Faster high-level Meataxe functions for irreducible modules (e.g. MTX.IsomorphismModules, MTX.Indecomposition, MTX.BasisModuleEndomorphisms, MTX.BasisModuleHomomorphisms) (#6276)

Several high-level Meataxe functions were much, much slower for
irreducible modules than their low-level counterparts (the ones
which *only* work for irreducible modules).

As an example, consider this test input:

    n:=10;;   # increase this to make the effect even stronger
    G:=GL(56,GF(25));;
    H:=Subgroup(G, Concatenation(GeneratorsOfGroup(G),List([1..n],i->PseudoRandom(G))));;

Then before these changes, we had:

    gap> MTX.Indecomposition(NaturalGModule(H));; time;
    1818
    gap> MTX.IsomorphismModules(NaturalGModule(H),NaturalGModule(H));; time;
    5408

After these changes:

    gap> MTX.Indecomposition(NaturalGModule(H));; time;
    22
    gap> MTX.IsomorphismModules(NaturalGModule(H),NaturalGModule(H));; time;
    23

To some extent this papers over a deeper issue: the general code in
MTX.Indecomposition and MTX.BasisModuleEndomorphisms ought to be way
faster: it is trivial to take the example here and e.g. form a direct
sum of modules to make it slow again.

Author: fingolfin

lib/meatauto.gi

@@ -1320,6 +1320,10 @@ local n, hc1, hc2, nc, b1, b2, map, remain, j, found, hom, i, k;
     Length(SMTX.BasisEndomorphismsRadical(M2)) ) then
     # different endomorphism algebra dimensions
     return fail;
+  elif MTX.IsIrreducible(M1) and MTX.IsIrreducible(M2) then
+    return MTX.IsomorphismIrred(M1, M2);
+  elif MTX.IsIrreducible(M1) <> MTX.IsIrreducible(M2) then
+    return fail;
   fi;
 
   hc1:=SMTX.HomogeneousComponents(M1);
@@ -1637,7 +1641,9 @@ end;
 SMTX.BasisModuleHomomorphisms:=function(m1,m2)
 local b;
   TestModulesFitTogether(m1,m2);
-  if m1.dimension>5 then
+  if MTX.IsIrreducible(m1) then
+    b:=MTX.Homomorphisms(m1,m2);
+  elif m1.dimension>5 then
     b:= SpinHom(m1,m2);
     Assert(1,Length(b)=Length(SmalldimHomomorphismsModules(m1,m2)));
   else

tst/testbugfix/2026-03-23-meataxe.tst

@@ -0,0 +1,12 @@
+# Handling of irreducible Meataxe modules with lots of generators was far
+# slower than necessary at least via the "high level" Meataxe APIs.
+# See also <https://github.com/gap-system/gap/issues/6271>.
+#
+# The main test here is for performance: before the fix for issue #6271 this
+# would have run for minutes, with the fix it should take far less than a
+# second on a modern computer.
+gap> n:=200;;   # increase this to make the effect even stronger
+gap> G:=GL(56,GF(25));;
+gap> H:=Subgroup(G, Concatenation(GeneratorsOfGroup(G),List([1..n],i->PseudoRandom(G))));;
+gap> MTX.IsomorphismModules(NaturalGModule(H), NaturalGModule(H)) <> fail;
+true