Fixing some details; adding one more doctest for coverage.

Author: tscrim

src/sage/algebras/orlik_solomon.py

@@ -541,7 +541,7 @@ def aomoto_complex(self, omega):
         Return the Aomoto complex of ``self`` defined by ``omega``.
 
         Let `A(M)` be an Orlik-Solomon algebra of a matroid `M`. Let
-        `\omega \in A(M)_1` be an element of (homoegenous) degree 1.
+        `\omega \in A(M)_1` be an element of (homogeneous) degree 1.
         The Aomoto complete is the chain complex defined on `A(M)`
         with the differential defined by `\omega \wedge`.
 
@@ -570,6 +570,15 @@ def aomoto_complex(self, omega):
              1: Vector space of dimension 1 over Rational Field,
              2: Vector space of dimension 1 over Rational Field}
 
+        TESTS::
+
+            sage: OS = hyperplane_arrangements.braid(4).orlik_solomon_algebra(QQ)
+            sage: gens = OS.algebra_generators()
+            sage: OS.aomoto_complex(gens[0] * gens[1] * gens[3])
+            Traceback (most recent call last):
+            ...
+            ValueError: omega must be a homogeneous element of degree 1
+
         REFERENCES:
 
         - [BY2016]_

src/sage/categories/filtered_modules_with_basis.py

@@ -259,10 +259,11 @@ def hilbert_series(self, prec=None):
 
                 H(t) = \sum_{n=0}^{\infty} \ell(M_n / M_{n-1}) t^n,
 
-            where `\ell(M_n)` is the *length* of `M_n`, which is the
+            where `\ell(N)` is the *length* of `N`, which is the
             longest chain of submodules (over `R`), and by convention
-            `M_{-1} = \{0\}`. By the assumptions of the category, `M_n` is a
-            free `R`-module, and so `\ell(M_n)` is equal to the rank of `M_n`.
+            `M_{-1} = \{0\}`. By the assumptions of the category,
+            `M_n / M_{n-1}` is a free `R`-module, and so `\ell(M_n / M_{n-1})`
+            is equal to the rank of `M_n / M_{n-1}`.
 
             INPUT:
 
@@ -1171,12 +1172,13 @@ def hilbert_series(self, prec=None):
 
                 .. MATH::
 
-                    H(t) = \sum_{n=0}^{\infty} \ell(M_n) t^n,
+                    H(t) = \sum_{n=0}^{\infty} \ell(M_n / M_{n-1}) t^n,
 
-                where `\ell(M_n)` is the *length* of `M_n`, which is the
-                longest chain of submodules (over `R`). By the assumptions of
-                the category, `M_n` is a free `R`-module, and so `\ell(M_n)`
-                is equal to the rank of `M_n`.
+                where `\ell(N)` is the *length* of `N`, which is the
+                longest chain of submodules (over `R`), and by convention
+                `M_{-1} = \{0\}`. By the assumptions of the category,
+                `M_n / M_{n-1}` is a free `R`-module, and so
+                `\ell(M_n / M_{n-1})` is equal to the rank of `M_n / M_{n-1}`.
 
                 EXAMPLES::