From 9ebc78151e7cdbdc00495cc75c543211a15722a6 Mon Sep 17 00:00:00 2001
From: Max Horn <max@quendi.de>
Date: Thu, 10 Oct 2024 13:58:17 +0200
Subject: [PATCH] Add `is_finite` methods for various ring types (#1842)

Also add missing (but documented) `characteristic` method for
`FreeAssociativeAlgebra`
---
 src/FreeAssociativeAlgebra.jl |  4 ++++
 src/LaurentMPoly.jl           | 10 ++++++++++
 src/LaurentPoly.jl            | 10 ++++++++++
 src/MPoly.jl                  |  7 ++++---
 src/MatRing.jl                |  4 +++-
 src/NCPoly.jl                 |  2 ++
 src/Poly.jl                   |  2 ++
 src/Rings.jl                  |  7 ++++++-
 src/generic/LaurentMPoly.jl   |  2 --
 9 files changed, 41 insertions(+), 7 deletions(-)

diff --git a/src/FreeAssociativeAlgebra.jl b/src/FreeAssociativeAlgebra.jl
index 2e31cdae6..752c8a397 100644
--- a/src/FreeAssociativeAlgebra.jl
+++ b/src/FreeAssociativeAlgebra.jl
@@ -20,6 +20,10 @@ function is_exact_type(a::Type{S}) where {T <: RingElement, S <: FreeAssociative
    return is_exact_type(T)
 end
 
+characteristic(R::FreeAssociativeAlgebra) = characteristic(base_ring(R))
+
+is_finite(R::FreeAssociativeAlgebra) = is_trivial(base_ring(R)) || (nvars(R) == 0 && is_finite(base_ring(R)))
+
 ###############################################################################
 #
 #   String IO
diff --git a/src/LaurentMPoly.jl b/src/LaurentMPoly.jl
index c5018b271..38755573f 100644
--- a/src/LaurentMPoly.jl
+++ b/src/LaurentMPoly.jl
@@ -4,6 +4,16 @@
 #
 ###############################################################################
 
+###############################################################################
+#
+#   Data type and parent object methods
+#
+###############################################################################
+
+characteristic(R::LaurentMPolyRing) = characteristic(base_ring(R))
+
+is_finite(R::LaurentMPolyRing) = is_trivial(base_ring(R)) || (nvars(R) == 0 && is_finite(base_ring(R)))
+
 ###############################################################################
 #
 #   String I/O
diff --git a/src/LaurentPoly.jl b/src/LaurentPoly.jl
index 9ed6200ae..77fdacee4 100644
--- a/src/LaurentPoly.jl
+++ b/src/LaurentPoly.jl
@@ -4,6 +4,16 @@
 #
 ###############################################################################
 
+###############################################################################
+#
+#   Data type and parent object methods
+#
+###############################################################################
+
+characteristic(R::LaurentPolyRing) = characteristic(base_ring(R))
+
+is_finite(R::LaurentPolyRing) = is_trivial(R)
+
 ###############################################################################
 #
 #   laurent_polynomial_ring constructor
diff --git a/src/MPoly.jl b/src/MPoly.jl
index 0c6e85e5a..e626c3814 100644
--- a/src/MPoly.jl
+++ b/src/MPoly.jl
@@ -138,9 +138,10 @@ function var_index(x::MPolyRingElem{T}) where {T <: RingElement}
    return index
 end
 
-function characteristic(a::MPolyRing{T}) where T <: RingElement
-   return characteristic(base_ring(a))
-end
+characteristic(R::MPolyRing) = characteristic(base_ring(R))
+
+is_finite(R::MPolyRing) = is_trivial(base_ring(R)) || (nvars(R) == 0 && is_finite(base_ring(R)))
+
 
 ###############################################################################
 #
diff --git a/src/MatRing.jl b/src/MatRing.jl
index f778d255f..7791420a0 100644
--- a/src/MatRing.jl
+++ b/src/MatRing.jl
@@ -66,10 +66,12 @@ end
 
 
 function characteristic(a::MatRing)
-   iszero(a.n) && return 1
+   iszero(nrows(a)) && return 1
    return characteristic(base_ring(a))
 end
 
+is_finite(R::MatRing) = iszero(nrows(a)) || is_finite(base_ring(R))
+
 ###############################################################################
 #
 #   Similar and zero
diff --git a/src/NCPoly.jl b/src/NCPoly.jl
index 5e45040a2..e27c49c39 100644
--- a/src/NCPoly.jl
+++ b/src/NCPoly.jl
@@ -102,6 +102,8 @@ number_of_variables(a::NCPolyRing) = 1
 
 characteristic(a::NCPolyRing) = characteristic(base_ring(a))
 
+is_finite(a::NCPolyRing) = is_trivial(a)
+
 ###############################################################################
 #
 #   Basic manipulation
diff --git a/src/Poly.jl b/src/Poly.jl
index 59e171c2f..2bbaf01c1 100644
--- a/src/Poly.jl
+++ b/src/Poly.jl
@@ -49,6 +49,8 @@ number_of_variables(a::PolyRing) = 1
 
 characteristic(a::PolyRing) = characteristic(base_ring(a))
 
+is_finite(a::PolyRing) = is_trivial(a)
+
 Base.copy(a::PolyRingElem) = deepcopy(a)
 
 ###############################################################################
diff --git a/src/Rings.jl b/src/Rings.jl
index c6be31e71..7a14c0d77 100644
--- a/src/Rings.jl
+++ b/src/Rings.jl
@@ -207,4 +207,9 @@ is_perfect(F::Field) = characteristic(F) == 0 || F isa FinField ||
 
 is_finite(F::FinField) = true
 
-is_finite(F::Field) = characteristic(F) != 0 && throw(NotImplementedError(:is_finite, F))
+function is_finite(R::NCRing)
+  c = characteristic(R)
+  c == 0 && return false
+  c == 1 && return true
+  throw(NotImplementedError(:is_finite, R))
+end
diff --git a/src/generic/LaurentMPoly.jl b/src/generic/LaurentMPoly.jl
index 62fb1c1a2..2c00ddc84 100644
--- a/src/generic/LaurentMPoly.jl
+++ b/src/generic/LaurentMPoly.jl
@@ -29,8 +29,6 @@ number_of_variables(R::LaurentMPolyWrapRing) = number_of_variables(R.mpolyring)
 
 number_of_generators(R::LaurentMPolyWrapRing) = number_of_variables(R.mpolyring)
 
-characteristic(R::LaurentMPolyWrapRing) = characteristic(R.mpolyring)
-
 ###############################################################################
 #
 #   Basic manipulation