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Add support for words and refactor
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@ChamanAgrawal
ChamanAgrawal committed Jul 18, 2019
1 parent 05712e0 commit dd1d6dc
Showing 1 changed file with 50 additions and 31 deletions.
81 changes: 50 additions & 31 deletions src/sage/combinat/rsk.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1942,7 +1942,7 @@ class RuleSuperRSK(RuleRSK):
[[[1, 3], [3']], [[1, 2], [3]]]
sage: RSK([PrimedEntry(1), PrimedEntry(3), PrimedEntry("3p"),
....: PrimedEntry("2p")], insertion='superRSK')
[[[1, 3'], [2', 3]], [[1, 2], [3, 4]]]
[[[1, 3', 3], [2']], [[1', 1, 2'], [2]]]
sage: RSK([PrimedEntry("1p"), PrimedEntry("2p"), PrimedEntry(2),
....: PrimedEntry(2), PrimedEntry("3p"), PrimedEntry("3p"),
....: PrimedEntry(3), PrimedEntry(3)], [PrimedEntry("1p"),
Expand Down Expand Up @@ -2077,7 +2077,7 @@ def to_pairs(self, obj1=None, obj2=None, check=True):
[(2, 1), (1', 1), (1, 1')]
sage: list(RuleSuperRSK().to_pairs([PrimedEntry(1),
....: PrimedEntry('1p'), PrimedEntry('2p')]))
[(1, 1), (2, 1'), (3, 2')]
[(1', 1), (1, 1'), (2', 2')]
sage: list(RuleSuperRSK().to_pairs([PrimedEntry(1),
....: PrimedEntry(1)], [PrimedEntry('1p'),
....: PrimedEntry('1p')]))
Expand All @@ -2098,18 +2098,14 @@ def to_pairs(self, obj1=None, obj2=None, check=True):
try:
itr = obj1._rsk_iter()
except AttributeError:
# make recording list default to [1, 2, ...]
# try:
# t = []
# b = []
# for i, row in enumerate(obj1):
# for j, mult in enumerate(row):
# if mult > 0:
# t.extend([PrimedEntry(i+1)]*mult)
# b.extend([PrimedEntry(j+1)]*mult)
# make recording list default to [1', 1, 2', 2, ...]
if obj1 and hasattr(obj1[0], '__getitem__'):
raise NotImplementedError("forward rule for matrices is not yet implemented")
rec = []
a = PrimedEntry('1p')
for i in range(len(obj1)):
rec.append(PrimedEntry(i+1))
rec.append(a)
a = a.increase_half()
itr = zip(rec, obj1)
else:
if check:
Expand Down Expand Up @@ -2194,7 +2190,7 @@ def _set_col(self, t, col_index, col):
# set value
t[row_index][col_index] = val

def forward_rule(self, obj1, obj2, check_standard=False):
def forward_rule(self, obj1, obj2, check_standard=False, check=True):
r"""
Return a pair of tableaux obtained by applying forward
insertion to the restricted super biword ``[obj1, obj2]``.
Expand All @@ -2209,9 +2205,9 @@ def forward_rule(self, obj1, obj2, check_standard=False):
to be interpreted as the top row and the bottom row of
the biword;
# - a matrix ``obj1`` of nonnegative integers, to be
# interpreted as the generalized permutation in matrix
# form (in this case, ``obj2`` is ``None``);
- a matrix ``obj1`` of nonnegative integers, to be
interpreted as the generalized permutation in matrix
form (in this case, ``obj2`` is ``None``);
- a word ``obj1`` in an ordered alphabet, to be
interpreted as the bottom row of the biword (in this
Expand All @@ -2224,9 +2220,9 @@ def forward_rule(self, obj1, obj2, check_standard=False):
entries and bottom entries in the biword (in this case,
``obj2`` is ``None``).
# - ``check_standard`` -- (default: ``False``) check if either of the
# resulting tableaux is a standard tableau, and if so, typecast it
# as such
- ``check_standard`` -- (default: ``False``) check if either of the
resulting tableaux is a standard super tableau, and if so, typecast it
as such
- ``check`` -- (default: ``True``) whether to check
that ``obj1`` and ``obj2`` actually define a valid
Expand All @@ -2247,7 +2243,7 @@ def forward_rule(self, obj1, obj2, check_standard=False):
sage: isinstance(q, SemistandardSuperTableau)
True
"""
itr = self.to_pairs(obj1, obj2)
itr = self.to_pairs(obj1, obj2, check=check)
p = [] # the "insertion" tableau
q = [] # the "recording" tableau
for i, j in itr:
Expand All @@ -2271,11 +2267,10 @@ def forward_rule(self, obj1, obj2, check_standard=False):
break
else:
j = j1

else:
# column insertion
col_index += 1
if len(p) == 0 or col_index == len(p[0]):
if not p or col_index == len(p[0]):
self._set_col(p, col_index, [j])
self._set_col(q, col_index, [i])
break
Expand Down Expand Up @@ -2376,7 +2371,7 @@ def _forward_format_output(self, p, q, check_standard):
"""
from sage.combinat.tableau import SemistandardSuperTableau, StandardTableau, StandardSuperTableau

if len(p) == 0:
if not p:
return [StandardTableau([]), StandardTableau([])]
if check_standard:
try:
Expand All @@ -2402,7 +2397,7 @@ def backward_rule(self, p, q, output='array'):
- ``output`` -- (default: ``'array'``) if ``q`` is row-strict:
- ``'array'`` -- as a two-line array (i.e. restricted super biword)
# - ``'matrix'`` -- as a `\{0, 1\}`-matrix
- ``'matrix'`` -- as a matrix
and if ``q`` is standard, we can have the output:
Expand Down Expand Up @@ -2457,7 +2452,6 @@ def backward_rule(self, p, q, output='array'):
if row_index < 0:
break
x, col_index = self.reverse_insertion(x, p_copy[row_index], epsilon=epsilon)

else:
# column bumping
col_index -= 1
Expand All @@ -2468,7 +2462,7 @@ def backward_rule(self, p, q, output='array'):
self._set_col(p_copy, col_index, c)
upper_row.append(value)
lower_row.append(x)
return self._backward_format_output(lower_row, upper_row, output, p.is_standard(), q.is_standard())
return self._backward_format_output(lower_row, upper_row, output, q.is_standard())

def reverse_insertion(self, x, row, epsilon=0):
r"""
Expand Down Expand Up @@ -2518,7 +2512,8 @@ def reverse_insertion(self, x, row, epsilon=0):
x, row[y_pos] = row[y_pos], x
return x, y_pos

def _backward_format_output(self, lower_row, upper_row, output, p_is_standard, q_is_standard):
def _backward_format_output(self, lower_row, upper_row, output,
q_is_standard):
r"""
Return the final output of the ``RSK_inverse`` correspondence
from the output of the corresponding ``backward_rule``.
Expand All @@ -2537,14 +2532,38 @@ def _backward_format_output(self, lower_row, upper_row, output, p_is_standard, q
sage: RuleSuperRSK()._backward_format_output([PrimedEntry('1p'),
....: PrimedEntry(1), PrimedEntry('3p'), PrimedEntry(9)],
....: [PrimedEntry(1), PrimedEntry('2p'), PrimedEntry('3p'),
....: PrimedEntry(4)], 'array', False, False)
....: PrimedEntry(4)], 'array', False)
[[4, 3', 2', 1], [9, 3', 1, 1']]
sage: RuleSuperRSK()._backward_format_output([PrimedEntry(1),
....: PrimedEntry('2p'), PrimedEntry('3p'), PrimedEntry(4)],
....: [PrimedEntry('1p'), PrimedEntry(1), PrimedEntry('2p'),
....: PrimedEntry(2)], 'word', True)
word: 4,3',2',1
sage: RuleSuperRSK()._backward_format_output([PrimedEntry(1),
....: PrimedEntry(2), PrimedEntry(3), PrimedEntry(4)],
....: [PrimedEntry('1p'), PrimedEntry(1), PrimedEntry('2p'),
....: PrimedEntry(2)], 'word', True)
word: 4321
sage: RuleSuperRSK()._backward_format_output([PrimedEntry('1p'),
....: PrimedEntry(1), PrimedEntry('3p'), PrimedEntry(9)],
....: [PrimedEntry(1), PrimedEntry('2p'), PrimedEntry('3p'),
....: PrimedEntry(4)], 'matrix', True)
Traceback (most recent call last):
...
NotImplementedError: backward rule for matrices is not yet implemented
"""
# if output == 'matrix':
# return to_matrix(list(reversed(upper_row)), list(reversed(lower_row)))
if output == 'matrix':
raise NotImplementedError("backward rule for matrices is not yet implemented")
if output == 'array':
return [list(reversed(upper_row)), list(reversed(lower_row))]
if output == 'word':
if q_is_standard:
from sage.combinat.words.word import Word
return Word(reversed(lower_row))
else:
raise TypeError("q must be standard to have a %s as valid output" %output)
raise ValueError("invalid output option")


class InsertionRules(object):
r"""
Expand Down

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