From: Fabian Seoane <fab...@fseoane.net>
variations is a routine that calculates all possible variations
of size n (with or without repetition) of a given set.
---
doc/src/modules.txt | 1 +
doc/src/modules/utilities/index.txt | 11 ++++++++
doc/src/modules/utilities/iterables.txt | 39 +++++++++++++++++++++++++++++++
sympy/utilities/iterables.py | 36 ++++++++++++++++++++++++++++
sympy/utilities/tests/test_iterables.py | 6 ++++-
5 files changed, 92 insertions(+), 1 deletions(-)
create mode 100644 doc/src/modules/utilities/index.txt
create mode 100644 doc/src/modules/utilities/iterables.txt
diff --git a/doc/src/modules.txt b/doc/src/modules.txt
index fca4eb6..6c46683 100644
--- a/doc/src/modules.txt
+++ b/doc/src/modules.txt
@@ -31,6 +31,7 @@ access any SymPy module, or use this contens:
modules/statistics.txt
modules/concrete.txt
modules/solvers.txt
+ modules/utilities/index.txt
Contributions to docs
---------------------
diff --git a/doc/src/modules/utilities/index.txt
b/doc/src/modules/utilities/index.txt
new file mode 100644
index 0000000..3e1e692
--- /dev/null
+++ b/doc/src/modules/utilities/index.txt
@@ -0,0 +1,11 @@
+Utilities
+=========
+
+This module contains some general purpose utilities that are used across SymPy
+
+Contents:
+
+.. toctree::
+ :maxdepth: 2
+
+ iterables.txt
\ No newline at end of file
diff --git a/doc/src/modules/utilities/iterables.txt
b/doc/src/modules/utilities/iterables.txt
new file mode 100644
index 0000000..023a3bc
--- /dev/null
+++ b/doc/src/modules/utilities/iterables.txt
@@ -0,0 +1,39 @@
+Iterables
+=========
+
+cartes
+------
+
+Returns the cartesian product of two sequences
+
+Examples::
+ >>> from sympy.utilities.iterables import cartes
+ >>> cartes([1,2,3], ['a', 'b', 'c'])
+ [[1, 'a'],
+ [1, 'b'],
+ [1, 'c'],
+ [2, 'a'],
+ [2, 'b'],
+ [2, 'c'],
+ [3, 'a'],
+ [3, 'b'],
+ [3, 'c']]
+
+
+
+variations
+----------
+
+variations(seq, n) Returns all the variations of the list of size n.
+
+Has an optional third argument. Must be a boolean value and makes the method
+return the variations with repetition if set to True, or the variations
+without repetition if set to False.
+
+Examples::
+ >>> from sympy.utilities.iterables import variations
+ >>> variations([1,2,3], 2)
+ [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1], [3, 2]]
+ >>> variations([1,2,3], 2, True)
+ [[1, 1], [1, 2], [1, 3], [2, 1], [2, 2], [2, 3], [3, 1], [3, 2], [3, 3]]
+
diff --git a/sympy/utilities/iterables.py b/sympy/utilities/iterables.py
index 6179622..24ebcd0 100644
--- a/sympy/utilities/iterables.py
+++ b/sympy/utilities/iterables.py
@@ -173,3 +173,39 @@ def recursion(result, M, k):
for elem in recursion([item], M[i + 1:], k - 1):
yield elem
+
+def cartes(seq0, seq1, modus='pair'):
+ """Return the cartesian product of two sequences """
+ if modus == 'pair':
+ return [[item0, item1] for item0 in seq0 for item1 in seq1]
+ elif modus == 'triple':
+ return [item0 + [item1] for item0 in seq0 for item1 in seq1]
+
+def variations(seq, n, repetition=False):
+ """Returns all the variations of the list of size n.
+
+ variations(seq, n, True) will return all the variations of the list of
+ size n with repetitions
+
+ variations(seq, n, False) will return all the variations of the list of
+ size n without repetitions
+ """
+ def setrep(seq): # remove sets with duplicates (repetition is relevant)
+ def delrep(seq): # remove duplicates while maintaining order
+ result = []
+ for item in seq:
+ if item not in result:
+ result.append(item)
+ return result
+ return [item for item in seq if item == delrep(item)]
+
+ if n == 1:
+ return [[item] for item in seq]
+ result = range(len(seq))
+ cartesmodus = 'pair'
+ for i in range(n-1):
+ result = cartes(result, range(len(seq)), cartesmodus)
+ if not repetition:
+ result = setrep(result)
+ cartesmodus = 'triple'
+ return [[seq[index] for index in indices] for indices in result]
diff --git a/sympy/utilities/tests/test_iterables.py
b/sympy/utilities/tests/test_iterables.py
index 1eea497..959c900 100644
--- a/sympy/utilities/tests/test_iterables.py
+++ b/sympy/utilities/tests/test_iterables.py
@@ -1,6 +1,6 @@
from sympy import symbols
from sympy.utilities.iterables import postorder_traversal, \
- preorder_traversal, flatten, subsets
+ preorder_traversal, flatten, subsets, variations
w,x,y,z= symbols('wxyz')
@@ -31,3 +31,7 @@ def test_subsets():
assert list(subsets([1, 2, 3], 2)) == [[1, 2], [1,3], [2, 3]]
assert list(subsets([1, 2, 3], 3)) == [[1, 2, 3]]
+def test_variations():
+ assert variations([1,2,3], 2) == [[1, 2], [1, 3], [2, 1], [2, 3], [3, 1],
[3, 2]]
+ assert variations([1,2,3], 2, True) == [[1, 1], [1, 2], [1, 3], [2, 1],
[2, 2], [2, 3], \
+ [3,1], [3,2], [3,3]]
--
1.6.1.2
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