From 69064893c437aaf7ee206839115a51caea9f37eb Mon Sep 17 00:00:00 2001
From: Andrew Tonks <48631703+0-andy-0@users.noreply.github.com>
Date: Mon, 15 Jul 2024 11:58:11 +0200
Subject: [PATCH 1/2] Update ncsf.py

Correction lines 184-189: Psi is not the tensor algebra on the primitives but on the generators of this free Lie algebra.
---
 src/sage/combinat/ncsf_qsym/ncsf.py | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/src/sage/combinat/ncsf_qsym/ncsf.py b/src/sage/combinat/ncsf_qsym/ncsf.py
index 65b03741885..731aa742ece 100644
--- a/src/sage/combinat/ncsf_qsym/ncsf.py
+++ b/src/sage/combinat/ncsf_qsym/ncsf.py
@@ -182,8 +182,11 @@ class NonCommutativeSymmetricFunctions(UniqueRepresentation, Parent):
     bialgebra structure, which cooperates with the grading to form a
     connected graded bialgebra. Thus, as any connected graded bialgebra,
     ``Psi`` is a Hopf algebra. Over ``QQ`` (or any other `\QQ`-algebra),
-    this Hopf algebra ``Psi`` is isomorphic to the tensor algebra of
-    its space of primitive elements.
+    this Hopf algebra ``Psi`` is isomorphic to the universal enveloping 
+    algebra of its space of primitive elements. Here, the primitives 
+    form a countably generated free Lie algebra, so ``Psi`` is isomorphic 
+    to the tensor algebra on a countably infinite dimensional vector 
+    space.
 
     The antipode is an anti-algebra morphism; in the ``Psi`` basis, it
     sends the generators to their opposites and changes their sign if

From fc78fd0f92e32c1798865a57688ee480b5299383 Mon Sep 17 00:00:00 2001
From: Andrew Tonks <48631703+0-andy-0@users.noreply.github.com>
Date: Mon, 15 Jul 2024 14:52:29 +0200
Subject: [PATCH 2/2] Update ncsf.py

trailing whitespace removed
---
 src/sage/combinat/ncsf_qsym/ncsf.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/src/sage/combinat/ncsf_qsym/ncsf.py b/src/sage/combinat/ncsf_qsym/ncsf.py
index 731aa742ece..dbab31a0080 100644
--- a/src/sage/combinat/ncsf_qsym/ncsf.py
+++ b/src/sage/combinat/ncsf_qsym/ncsf.py
@@ -182,10 +182,10 @@ class NonCommutativeSymmetricFunctions(UniqueRepresentation, Parent):
     bialgebra structure, which cooperates with the grading to form a
     connected graded bialgebra. Thus, as any connected graded bialgebra,
     ``Psi`` is a Hopf algebra. Over ``QQ`` (or any other `\QQ`-algebra),
-    this Hopf algebra ``Psi`` is isomorphic to the universal enveloping 
-    algebra of its space of primitive elements. Here, the primitives 
-    form a countably generated free Lie algebra, so ``Psi`` is isomorphic 
-    to the tensor algebra on a countably infinite dimensional vector 
+    this Hopf algebra ``Psi`` is isomorphic to the universal enveloping
+    algebra of its space of primitive elements. Here, the primitives
+    form a countably generated free Lie algebra, so ``Psi`` is isomorphic
+    to the tensor algebra on a countably infinite dimensional vector
     space.
 
     The antipode is an anti-algebra morphism; in the ``Psi`` basis, it