permutations: add one_based

sympy/combinatorics/permutations.py

@@ -33,6 +33,18 @@ def cyclic(cyclic_form1, n):
     rv.extend([[i] for i in sorted(need)])
     return rv
 
+def one_based(cyclic_form0, singletons=True):
+    """Return a cyclic form in 1-based cyclic form, omitting cycles
+    smaller than ``smallest``.
+    >>> from sympy.combinatorics.permutations import one_based
+    >>> one_based([[0, 1], [2]])
+    [[1, 2], [3]]
+    >>> one_based([[0, 1], [2]], singletons=False)
+    [[1, 2]]
+    """
+    min = 1 + (not bool(singletons))
+    return [[e + 1 for e in c] for c in cyclic_form0 if len(c) >= min]
+
 def _af_parity(pi):
     """
     Computes the parity of a permutation in array form.

sympy/combinatorics/tests/test_permutations.py

@@ -1,6 +1,6 @@
 from sympy.core import FiniteSet
 from sympy.combinatorics.permutations import (Permutation, _af_parity,
-    _af_mul, _af_mul, cyclic)
+    _af_mul, _af_mul, cyclic, one_based)
 
 from sympy.utilities.pytest import raises
 
@@ -21,6 +21,8 @@ def test_Permutation():
 
     assert cyclic([(2,3,5)], 5) == [[1, 2, 4], [0], [3]]
     assert cyclic([(2,3,5)], 3) == [[1, 2, 4], [0]]
+    assert one_based([[0, 1], [2]]) == [[1, 2], [3]]
+    assert one_based([[0, 1], [2]], singletons=False) == [[1, 2]]
     assert (Permutation([[1,2,3],[0,4]])*Permutation([[1,2,4],[0],[3]])).cyclic_form == \
         [[0, 4, 2], [1, 3]]
     assert q.array_form == [3, 1, 4, 5, 0, 6, 2]