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r"""

Free String Monoids

AUTHORS:

- David Kohel <kohel@maths.usyd.edu.au>, 2007-01

Sage supports a wide range of specific free string monoids.

"""

from __future__ import absolute_import

#*****************************************************************************

# This program is free software: you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation, either version 2 of the License, or

# (at your option) any later version.

# http://www.gnu.org/licenses/

#*****************************************************************************

from .free_monoid import FreeMonoid_class

from .string_monoid_element import StringMonoidElement

from .string_ops import strip_encoding

import weakref

_cache = {}

def BinaryStrings():

r"""

Returns the free binary string monoid on generators `\{ 0, 1 \}`.

OUTPUT:

- Free binary string monoid.

EXAMPLES::

sage: S = BinaryStrings(); S

Free binary string monoid

sage: u = S('')

sage: u

sage: x = S('0')

sage: x

sage: y = S('1')

sage: y

sage: z = S('01110')

sage: z

01110

sage: x*y^3*x == z

True

sage: u*x == x*u

True

"""

# Here we cache the binary strings to make them unique

if 2 in _cache:

S = _cache[2]()

if not S is None:

return S

S = BinaryStringMonoid()

_cache[2] = weakref.ref(S)

return S

def OctalStrings():

r"""

Returns the free octal string monoid on generators `\{ 0, 1, \dots, 7 \}`.

OUTPUT:

- Free octal string monoid.

EXAMPLES::

sage: S = OctalStrings(); S

Free octal string monoid

sage: x = S.gens()

sage: x[0]

sage: x[7]

sage: x[0] * x[3]^3 * x[5]^4 * x[6]

033355556

"""

# Here we cache the octal strings to make them unique

if 8 in _cache:

S = _cache[8]()

if not S is None:

return S

S = OctalStringMonoid()

_cache[8] = weakref.ref(S)

return S

def HexadecimalStrings():

r"""

Returns the free hexadecimal string monoid on generators

`\{ 0, 1, \dots , 9, a, b, c, d, e, f \}`.

OUTPUT:

- Free hexadecimal string monoid.

EXAMPLES::

sage: S = HexadecimalStrings(); S

Free hexadecimal string monoid

sage: x = S.gen(0)

sage: y = S.gen(10)

sage: z = S.gen(15)

sage: z

sage: x*y^3*z

0aaaf

"""

# Here we cache the hexadecimal strings to make them unique

if 16 in _cache:

S = _cache[16]()

if not S is None:

return S

S = HexadecimalStringMonoid()

_cache[16] = weakref.ref(S)

return S

def Radix64Strings():

r"""

Returns the free radix 64 string monoid on 64 generators

A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z,

a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,

0,1,2,3,4,5,6,7,8,9,+,/

OUTPUT:

- Free radix 64 string monoid.

EXAMPLES::

sage: S = Radix64Strings(); S

Free radix 64 string monoid

sage: x = S.gens()

sage: x[0]

sage: x[62]

sage: x[63]

"""

# Here we cache the radix-64 strings to make them unique

if 64 in _cache:

S = _cache[64]()

if not S is None:

return S

S = Radix64StringMonoid()

_cache[64] = weakref.ref(S)

return S

def AlphabeticStrings():

r"""

Returns the string monoid on generators A-Z:

`\{ A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z \}`.

OUTPUT:

- Free alphabetic string monoid on A-Z.

EXAMPLES::

sage: S = AlphabeticStrings(); S

Free alphabetic string monoid on A-Z

sage: x = S.gens()

sage: x[0]

sage: x[25]

"""

# Here we cache the alphabetic strings to make them unique

if 26 in _cache:

S = _cache[26]()

if not S is None:

return S

S = AlphabeticStringMonoid()

_cache[26] = weakref.ref(S)

return S

#*****************************************************************************

class StringMonoid_class(FreeMonoid_class):

r"""

A free string monoid on `n` generators.

"""

def __init__(self, n, alphabet=()):

r"""

Create free binary string monoid on `n` generators.

INPUT:

- ``n`` -- Integer

- ``alphabet`` -- String or tuple whose characters or elements denote

the generators.

EXAMPLES::

sage: S = BinaryStrings(); S

Free binary string monoid

sage: x = S.gens()

sage: x[0]*x[1]**5 * (x[0]*x[1])

01111101

"""

# Names must be alphabetical -- omitted since printing is

# defined locally.

# FreeMonoid_class.__init__(self, n, names = alphabet)

FreeMonoid_class.__init__(self, n)

self._alphabet = alphabet

def __contains__(self, x):

return isinstance(x, StringMonoidElement) and x.parent() == self

def alphabet(self):

return tuple(self._alphabet)

def one(self):

r"""

Return the identity element of ``self``.

EXAMPLES::

sage: b = BinaryStrings(); b

Free binary string monoid

sage: b.one() * b('1011')

1011

sage: b.one() * b('110') == b('110')

True

sage: b('10101') * b.one() == b('101011')

False

"""

return StringMonoidElement(self, '')

def gen(self, i=0):

r"""

The `i`-th generator of the monoid.

INPUT:

- ``i`` -- integer (default: 0)

EXAMPLES::

sage: S = BinaryStrings()

sage: S.gen(0)

sage: S.gen(1)

sage: S.gen(2)

Traceback (most recent call last):

...

IndexError: Argument i (= 2) must be between 0 and 1.

sage: S = HexadecimalStrings()

sage: S.gen(0)

sage: S.gen(12)

sage: S.gen(16)

Traceback (most recent call last):

...

IndexError: Argument i (= 16) must be between 0 and 15.

"""

n = self.ngens()

if i < 0 or not i < n:

raise IndexError(

"Argument i (= %s) must be between 0 and %s." % (i, n-1))

return StringMonoidElement(self, [int(i)])

#*****************************************************************************

# Specific global string monoids

#*****************************************************************************

class BinaryStringMonoid(StringMonoid_class):

r"""

The free binary string monoid on generators `\{ 0, 1 \}`.

"""

def __init__(self):

r"""

Create free binary string monoid on generators `\{ 0, 1 \}`.

EXAMPLES::

sage: S = BinaryStrings(); S

Free binary string monoid

sage: x = S.gens()

sage: x[0]*x[1]**5 * (x[0]*x[1])

01111101

"""

StringMonoid_class.__init__(self, 2, ['0', '1'])

def __cmp__(self, other):

if not isinstance(other, BinaryStringMonoid):

return -1

return 0

def __repr__(self):

return "Free binary string monoid"

def __call__(self, x, check=True):

r"""

Return ``x`` coerced into this free monoid.

One can create a free binary string monoid element from a

Python string of 0's and 1's or list of integers.

NOTE: Due to the ambiguity of the second generator '1' with

the identity element '' of the monoid, the syntax S(1) is not

permissible.

EXAMPLES::

sage: S = BinaryStrings()

sage: S('101')

101

sage: S.gen(0)

sage: S.gen(1)

"""

## There should really some careful type checking here...

if isinstance(x, StringMonoidElement) and x.parent() == self:

return x

elif isinstance(x, list):

return StringMonoidElement(self, x, check)

elif isinstance(x, str):

return StringMonoidElement(self, x, check)

else:

raise TypeError("Argument x (= %s) is of the wrong type." % x)

def encoding(self, S, padic=False):

r"""

The binary encoding of the string ``S``, as a binary string element.

The default is to keep the standard ASCII byte encoding, e.g.

A = 65 -> 01000001

B = 66 -> 01000010

Z = 90 -> 01001110

rather than a 2-adic representation 65 -> 10000010.

Set ``padic=True`` to reverse the bit string.

EXAMPLES::

sage: S = BinaryStrings()

sage: S.encoding('A')

01000001

sage: S.encoding('A',padic=True)

10000010

sage: S.encoding(' ',padic=True)

00000100

"""

bit_string = []

for i in range(len(S)):

n = ord(S[i])

bits = []

for i in range(8):

bits.append(n%2)

n = n >> 1

if not padic:

bits.reverse()

bit_string.extend(bits)

return self(bit_string)

# def ngens(self):

# r"""

# Return the number of generators of this free binary string monoid.

# There are only 2 elements in the binary number system. Hence, this

# is the number of generators.

# EXAMPLES::

# sage: S = BinaryStrings()

# sage: S.ngens()

# 2

# """

# return 2

class OctalStringMonoid(StringMonoid_class):

r"""

The free octal string monoid on generators `\{ 0, 1, \dots, 7 \}`.

"""

def __init__(self):

r"""

Create free octal string monoid on generators `\{ 0, 1, \dots, 7 \}`.

EXAMPLES::

sage: S = OctalStrings(); S

Free octal string monoid

sage: x = S.gens()

sage: (x[0]*x[7])**3 * (x[0]*x[1]*x[6]*x[5])**2

07070701650165

sage: S([ i for i in range(8) ])

01234567

"""

StringMonoid_class.__init__(self, 8, [ str(i) for i in range(8) ])

def __cmp__(self, other):

if not isinstance(other, OctalStringMonoid):

return -1

return 0

def __repr__(self):

return "Free octal string monoid"

def __call__(self, x, check=True):

r"""

Return ``x`` coerced into this free monoid.

One can create a free octal string monoid element from a

Python string of 0's to 7's or list of integers.

EXAMPLES::

sage: S = OctalStrings()

sage: S('07070701650165')

07070701650165

sage: S.gen(0)

sage: S.gen(1)

sage: S([ i for i in range(8) ])

01234567

"""

## There should really some careful type checking here...

if isinstance(x, StringMonoidElement) and x.parent() == self:

return x

elif isinstance(x, list):

return StringMonoidElement(self, x, check)

elif isinstance(x, str):

return StringMonoidElement(self, x, check)

else:

raise TypeError("Argument x (= %s) is of the wrong type." % x)

class HexadecimalStringMonoid(StringMonoid_class):

r"""

The free hexadecimal string monoid on generators

`\{ 0, 1, \dots, 9, a, b, c, d, e, f \}`.

"""

def __init__(self):

r"""

Create free hexadecimal string monoid on generators

`\{ 0, 1, \dots, 9, a, b, c, d, e, f \}`.

EXAMPLES::

sage: S = HexadecimalStrings(); S

Free hexadecimal string monoid

sage: x = S.gens()

sage: (x[0]*x[10])**3 * (x[0]*x[1]*x[9]*x[15])**2

0a0a0a019f019f

sage: S([ i for i in range(16) ])

0123456789abcdef

"""

alph = '0123456789abcdef'

StringMonoid_class.__init__(self, 16, [ alph[i] for i in range(16) ])

def __cmp__(self, other):

if not isinstance(other, HexadecimalStringMonoid):

return -1

return 0

def __repr__(self):

return "Free hexadecimal string monoid"

def __call__(self, x, check=True):

r"""

Return ``x`` coerced into this free monoid.

One can create a free hexadecimal string monoid element from a

Python string of a list of integers in `\{ 0, \dots, 15 \}`.

EXAMPLES::

sage: S = HexadecimalStrings()

sage: S('0a0a0a019f019f')

0a0a0a019f019f

sage: S.gen(0)

sage: S.gen(1)

sage: S([ i for i in range(16) ])

0123456789abcdef

"""

## There should really some careful type checking here...

if isinstance(x, StringMonoidElement) and x.parent() == self:

return x

elif isinstance(x, list):

return StringMonoidElement(self, x, check)

elif isinstance(x, str):

return StringMonoidElement(self, x, check)

else:

raise TypeError("Argument x (= %s) is of the wrong type." % x)

def encoding(self, S, padic=False):

r"""

The encoding of the string ``S`` as a hexadecimal string element.

The default is to keep the standard right-to-left byte encoding, e.g.

A = '\x41' -> 41

B = '\x42' -> 42

Z = '\x5a' -> 5a

rather than a left-to-right representation A = 65 -> 14.

Although standard (e.g., in the Python constructor '\xhh'),

this can be confusing when the string reads left-to-right.

Set ``padic=True`` to reverse the character encoding.

EXAMPLES::

sage: S = HexadecimalStrings()

sage: S.encoding('A')

sage: S.encoding('A',padic=True)

sage: S.encoding(' ',padic=False)

sage: S.encoding(' ',padic=True)

"""

hex_string = []

for i in range(len(S)):

n = ord(S[i])

n0 = n % 16

n1 = n // 16

if not padic:

hex_chars = [n1, n0]

else:

hex_chars = [n0, n1]

hex_string.extend(hex_chars)

return self(hex_string)

class Radix64StringMonoid(StringMonoid_class):

r"""

The free radix 64 string monoid on 64 generators.

"""

def __init__(self):

r"""

Create free radix 64 string monoid on 64 generators.

EXAMPLES::

sage: S = Radix64Strings(); S

Free radix 64 string monoid

sage: x = S.gens()

sage: (x[50]*x[10])**3 * (x[60]*x[1]*x[19]*x[35])**2

yKyKyK8BTj8BTj

sage: S([ i for i in range(64) ])

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/

"""

alph = 'ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'

StringMonoid_class.__init__(self, 64, [ alph[i] for i in range(64) ])

def __cmp__(self, other):

if not isinstance(other, Radix64StringMonoid):

return -1

return 0

def __repr__(self):

return "Free radix 64 string monoid"

def __call__(self, x, check=True):

r"""

Return ``x`` coerced into this free monoid.

One can create a free radix 64 string monoid element from a

Python string or a list of integers in `0, \dots, 63`, as for

generic ``FreeMonoids``.

EXAMPLES::

sage: S = Radix64Strings()

sage: S.gen(0)

sage: S.gen(1)

sage: S.gen(62)

sage: S.gen(63)

sage: S([ i for i in range(64) ])

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/

"""

## There should really some careful type checking here...

if isinstance(x, StringMonoidElement) and x.parent() == self:

return x

elif isinstance(x, list):

return StringMonoidElement(self, x, check)

elif isinstance(x, str):

return StringMonoidElement(self, x, check)

else:

raise TypeError("Argument x (= %s) is of the wrong type." % x)

class AlphabeticStringMonoid(StringMonoid_class):

"""

The free alphabetic string monoid on generators A-Z.

EXAMPLES::

sage: S = AlphabeticStrings(); S

Free alphabetic string monoid on A-Z

sage: S.gen(0)

sage: S.gen(25)

sage: S([ i for i in range(26) ])

ABCDEFGHIJKLMNOPQRSTUVWXYZ

"""

def __init__(self):

r"""

Create free alphabetic string monoid on generators A-Z.

EXAMPLES::

sage: S = AlphabeticStrings(); S

Free alphabetic string monoid on A-Z

sage: S.gen(0)

sage: S.gen(25)

sage: S([ i for i in range(26) ])

ABCDEFGHIJKLMNOPQRSTUVWXYZ

"""

from sage.rings.all import RealField

RR = RealField()

# The characteristic frequency probability distribution of

# Robert Edward Lewand.

self._characteristic_frequency_lewand = {

"A": RR(0.08167), "B": RR(0.01492),

"C": RR(0.02782), "D": RR(0.04253),

"E": RR(0.12702), "F": RR(0.02228),

"G": RR(0.02015), "H": RR(0.06094),

"I": RR(0.06966), "J": RR(0.00153),

"K": RR(0.00772), "L": RR(0.04025),

"M": RR(0.02406), "N": RR(0.06749),

"O": RR(0.07507), "P": RR(0.01929),

"Q": RR(0.00095), "R": RR(0.05987),

"S": RR(0.06327), "T": RR(0.09056),

"U": RR(0.02758), "V": RR(0.00978),

"W": RR(0.02360), "X": RR(0.00150),

"Y": RR(0.01974), "Z": RR(0.00074)}

# The characteristic frequency probability distribution of

# H. Beker and F. Piper.

self._characteristic_frequency_beker_piper = {

"A": RR(0.082), "B": RR(0.015),

"C": RR(0.028), "D": RR(0.043),

"E": RR(0.127), "F": RR(0.022),

"G": RR(0.020), "H": RR(0.061),

"I": RR(0.070), "J": RR(0.002),

"K": RR(0.008), "L": RR(0.040),

"M": RR(0.024), "N": RR(0.067),

"O": RR(0.075), "P": RR(0.019),

"Q": RR(0.001), "R": RR(0.060),

"S": RR(0.063), "T": RR(0.091),

"U": RR(0.028), "V": RR(0.010),

"W": RR(0.023), "X": RR(0.001),

"Y": RR(0.020), "Z": RR(0.001)}

alph = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'

StringMonoid_class.__init__(self, 26, [ alph[i] for i in range(26) ])

def __cmp__(self, other):

if not isinstance(other, AlphabeticStringMonoid):

return -1

return 0

def __repr__(self):

return "Free alphabetic string monoid on A-Z"

def __call__(self, x, check=True):

r"""

Return ``x`` coerced into this free monoid.

One can create a free alphabetic string monoid element from a

Python string, or a list of integers in `0, \dots,25`.

EXAMPLES::

sage: S = AlphabeticStrings()

sage: S.gen(0)

sage: S.gen(1)

sage: S.gen(25)

sage: S([ i for i in range(26) ])

ABCDEFGHIJKLMNOPQRSTUVWXYZ

"""

## There should really some careful type checking here...

if isinstance(x, StringMonoidElement) and x.parent() == self:

return x

elif isinstance(x, list):

return StringMonoidElement(self, x, check)

elif isinstance(x, str):

return StringMonoidElement(self, x, check)

else:

raise TypeError("Argument x (= %s) is of the wrong type." % x)

def characteristic_frequency(self, table_name="beker_piper"):

r"""

Return a table of the characteristic frequency probability

distribution of the English alphabet. In written English, various

letters of the English alphabet occur more frequently than others.

For example, the letter "E" appears more often than other

vowels such as "A", "I", "O", and "U". In long works of written

English such as books, the probability of a letter occurring tends

to stabilize around a value. We call this value the characteristic

frequency probability of the letter under consideration. When this

probability is considered for each letter of the English alphabet,

the resulting probabilities for all letters of this alphabet is

referred to as the characteristic frequency probability distribution.

Various studies report slightly different values for the

characteristic frequency probability of an English letter. For

instance, [Lew2000]_ reports that "E" has a characteristic

frequency probability of 0.12702, while [BP1982]_ reports this

value as 0.127. The concepts of characteristic frequency probability

and characteristic frequency probability distribution can also be

applied to non-empty alphabets other than the English alphabet.

The output of this method is different from that of the method

:func:`frequency_distribution()

<sage.monoids.string_monoid_element.StringMonoidElement.frequency_distribution>`.

One can think of the characteristic frequency probability of an

element in an alphabet `A` as the expected probability of that element

occurring. Let `S` be a string encoded using elements of `A`. The

frequency probability distribution corresponding to `S` provides us

with the frequency probability of each element of `A` as observed

occurring in `S`. Thus one distribution provides expected

probabilities, while the other provides observed probabilities.

INPUT:

- ``table_name`` -- (default ``"beker_piper"``) the table of

characteristic frequency probability distribution to use. The

following tables are supported:

- ``"beker_piper"`` -- the table of characteristic frequency

probability distribution by Beker and Piper [BP1982]_. This is

the default table to use.

- ``"lewand"`` -- the table of characteristic frequency

probability distribution by Lewand as described on page 36

of [Lew2000]_.

OUTPUT:

- A table of the characteristic frequency probability distribution

of the English alphabet. This is a dictionary of letter/probability

pairs.

EXAMPLES:

The characteristic frequency probability distribution table of

Beker and Piper [BP1982]_::

sage: A = AlphabeticStrings()

sage: table = A.characteristic_frequency(table_name="beker_piper")

sage: sorted(table.items())

[('A', 0.0820000000000000),

('B', 0.0150000000000000),

('C', 0.0280000000000000),

('D', 0.0430000000000000),

('E', 0.127000000000000),

('F', 0.0220000000000000),

('G', 0.0200000000000000),

('H', 0.0610000000000000),

('I', 0.0700000000000000),

('J', 0.00200000000000000),

('K', 0.00800000000000000),

('L', 0.0400000000000000),

('M', 0.0240000000000000),

('N', 0.0670000000000000),

('O', 0.0750000000000000),

('P', 0.0190000000000000),

('Q', 0.00100000000000000),

('R', 0.0600000000000000),

('S', 0.0630000000000000),

('T', 0.0910000000000000),

('U', 0.0280000000000000),

('V', 0.0100000000000000),

('W', 0.0230000000000000),

('X', 0.00100000000000000),

('Y', 0.0200000000000000),

('Z', 0.00100000000000000)]

The characteristic frequency probability distribution table

of Lewand [Lew2000]_::

sage: table = A.characteristic_frequency(table_name="lewand")

sage: sorted(table.items())

[('A', 0.0816700000000000),

('B', 0.0149200000000000),

('C', 0.0278200000000000),

('D', 0.0425300000000000),

('E', 0.127020000000000),

('F', 0.0222800000000000),

('G', 0.0201500000000000),

('H', 0.0609400000000000),

('I', 0.0696600000000000),

('J', 0.00153000000000000),

('K', 0.00772000000000000),

('L', 0.0402500000000000),

('M', 0.0240600000000000),

('N', 0.0674900000000000),

('O', 0.0750700000000000),

('P', 0.0192900000000000),

('Q', 0.000950000000000000),

('R', 0.0598700000000000),

('S', 0.0632700000000000),

('T', 0.0905600000000000),

('U', 0.0275800000000000),

('V', 0.00978000000000000),

('W', 0.0236000000000000),

('X', 0.00150000000000000),

('Y', 0.0197400000000000),

('Z', 0.000740000000000000)]

Illustrating the difference between :func:`characteristic_frequency`

and :func:`frequency_distribution() <sage.monoids.string_monoid_element.StringMonoidElement.frequency_distribution>`::

sage: A = AlphabeticStrings()

sage: M = A.encoding("abcd")

sage: FD = M.frequency_distribution().function()

sage: sorted(FD.items())

[(A, 0.250000000000000),

(B, 0.250000000000000),

(C, 0.250000000000000),

(D, 0.250000000000000)]

sage: CF = A.characteristic_frequency()

sage: sorted(CF.items())

[('A', 0.0820000000000000),

('B', 0.0150000000000000),

('C', 0.0280000000000000),

('D', 0.0430000000000000),

('E', 0.127000000000000),

('F', 0.0220000000000000),

('G', 0.0200000000000000),

('H', 0.0610000000000000),

('I', 0.0700000000000000),

('J', 0.00200000000000000),

('K', 0.00800000000000000),

('L', 0.0400000000000000),

('M', 0.0240000000000000),

('N', 0.0670000000000000),

('O', 0.0750000000000000),

('P', 0.0190000000000000),

('Q', 0.00100000000000000),

('R', 0.0600000000000000),

('S', 0.0630000000000000),

('T', 0.0910000000000000),

('U', 0.0280000000000000),

('V', 0.0100000000000000),

('W', 0.0230000000000000),

('X', 0.00100000000000000),

('Y', 0.0200000000000000),

('Z', 0.00100000000000000)]

TESTS:

The table name must be either "beker_piper" or "lewand"::

sage: table = A.characteristic_frequency(table_name="")

Traceback (most recent call last):

...

ValueError: Table name must be either 'beker_piper' or 'lewand'.

sage: table = A.characteristic_frequency(table_name="none")

Traceback (most recent call last):

...

ValueError: Table name must be either 'beker_piper' or 'lewand'.

"""

supported_tables = ["beker_piper", "lewand"]

if table_name not in supported_tables:

raise ValueError(

"Table name must be either 'beker_piper' or 'lewand'.")

from copy import copy

if table_name == "beker_piper":

return copy(self._characteristic_frequency_beker_piper)

if table_name == "lewand":

return copy(self._characteristic_frequency_lewand)

def encoding(self, S):

r"""

The encoding of the string ``S`` in the alphabetic string monoid,

obtained by the monoid homomorphism

A -> A, ..., Z -> Z, a -> A, ..., z -> Z

and stripping away all other characters. It should be noted that

this is a non-injective monoid homomorphism.

EXAMPLES::

sage: S = AlphabeticStrings()

sage: s = S.encoding("The cat in the hat."); s

THECATINTHEHAT

sage: s.decoding()

'THECATINTHEHAT'

"""

return self(strip_encoding(S))

Coverage for local/lib/python2.7/site-packages/sage/monoids/string_monoid.py : 63%

187 statements 117 run 70 missing 0 excluded