From 9cda843dfa5c3def261d3c592c9fc2434d961c52 Mon Sep 17 00:00:00 2001
From: Matthias Zach <85350711+HechtiDerLachs@users.noreply.github.com>
Date: Mon, 7 Oct 2024 21:27:43 +0200
Subject: [PATCH] Avoid bottlenecks in variable matching (#4178)

---
 src/Rings/MPolyMap/Types.jl         | 5 ++++-
 src/Rings/mpolyquo-localizations.jl | 4 ++++
 2 files changed, 8 insertions(+), 1 deletion(-)

diff --git a/src/Rings/MPolyMap/Types.jl b/src/Rings/MPolyMap/Types.jl
index 9f22448a96e9..6c56fd1cf626 100644
--- a/src/Rings/MPolyMap/Types.jl
+++ b/src/Rings/MPolyMap/Types.jl
@@ -35,12 +35,15 @@ const _DomainTypes = Union{MPolyRing, MPolyQuoRing}
     # can safely be disabled.
     if check_for_mapping_of_vars && all(_is_gen, img_gens) && _allunique(img_gens)
       gens_codomain = gens(codomain)
-      result.variable_indices = [findfirst(==(x), gens_codomain) for x in img_gens]
+      result.variable_indices = [findfirst(_cmp_reps(x), gens_codomain) for x in img_gens]
     end
     return result
   end
 end
 
+# This can be overwritten in order to avoid making the above check a bottleneck.
+_cmp_reps(a) = ==(a)
+
 function MPolyAnyMap(d::D, c::C, cm::U, ig::Vector{V}) where {D, C, U, V}
   return MPolyAnyMap{D, C, U, V}(d, c, cm, ig)
 end
diff --git a/src/Rings/mpolyquo-localizations.jl b/src/Rings/mpolyquo-localizations.jl
index f9357af03df5..e0e3ecf557d3 100644
--- a/src/Rings/mpolyquo-localizations.jl
+++ b/src/Rings/mpolyquo-localizations.jl
@@ -2804,3 +2804,7 @@ _exponents(x::MPolyQuoRingElem) = AbstractAlgebra.exponent_vectors(lift(x))
 _exponents(x::MPolyLocRingElem) = AbstractAlgebra.exponent_vectors(numerator(x))
 _exponents(x::MPolyQuoLocRingElem) = AbstractAlgebra.exponent_vectors(lifted_numerator(x))
 
+# overwriting the comparison method to avoid computing saturations and groebner bases.
+_cmp_reps(a::MPolyLocRingElem) = y->(fraction(y) == fraction(a))
+_cmp_reps(a::MPolyQuoLocRingElem) = y->(fraction(y) == fraction(a))
+