From 6ff6a06261330d2e11aa862e1c59ac2c632a8da1 Mon Sep 17 00:00:00 2001
From: Nathann Cohen <nathann.cohen@gmail.com>
Date: Fri, 10 Jan 2014 12:27:28 +0100
Subject: [PATCH] trac #15285: Doc of AffineGeometryDesign

---
 src/sage/combinat/designs/block_design.py | 28 +++++++++++++++++------
 1 file changed, 21 insertions(+), 7 deletions(-)

diff --git a/src/sage/combinat/designs/block_design.py b/src/sage/combinat/designs/block_design.py
index 82c00a13e09..6916bdb4d86 100644
--- a/src/sage/combinat/designs/block_design.py
+++ b/src/sage/combinat/designs/block_design.py
@@ -219,14 +219,18 @@ def ProjectivePlaneDesign(n, type="Desarguesian"):
 
 def AffineGeometryDesign(n, d, F):
     r"""
+    Returns an Affine Geometry Design.
+
     INPUT:
 
-    - ``n`` is the Euclidean dimension, so the number of points is
+    - `n` (integer) -- the Euclidean dimension. The number of points is
+      `v=|F^n|`.
 
-    - ``v`` is the number of points `v = |F^n|` (`F = GF(q)`, some `q`)
+    - `d` (integer) -- the dimension of the (affine) subspaces of `P = GF(q)^n`
+      which make up the blocks.
 
-    - `d` is the dimension of the (affine) subspaces of `P = GF(q)^n` which make
-      up the blocks.
+    - `F` -- a Finite Field (i.e. ``FiniteField(17)``), or a prime power
+      (i.e. an integer)
 
     `AG_{n,d} (F)`, as it is sometimes denoted, is a `2` - `(v, k, \lambda)`
     design of points and `d`- flats (cosets of dimension `n`) in the affine
@@ -237,8 +241,8 @@ def AffineGeometryDesign(n, d, F):
              v = q^n,\  k = q^d ,
              \lambda =\frac{(q^{n-1}-1) \cdots (q^{n+1-d}-1)}{(q^{n-1}-1) \cdots (q-1)}.
 
-    Wraps some functions used in GAP Design's PGPointFlatBlockDesign.
-    Does *not* require GAP's Design.
+    Wraps some functions used in GAP Design's ``PGPointFlatBlockDesign``.  Does
+    *not* require GAP's Design package.
 
     EXAMPLES::
 
@@ -252,8 +256,18 @@ def AffineGeometryDesign(n, d, F):
         (2, 8, 4, 3)
         sage: BD.is_block_design()
         (True, [3, 8, 4, 1])
+
+    With an integer instead of a Finite Field::
+
+        sage: BD = designs.AffineGeometryDesign(3, 2, 4)
+        sage: BD.parameters()
+        (2, 64, 16, 5)
     """
-    q = F.order()
+    try:
+        q = int(F)
+    except TypeError:
+        q = F.order()
+
     from sage.interfaces.gap import gap, GapElement
     from sage.sets.set import Set
     gap.eval("V:=GaloisField(%s)^%s"%(q,n))