Added comment on convention

docs/src/InvariantTheory/reductive_groups.md

@@ -45,7 +45,8 @@ subfield $k$ of $K$ which is supported by OSCAR:
 
 In OSCAR, the basic set-up for a linearly reductive group in the context of Derksen's algorithm is provided by the 
 function `linearly_reductive_group`. At current state, this only supports rational actions of  the special linear group
-(in characteristic zero). For the action of this group by linear substitution on forms, an explicit Reynolds operator is
+(in characteristic zero). For the action of this group by linear
+substitution on, say, $n$-ary forms of degree $d$, an explicit Reynolds operator is
 given by Cayley's Omega-process. We show this at work later in this section.
 
 

experimental/InvariantTheory/src/InvariantTheory.jl

@@ -151,7 +151,11 @@ vector_space_dimension(R::RepresentationLinearlyReductiveGroup) = ncols(R.rep_ma
 @doc raw"""
     representation_on_forms(G::LinearlyReductiveGroup, d::Int)
 
-If `G` is the special linear group acting by linear substitution on forms of degree `d`, return the corresponding representation.
+If `G` is the special linear group acting by linear substitution on, say, `n`-ary forms of degree `d`, return the corresponding representation.
+
+!!! note
+    In accordance with classical papers, an $n$-ary form of degree $d$ in $K[x_1, \dots, x_n]$ is written as a $K$-linear combination
+    of the $K$-basis with elements $\binom{n}{I}x^I$. Here, $I = (i_1, \dots, i_n)\in\mathbb Z_{\geq 0}^n$ with $i_1+\dots +i_n =d$.
 
 # Examples
 ```jldoctest