Add a reference and examples for __getitem__

sagemath · Nov 28, 2023 · 486c776 · 486c776
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diff --git a/src/doc/en/reference/references/index.rst b/src/doc/en/reference/references/index.rst
@@ -1044,6 +1044,11 @@ REFERENCES:
             *Guide to using plantri*, version 5.0, 2016.
             http://cs.anu.edu.au/~bdm/plantri/plantri-guide.txt
 
+.. [BM2021] Alin Bostan and Ryuhei Mori,
+            *A simple and fast algorithm for computing the N-th term of a linearly recurrent sequence*,
+            Proceedings of Symposium on Simplicity in Algorithms (SOSA), pp. 118--132, 2021.
+            :doi:`10.1137/1.9781611976496.14`
+
 .. [BMBFLR2008] A. Blondin-Massé, S. Brlek, A. Frosini, S. Labbé,
                 S. Rinaldi, *Reconstructing words from a fixed
                 palindromic length sequence*, Proc. TCS 2008, 5th IFIP

diff --git a/src/sage/rings/cfinite_sequence.py b/src/sage/rings/cfinite_sequence.py
@@ -644,6 +644,14 @@ def __getitem__(self, key):
             [0, 0, 1, 2, 3, 4, 5, 6, 7, 8]
             sage: s = C(x^3 * (1 - x)^-2); s[0:10]
             [0, 0, 0, 1, 2, 3, 4, 5, 6, 7]
+            sage: s = C(1/(1-x^1000)); s[10^18]
+            1
+            sage: s = C(1/(1-x^1000)); s[10^20]
+            1
+
+        REFERENCES:
+
+        - [BM2021]_
         """
         if isinstance(key, slice):
             m = max(key.start, key.stop)