits(N)) == true