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)
A
sage: S.gen(1)
B
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)
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)
A
sage: S.gen(1)
B
sage: S.gen(25)
Z
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 __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)
0
sage: S.gen(1)
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 __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)
0
sage: S.gen(1)
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)
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)
0
sage: S.gen(1)
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 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)
0
sage: S.gen(1)
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)
0
sage: S.gen(12)
c
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)])
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, '')
