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documentation and test changes
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@ChamanAgrawal
ChamanAgrawal committed Aug 1, 2019
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Showing 1 changed file with 55 additions and 55 deletions.
110 changes: 55 additions & 55 deletions src/sage/combinat/rsk.py
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Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,7 @@
of columns).
- Dual RSK (:class:`~sage.combinat.rsk.RuleDualRSK`).
- CoRSK (:class:`~sage.combinat.rsk.RuleCoRSK`), defined in [GR2018v5sol]_.
- Super RSK (:class:`~sage.combinat.rsk.RuleSuperRSK`), a combiantion of row
- Super RSK (:class:`~sage.combinat.rsk.RuleSuperRSK`), a combiantion of row
and column insertions defined in [RM2017]_.
Implementing your own insertion rule
Expand Down Expand Up @@ -1162,6 +1162,7 @@ def _backward_format_output(self, lower_row, upper_row, output,
return list(reversed(lower_row))
raise ValueError("invalid output option")


class RuleDualRSK(Rule):
r"""
A rule modeling the Dual RSK insertion.
Expand Down Expand Up @@ -1482,7 +1483,7 @@ def reverse_insertion(self, x, row):
x, row[y_pos] = row[y_pos], x
return x

def _backward_format_output(self, lower_row, upper_row, output,
def _backward_format_output(self, lower_row, upper_row, output,
p_is_standard, q_is_standard):
r"""
Return the final output of the ``RSK_inverse`` correspondence
Expand Down Expand Up @@ -1909,10 +1910,10 @@ class RuleSuperRSK(RuleRSK):
r"""
A rule modeling the SuperRSK insertion.
SuperRSK is based on :math:`\epsilon`-insertion which itself is a
SuperRSK is based on :math:`\epsilon`-insertion which is a
combination of row and column classical RSK insertion.
Super RSK insertion differs from classical RSK insertion in the
Super RSK insertion differs from the classical RSK insertion in the
following ways:
* The input (in terms of biwords) is no longer an arbitrary biword,
Expand All @@ -1926,11 +1927,11 @@ class RuleSuperRSK(RuleRSK):
they are semistandard super tableax.
* The main difference is in the way bumping works. Instead of having
only row bumping SuperRSK is based on :math:`\epsilon`-insertion
which is a combination of classical RSK bumping along the row and
a Dual RSK like bumping (i.e. when a number `k_i` is inserted into
the `i`-th row of `P`,it bumps out the first integer greater **or
equal to** `k_i` in the column) along the column.
only row bumping SuperRSK uses :math:`\epsilon`-insertion, a combination
of classical RSK bumping along the rows and a Dual RSK like bumping
(i.e. when a number `k_i` is inserted into the `i`-th row of `P`,it
bumps out the first integer greater **or equal to** `k_i` in the column)
along the column.
EXAMPLES::
Expand All @@ -1945,7 +1946,6 @@ class RuleSuperRSK(RuleRSK):
sage: RSK(["1p", "2p", 2, 2, "3p", "3p", 3, 3],
....: ["1p", 1, "2p", 2, "3p", "3p", "3p", 3], insertion='superRSK')
[[[1', 2, 3', 3], [1, 3'], [2'], [3']], [[1', 2, 3', 3], [2', 3'], [2], [3]]]
sage: from sage.combinat.super_tableau import SemistandardSuperTableau
sage: P = SemistandardSuperTableau([[1, '3p', 3], ['2p']])
sage: Q = SemistandardSuperTableau([['1p', 1, '2p'], [2]])
sage: RSK_inverse(P, Q, insertion=RSK.rules.superRSK)
Expand Down Expand Up @@ -1986,7 +1986,6 @@ class RuleSuperRSK(RuleRSK):
sage: t2 = Tableau([[1, 2, 3], [4], [5]])
sage: RSK_inverse(t1, t2, insertion=RSK.rules.RSK)
[[1, 2, 3, 4, 5], [1, 4, 5, 3, 2]]
sage: from sage.combinat.super_tableau import SemistandardSuperTableau
sage: t1 = SemistandardSuperTableau([[1, 2, 5], [3], [4]])
sage: t2 = SemistandardSuperTableau([[1, 2, 3], [4], [5]])
sage: RSK_inverse(t1, t2, insertion=RSK.rules.superRSK)
Expand All @@ -2012,12 +2011,7 @@ class RuleSuperRSK(RuleRSK):
[[], []]
sage: f = lambda p: RSK_inverse(*RSK(p, insertion=RSK.rules.superRSK),
....: insertion=RSK.rules.superRSK)
sage: def toPrimedEntry(p):
....: p1 = list(p)
....: for i in range(len(p)):
....: p1[i] = PrimedEntry(p[i])
....: return p1
sage: all(toPrimedEntry(p) == f(list(p))[1] for n in range(5)
sage: all(p == f(p)[1] for n in range(5)
....: for p in Permutations(n))
True
Expand Down Expand Up @@ -2062,30 +2056,22 @@ def to_pairs(self, obj1=None, obj2=None, check=True):
ValueError: invalid restricted superbiword
"""
from sage.combinat.shifted_primed_tableau import PrimedEntry
# Initializing itr for itr = None case
itr = None
if obj2 is None:
try:
itr = obj1._rsk_iter()
except AttributeError:
# If this is (something which looks like) a matrix
if obj1 and hasattr(obj1[0], '__getitem__'):
raise NotImplementedError("forward rule for matrices is not yet implemented")
# set recording list to default value [1', 1, 2', 2, ...]
rec = []
a = PrimedEntry('1p')
for i in range(len(obj1)):
rec.append(a)
a = a.increase_half()
# Converting entries of obj1 to PrimedEntry
for i in range(len(obj1)):
obj1[i] = PrimedEntry(obj1[i])
itr = zip(rec, obj1)
# set recording list (obj1) to default value [1', 1, 2', 2, ...]
obj2, obj1 = obj1, []
a = 0.5
for i in range(len(obj2)):
obj1.append(a)
a = a + 0.5
else:
# Converting entries of obj1 to PrimedEntry
for i in range(len(obj1)):
obj1[i] = PrimedEntry(obj1[i])
# Converting entries of obj2 to PrimedEntry
for i in range(len(obj2)):
obj2[i] = PrimedEntry(obj2[i])
if check:
if len(obj1) != len(obj2):
raise ValueError("the two arrays must be the same length")
Expand All @@ -2095,19 +2081,29 @@ def to_pairs(self, obj1=None, obj2=None, check=True):
# the pairs of corresponding entries of obj1
# and obj2 with mixed-parity is not allowed
for t, b in zip(obj1, obj2):
if t.is_primed() != b.is_primed():
if PrimedEntry(t).is_primed() != PrimedEntry(b).is_primed():
if (t, b) in mixed_parity:
raise ValueError("invalid restricted superbiword")
else:
mixed_parity.append((t, b))
itr = zip(obj1, obj2)
return itr
# Since the _rsk_iter() gives unprimed entries
# We will create obj1 and obj2 from it.
if itr:
obj1, obj2 = [], []
for i, j in itr:
obj1.append(i)
obj2.append(j)
# Converting entries of obj1 and obj2 to PrimedEntry
for i in range(len(obj1)):
obj1[i] = PrimedEntry(obj1[i])
obj2[i] = PrimedEntry(obj2[i])
return zip(obj1, obj2)

def _get_col(self, t, col_index):
r"""
Return the column as a list of a given tableau ``t`` (list of lists)
at index ``col_index`` (Indexing starting from zero).
EXAMPLES::
sage: from sage.combinat.rsk import RuleSuperRSK
Expand Down Expand Up @@ -2144,7 +2140,7 @@ def _set_col(self, t, col_index, col):
those entries of the corresponding column in ``t`` which have row
index less than ``length(col)`` will be set, rest will remain
unchanged.
EXAMPLES::
sage: from sage.combinat.rsk import RuleSuperRSK
Expand All @@ -2165,7 +2161,7 @@ def _set_col(self, t, col_index, col):
t[row_index].append(None)
# set value
t[row_index][col_index] = val

def forward_rule(self, obj1, obj2, check_standard=False, check=True):
r"""
Return a pair of tableaux obtained by applying forward
Expand Down Expand Up @@ -2207,7 +2203,6 @@ def forward_rule(self, obj1, obj2, check_standard=False, check=True):
EXAMPLES::
sage: from sage.combinat.rsk import RuleSuperRSK
sage: from sage.combinat.super_tableau import SemistandardSuperTableau
sage: p, q = RuleSuperRSK().forward_rule([1, 2], [1, 3]); p
[[1, 3]]
sage: q
Expand Down Expand Up @@ -2322,7 +2317,6 @@ def _forward_format_output(self, p, q, check_standard):
EXAMPLES::
sage: from sage.combinat.rsk import RuleSuperRSK
sage: from sage.combinat.super_tableau import SemistandardSuperTableau, StandardSuperTableau
sage: isinstance(RuleSuperRSK()._forward_format_output(
....: [['1p', 1, '2p']], [['1p', '1', '2p']], True)[0],
....: StandardSuperTableau)
Expand Down Expand Up @@ -2374,7 +2368,6 @@ def backward_rule(self, p, q, output='array'):
EXAMPLES::
sage: from sage.combinat.rsk import RuleSuperRSK
sage: from sage.combinat.super_tableau import SemistandardSuperTableau
sage: t1 = SemistandardSuperTableau([['1p', '3p', '4p'], [2], [3]])
sage: t2 = SemistandardSuperTableau([[1, 2, 4], [3], [5]])
sage: RuleSuperRSK().backward_rule(t1, t2, 'array')
Expand Down Expand Up @@ -2405,7 +2398,7 @@ def backward_rule(self, p, q, output='array'):
iter_dict = {v: k for k, v in iter_dict.items()}
for key in sorted(iter_dict, reverse=True):
row_index, col_index = (iter_dict[key], key) if epsilon == 0 else (key, iter_dict[key])
x = p_copy[row_index].pop() # Always the right-most entry
x = p_copy[row_index].pop() # Always the right-most entry
while True:
if value.is_primed() == x.is_primed():
# row bumping
Expand Down Expand Up @@ -2440,27 +2433,27 @@ def reverse_insertion(self, x, row, epsilon=0):
sage: from bisect import bisect_left, bisect_right
sage: r = [1, 3, 3, 3, 4]
sage: j = 2
sage: j, y_pos = RuleSuperRSK().reverse_insertion(j, r, epsilon=0); r
sage: j, y = RuleSuperRSK().reverse_insertion(j, r, epsilon=0); r
[2, 3, 3, 3, 4]
sage: j
1
sage: y_pos
sage: y
0
sage: r = [1, 3, 3, 3, 4]
sage: j = 3
sage: j, y_pos = RuleSuperRSK().reverse_insertion(j, r, epsilon=0); r
sage: j, y = RuleSuperRSK().reverse_insertion(j, r, epsilon=0); r
[3, 3, 3, 3, 4]
sage: j
1
sage: y_pos
sage: y
0
sage: r = [1, 3, 3, 3, 4]
sage: j = (3)
sage: j, y_pos = RuleSuperRSK().reverse_insertion(j, r, epsilon=1); r
sage: j, y = RuleSuperRSK().reverse_insertion(j, r, epsilon=1); r
[1, 3, 3, 3, 4]
sage: j
3
sage: y_pos
sage: y
3
"""
bisect = bisect_left if epsilon == 0 else bisect_right
Expand Down Expand Up @@ -2501,24 +2494,26 @@ def _backward_format_output(self, lower_row, upper_row, output,
....: [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'),
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':
raise NotImplementedError("backward rule for matrices is not yet implemented")
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 TypeError("q must be standard to have a %s as "
"valid output" %output)
raise ValueError("invalid output option")


Expand All @@ -2531,6 +2526,7 @@ class InsertionRules(object):
Hecke = RuleHecke
dualRSK = RuleDualRSK
coRSK = RuleCoRSK
superRSK = RuleSuperRSK

#####################################################################

Expand Down Expand Up @@ -2712,6 +2708,8 @@ def RSK(obj1=None, obj2=None, insertion=InsertionRules.RSK, check_standard=False
insertion = RSK.rules.dualRSK
elif insertion == 'coRSK':
insertion = RSK.rules.coRSK
elif insertion == 'superRSK':
insertion = RSK.rules.superRSK
else:
raise ValueError("invalid input")

Expand Down Expand Up @@ -2907,6 +2905,8 @@ def RSK_inverse(p, q, output='array', insertion=InsertionRules.RSK):
insertion = RSK.rules.dualRSK
elif insertion == 'coRSK':
insertion = RSK.rules.coRSK
elif insertion == 'superRSK':
insertion = RSK.rules.superRSK
else:
raise ValueError("invalid input")

Expand All @@ -2922,6 +2922,7 @@ def RSK_inverse(p, q, output='array', insertion=InsertionRules.RSK):

robinson_schensted_knuth_inverse = RSK_inverse


def to_matrix(t, b):
r"""
Return the integer matrix corresponding to a two-line array.
Expand Down Expand Up @@ -2960,4 +2961,3 @@ def to_matrix(t, b):
else:
entries[pos] = 1
return matrix(entries, sparse=True)

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