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RingSeq

Info

Listed here below are methods in the form RingSeq(Seq).method(...) via the wrapper class RingSeq. The same exact methods exist in their original form method(Seq, ...) and are available in the ring_seq.methods module.

ring_seq.RingSeq.RingSeq

Wrapper class for circular methods.

Use this class to enable dot notation.

Attributes:

Name Type Description
underlying

The wrapped sequence.
Source code in src/ring_seq/RingSeq.py 
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class RingSeq:
    """Wrapper class for circular methods.

    Use this class to enable dot notation.

    Attributes:
        underlying: The wrapped sequence.
    """

    def __init__(self, underlying: Seq):
        """Initializes the instance with the sequence."""
        self.underlying = underlying

    def index_from(self, i: IndexO) -> Index:
        """Normalizes a given circular index of a sequence.

        Examples:
          >>> RingSeq('ABC').index_from(-1)
          2
          >>> RingSeq('ABC').index_from(3)
          0

        Args:
          i: circular index

        Returns:
          A standard index

        Raises:
          ArithmeticError: An error occurs if the sequence is empty.
        """
        return index_from(self.underlying, i)

    def apply_o(self, i: IndexO) -> Any:
        """Gets the element at some circular index.

        Examples:
          >>> RingSeq('ABC').apply_o(-1)
          'C'
          >>> RingSeq('ABC').apply_o(3)
          'A'
          >>> 'ABC'[-1]
          'C'
          >>> 'ABC'[3] # doctest: +SKIP
          IndexError: string index out of range

        Notes:
          As shown in the examples, behaves differently from standard method `[i]`.

        Args:
          i: circular index

        Returns:
          The element at circular index
        """
        return apply_o(self.underlying, i)

    def rotate_right(self, step: int) -> Seq:
        """Rotates the sequence to the right by some steps.

        Examples:
          >>> RingSeq('ABC').rotate_right(1)
          'CAB'

        Args:
          step: number of rotation steps to the right

        Returns:
          The rotated sequence
        """
        return rotate_right(self.underlying, step)

    def rotate_left(self, step: int) -> Seq:
        """Rotates the sequence to the left by some steps.

        Examples:
          >>> RingSeq('ABC').rotate_left(1)
          'BCA'

        Args:
          step: number of rotation steps to the left

        Returns:
          The rotated sequence
        """
        return rotate_left(self.underlying, step)

    def start_at(self, i: IndexO) -> Seq:
        """Rotates the sequence to start at some circular index.

        Examples:
          >>> RingSeq('ABC').start_at(1)
          'BCA'

        Notes:
          Is equivalent to `rotate_left`.

        Args:
          i: circular index where the sequence starts

        Returns:
          The rotated sequence
        """
        return start_at(self.underlying, i)

    def reflect_at(self, i: IndexO = 0) -> Seq:
        """Reflects the sequence to start at some circular index.

        Examples:
          >>> RingSeq('ABC').reflect_at()
          'ACB'
          >>> RingSeq('ABC').reflect_at(1)
          'BAC'

        Notes:
          `reflect_at(-1)` is equivalent to `reversed`.

        Args:
          i: circular index where the reflected sequence starts

        Returns:
          The reflected sequence
        """
        return reflect_at(self.underlying, i)

    def slice_o(self, start: IndexO, end: IndexO, step: int = 1) -> Seq:
        """Selects an interval of elements.

        Examples:
          >>> RingSeq('ABC').slice_o(-1, 5)
          'CABCAB'
          >>> 'ABC'[-1:5]
          'C'
          >>> RingSeq('ABC').slice_o(-1, 5, 2)
          'CBA'
          >>> 'ABC'[-1:5:2]
          'C'

        Notes:
          Given the definition of circular sequence, a slice can contain more elements than the sequence itself.
          As shown in the examples, behaves differently from standard methods `[i:j]` and `[i:j:k]`.

        Args:
          start: circular index where the slice starts
          end: circular index where the slice ends
          step: number of steps for filtering

        Returns:
          The sliced sequence, with only the first element every each step

        Raises:
          ValueError: An error occurs if slice step is zero.
        """
        return slice_o(self.underlying, start, end, step)

    def rotations(self) -> Iterator[Seq]:
        """Computes all the rotations of this circular sequence

        Examples:
          >>> list(RingSeq('ABC').rotations())
          ['ABC', 'BCA', 'CAB']
          >>> list(RingSeq('').rotations())
          []

        Returns:
          The sequence and its rotations, 1 step at a time to the left
        """
        return rotations(self.underlying)

    def index_o(self, x: Any, start: IndexO = 0, end: IndexO = maxsize) -> Index:
        """Gets the index of the first occurrence of a sub-sequence.

        Examples:
          >>> RingSeq('ABC').index_o('B', 2, 7)
          1
          >>> 'ABC'.index('B', 2, 7) # doctest: +SKIP
          ValueError: substring not found
          >>> RingSeq('ABC').index_o('BCAB', 2, 8)
          1

        Notes:
          Given the definition of circular sequence, the searched slice can contain more elements than the sequence itself.
          As shown in the examples, behaves differently from standard method `index(x[, i[, j]])`.

        Args:
          x: sub-sequence to be found, can be a `str` or a single element from a `list` or from a `tuple`
          start: circular index where the search starts
          end: circular index where the search ends

        Returns:
          A standard index

        Raises:
          Value error: An error occurs if the sub-sequence is invalid or not found.
        """
        return index_o(self.underlying, x, start, end)

    def reflections(self) -> Iterator[Seq]:
        """Computes all the reflections of this circular sequence

        Examples:
          >>> list(RingSeq('ABC').reflections())
          ['ABC', 'ACB']
          >>> list(RingSeq('').reflections())
          []

        Returns:
          The sequence and its reflection
        """
        return reflections(self.underlying)

    def reversions(self) -> Iterator[Seq]:
        """Computes all the reversions of this circular sequence

        Examples:
          >>> list(RingSeq('ABC').reversions())
          ['ABC', 'CBA']
          >>> list(RingSeq('').reversions())
          []

        Returns:
          The sequence and its reversion
        """
        return reversions(self.underlying)

    def rotations_and_reflections(self) -> Iterator[Seq]:
        """Computes all the rotations and reflections of this circular sequence

        Examples:
          >>> list(RingSeq('ABC').rotations_and_reflections())
          ['ABC', 'BCA', 'CAB', 'ACB', 'CBA', 'BAC']
          >>> list(RingSeq('').rotations_and_reflections())
          []

        Returns:
          The sequence and its rotations, and their reflections
        """
        return rotations_and_reflections(self.underlying)

    def is_rotation_of(self, that: Seq) -> bool:
        """Tests whether this circular sequence is a rotation of a given sequence.

        Examples:
          >>> RingSeq('ABC').is_rotation_of('BCA')
          True
          >>> RingSeq('ABC').is_rotation_of('ABC')
          True

        Args:
          that: sequence to be compared

        Returns:
          True if equal to any rotation of that
        """
        return is_rotation_of(self.underlying, that)

    def is_reflection_of(self, that: Seq) -> bool:
        """Tests whether this circular sequence is a reflection of a given sequence.

        Examples:
          >>> RingSeq('ABC').is_reflection_of('ACB')
          True
          >>> RingSeq('ABC').is_reflection_of('ABC')
          True

        Args:
          that: sequence to be compared

        Returns:
          True if equal to any reflection of that
        """
        return is_reflection_of(self.underlying, that)

    def is_reversion_of(self, that: Seq) -> bool:
        """Tests whether this circular sequence is a reversion of a given sequence.

        Examples:
          >>> RingSeq('ABC').is_reversion_of('CBA')
          True
          >>> RingSeq('ABC').is_reversion_of('ABC')
          True

        Args:
          that: sequence to be compared

        Returns:
          True if equal to any reversion of that
        """
        return is_reversion_of(self.underlying, that)

    def is_rotation_or_reflection_of(self, that: Seq) -> bool:
        """Tests whether this circular sequence is a rotation and/or reflection of a given sequence.

        Examples:
          >>> RingSeq('ABC').is_rotation_or_reflection_of('BAC')
          True
          >>> RingSeq('ABC').is_rotation_or_reflection_of('ABC')
          True

        Args:
          that: sequence to be compared

        Returns:
          True if equal to any combination of rotation and reflection of that
        """
        return is_rotation_or_reflection_of(self.underlying, that)

    def rotational_symmetry(self) -> int:
        """Computes the order of rotational symmetry possessed by this circular sequence.

        Examples:
          >>> RingSeq('-|--|--|--|-').rotational_symmetry()
          4
          >>> RingSeq('-|+-|+-|+-|+').rotational_symmetry()
          4

        Returns:
          The rotational symmetry order, that is the number >= 1 of rotations
          in which a circular sequence looks exactly the same
        """
        return rotational_symmetry(self.underlying)

    def symmetry_indices(self) -> list[Index]:
        """Finds the indices of each element of this circular sequence close to an axis of reflectional symmetry.

        Examples:
          >>> RingSeq('-|--|--|--|-').symmetry_indices()
          [1, 4, 7, 10]
          >>> RingSeq('-|+-|+-|+-|+').symmetry_indices()
          []

        Returns:
          The indices of each element close to an axis of reflectional symmetry,
          that is a line of symmetry that splits the sequence in two identical halves
        """
        return symmetry_indices(self.underlying)

    def symmetry(self) -> int:
        """Computes the order of reflectional (mirror) symmetry possessed by this circular sequence.

        Examples:
          >>> RingSeq('-|--|--|--|-').symmetry()
          4
          >>> RingSeq('-|+-|+-|+-|+').symmetry()
          0

        Notes:
          Reflectional symmetry is always lower or equal than rotational symmetry.

        Returns:
          The reflectional (mirror) symmetry order, that is the number >= 0 of reflections
          in which a circular sequence looks exactly the same
        """
        return symmetry(self.underlying)

__init__(underlying)

Initializes the instance with the sequence.

Source code in src/ring_seq/RingSeq.py 
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def __init__(self, underlying: Seq):
    """Initializes the instance with the sequence."""
    self.underlying = underlying

apply_o(i)

Gets the element at some circular index.

Examples:

>>> RingSeq('ABC').apply_o(-1)
'C'
>>> RingSeq('ABC').apply_o(3)
'A'
>>> 'ABC'[-1]
'C'
>>> 'ABC'[3]
IndexError: string index out of range
Notes

As shown in the examples, behaves differently from standard method [i].

Parameters:

Name Type Description Default
i IndexO

circular index

 required

Returns:

Type Description
Any

The element at circular index
Source code in src/ring_seq/RingSeq.py 
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def apply_o(self, i: IndexO) -> Any:
    """Gets the element at some circular index.

    Examples:
      >>> RingSeq('ABC').apply_o(-1)
      'C'
      >>> RingSeq('ABC').apply_o(3)
      'A'
      >>> 'ABC'[-1]
      'C'
      >>> 'ABC'[3] # doctest: +SKIP
      IndexError: string index out of range

    Notes:
      As shown in the examples, behaves differently from standard method `[i]`.

    Args:
      i: circular index

    Returns:
      The element at circular index
    """
    return apply_o(self.underlying, i)

index_from(i)

Normalizes a given circular index of a sequence.

Examples:

>>> RingSeq('ABC').index_from(-1)
2
>>> RingSeq('ABC').index_from(3)
0

Parameters:

Name Type Description Default
i IndexO

circular index

 required

Returns:

Type Description
Index

A standard index

Raises:

Type Description
ArithmeticError

An error occurs if the sequence is empty.
Source code in src/ring_seq/RingSeq.py 
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def index_from(self, i: IndexO) -> Index:
    """Normalizes a given circular index of a sequence.

    Examples:
      >>> RingSeq('ABC').index_from(-1)
      2
      >>> RingSeq('ABC').index_from(3)
      0

    Args:
      i: circular index

    Returns:
      A standard index

    Raises:
      ArithmeticError: An error occurs if the sequence is empty.
    """
    return index_from(self.underlying, i)

index_o(x, start=0, end=maxsize)

Gets the index of the first occurrence of a sub-sequence.

Examples:

>>> RingSeq('ABC').index_o('B', 2, 7)
1
>>> 'ABC'.index('B', 2, 7)
ValueError: substring not found
>>> RingSeq('ABC').index_o('BCAB', 2, 8)
1
Notes

Given the definition of circular sequence, the searched slice can contain more elements than the sequence itself. As shown in the examples, behaves differently from standard method index(x[, i[, j]]).

Parameters:

Name Type Description Default
x Any

sub-sequence to be found, can be a str or a single element from a list or from a tuple

 required
start IndexO

circular index where the search starts

 0
end IndexO

circular index where the search ends

 maxsize

Returns:

Type Description
Index

A standard index

Raises:

Type Description
Value error

An error occurs if the sub-sequence is invalid or not found.
Source code in src/ring_seq/RingSeq.py 
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def index_o(self, x: Any, start: IndexO = 0, end: IndexO = maxsize) -> Index:
    """Gets the index of the first occurrence of a sub-sequence.

    Examples:
      >>> RingSeq('ABC').index_o('B', 2, 7)
      1
      >>> 'ABC'.index('B', 2, 7) # doctest: +SKIP
      ValueError: substring not found
      >>> RingSeq('ABC').index_o('BCAB', 2, 8)
      1

    Notes:
      Given the definition of circular sequence, the searched slice can contain more elements than the sequence itself.
      As shown in the examples, behaves differently from standard method `index(x[, i[, j]])`.

    Args:
      x: sub-sequence to be found, can be a `str` or a single element from a `list` or from a `tuple`
      start: circular index where the search starts
      end: circular index where the search ends

    Returns:
      A standard index

    Raises:
      Value error: An error occurs if the sub-sequence is invalid or not found.
    """
    return index_o(self.underlying, x, start, end)

is_reflection_of(that)

Tests whether this circular sequence is a reflection of a given sequence.

Examples:

>>> RingSeq('ABC').is_reflection_of('ACB')
True
>>> RingSeq('ABC').is_reflection_of('ABC')
True

Parameters:

Name Type Description Default
that Seq

sequence to be compared

 required

Returns:

Type Description
bool

True if equal to any reflection of that
Source code in src/ring_seq/RingSeq.py 
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def is_reflection_of(self, that: Seq) -> bool:
    """Tests whether this circular sequence is a reflection of a given sequence.

    Examples:
      >>> RingSeq('ABC').is_reflection_of('ACB')
      True
      >>> RingSeq('ABC').is_reflection_of('ABC')
      True

    Args:
      that: sequence to be compared

    Returns:
      True if equal to any reflection of that
    """
    return is_reflection_of(self.underlying, that)

is_reversion_of(that)

Tests whether this circular sequence is a reversion of a given sequence.

Examples:

>>> RingSeq('ABC').is_reversion_of('CBA')
True
>>> RingSeq('ABC').is_reversion_of('ABC')
True

Parameters:

Name Type Description Default
that Seq

sequence to be compared

 required

Returns:

Type Description
bool

True if equal to any reversion of that
Source code in src/ring_seq/RingSeq.py 
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def is_reversion_of(self, that: Seq) -> bool:
    """Tests whether this circular sequence is a reversion of a given sequence.

    Examples:
      >>> RingSeq('ABC').is_reversion_of('CBA')
      True
      >>> RingSeq('ABC').is_reversion_of('ABC')
      True

    Args:
      that: sequence to be compared

    Returns:
      True if equal to any reversion of that
    """
    return is_reversion_of(self.underlying, that)

is_rotation_of(that)

Tests whether this circular sequence is a rotation of a given sequence.

Examples:

>>> RingSeq('ABC').is_rotation_of('BCA')
True
>>> RingSeq('ABC').is_rotation_of('ABC')
True

Parameters:

Name Type Description Default
that Seq

sequence to be compared

 required

Returns:

Type Description
bool

True if equal to any rotation of that
Source code in src/ring_seq/RingSeq.py 
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def is_rotation_of(self, that: Seq) -> bool:
    """Tests whether this circular sequence is a rotation of a given sequence.

    Examples:
      >>> RingSeq('ABC').is_rotation_of('BCA')
      True
      >>> RingSeq('ABC').is_rotation_of('ABC')
      True

    Args:
      that: sequence to be compared

    Returns:
      True if equal to any rotation of that
    """
    return is_rotation_of(self.underlying, that)

is_rotation_or_reflection_of(that)

Tests whether this circular sequence is a rotation and/or reflection of a given sequence.

Examples:

>>> RingSeq('ABC').is_rotation_or_reflection_of('BAC')
True
>>> RingSeq('ABC').is_rotation_or_reflection_of('ABC')
True

Parameters:

Name Type Description Default
that Seq

sequence to be compared

 required

Returns:

Type Description
bool

True if equal to any combination of rotation and reflection of that
Source code in src/ring_seq/RingSeq.py 
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def is_rotation_or_reflection_of(self, that: Seq) -> bool:
    """Tests whether this circular sequence is a rotation and/or reflection of a given sequence.

    Examples:
      >>> RingSeq('ABC').is_rotation_or_reflection_of('BAC')
      True
      >>> RingSeq('ABC').is_rotation_or_reflection_of('ABC')
      True

    Args:
      that: sequence to be compared

    Returns:
      True if equal to any combination of rotation and reflection of that
    """
    return is_rotation_or_reflection_of(self.underlying, that)

reflect_at(i=0)

Reflects the sequence to start at some circular index.

Examples:

>>> RingSeq('ABC').reflect_at()
'ACB'
>>> RingSeq('ABC').reflect_at(1)
'BAC'
Notes

reflect_at(-1) is equivalent to reversed.

Parameters:

Name Type Description Default
i IndexO

circular index where the reflected sequence starts

 0

Returns:

Type Description
Seq

The reflected sequence
Source code in src/ring_seq/RingSeq.py 
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def reflect_at(self, i: IndexO = 0) -> Seq:
    """Reflects the sequence to start at some circular index.

    Examples:
      >>> RingSeq('ABC').reflect_at()
      'ACB'
      >>> RingSeq('ABC').reflect_at(1)
      'BAC'

    Notes:
      `reflect_at(-1)` is equivalent to `reversed`.

    Args:
      i: circular index where the reflected sequence starts

    Returns:
      The reflected sequence
    """
    return reflect_at(self.underlying, i)

reflections()

Computes all the reflections of this circular sequence

Examples:

>>> list(RingSeq('ABC').reflections())
['ABC', 'ACB']
>>> list(RingSeq('').reflections())
[]

Returns:

Type Description
Iterator[Seq]

The sequence and its reflection
Source code in src/ring_seq/RingSeq.py 
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def reflections(self) -> Iterator[Seq]:
    """Computes all the reflections of this circular sequence

    Examples:
      >>> list(RingSeq('ABC').reflections())
      ['ABC', 'ACB']
      >>> list(RingSeq('').reflections())
      []

    Returns:
      The sequence and its reflection
    """
    return reflections(self.underlying)

reversions()

Computes all the reversions of this circular sequence

Examples:

>>> list(RingSeq('ABC').reversions())
['ABC', 'CBA']
>>> list(RingSeq('').reversions())
[]

Returns:

Type Description
Iterator[Seq]

The sequence and its reversion
Source code in src/ring_seq/RingSeq.py 
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def reversions(self) -> Iterator[Seq]:
    """Computes all the reversions of this circular sequence

    Examples:
      >>> list(RingSeq('ABC').reversions())
      ['ABC', 'CBA']
      >>> list(RingSeq('').reversions())
      []

    Returns:
      The sequence and its reversion
    """
    return reversions(self.underlying)

rotate_left(step)

Rotates the sequence to the left by some steps.

Examples:

>>> RingSeq('ABC').rotate_left(1)
'BCA'

Parameters:

Name Type Description Default
step int

number of rotation steps to the left

 required

Returns:

Type Description
Seq

The rotated sequence
Source code in src/ring_seq/RingSeq.py 
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def rotate_left(self, step: int) -> Seq:
    """Rotates the sequence to the left by some steps.

    Examples:
      >>> RingSeq('ABC').rotate_left(1)
      'BCA'

    Args:
      step: number of rotation steps to the left

    Returns:
      The rotated sequence
    """
    return rotate_left(self.underlying, step)

rotate_right(step)

Rotates the sequence to the right by some steps.

Examples:

>>> RingSeq('ABC').rotate_right(1)
'CAB'

Parameters:

Name Type Description Default
step int

number of rotation steps to the right

 required

Returns:

Type Description
Seq

The rotated sequence
Source code in src/ring_seq/RingSeq.py 
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def rotate_right(self, step: int) -> Seq:
    """Rotates the sequence to the right by some steps.

    Examples:
      >>> RingSeq('ABC').rotate_right(1)
      'CAB'

    Args:
      step: number of rotation steps to the right

    Returns:
      The rotated sequence
    """
    return rotate_right(self.underlying, step)

rotational_symmetry()

Computes the order of rotational symmetry possessed by this circular sequence.

Examples:

>>> RingSeq('-|--|--|--|-').rotational_symmetry()
4
>>> RingSeq('-|+-|+-|+-|+').rotational_symmetry()
4

Returns:

Type Description
int

The rotational symmetry order, that is the number >= 1 of rotations
int

in which a circular sequence looks exactly the same
Source code in src/ring_seq/RingSeq.py 
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def rotational_symmetry(self) -> int:
    """Computes the order of rotational symmetry possessed by this circular sequence.

    Examples:
      >>> RingSeq('-|--|--|--|-').rotational_symmetry()
      4
      >>> RingSeq('-|+-|+-|+-|+').rotational_symmetry()
      4

    Returns:
      The rotational symmetry order, that is the number >= 1 of rotations
      in which a circular sequence looks exactly the same
    """
    return rotational_symmetry(self.underlying)

rotations()

Computes all the rotations of this circular sequence

Examples:

>>> list(RingSeq('ABC').rotations())
['ABC', 'BCA', 'CAB']
>>> list(RingSeq('').rotations())
[]

Returns:

Type Description
Iterator[Seq]

The sequence and its rotations, 1 step at a time to the left
Source code in src/ring_seq/RingSeq.py 
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def rotations(self) -> Iterator[Seq]:
    """Computes all the rotations of this circular sequence

    Examples:
      >>> list(RingSeq('ABC').rotations())
      ['ABC', 'BCA', 'CAB']
      >>> list(RingSeq('').rotations())
      []

    Returns:
      The sequence and its rotations, 1 step at a time to the left
    """
    return rotations(self.underlying)

rotations_and_reflections()

Computes all the rotations and reflections of this circular sequence

Examples:

>>> list(RingSeq('ABC').rotations_and_reflections())
['ABC', 'BCA', 'CAB', 'ACB', 'CBA', 'BAC']
>>> list(RingSeq('').rotations_and_reflections())
[]

Returns:

Type Description
Iterator[Seq]

The sequence and its rotations, and their reflections
Source code in src/ring_seq/RingSeq.py 
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def rotations_and_reflections(self) -> Iterator[Seq]:
    """Computes all the rotations and reflections of this circular sequence

    Examples:
      >>> list(RingSeq('ABC').rotations_and_reflections())
      ['ABC', 'BCA', 'CAB', 'ACB', 'CBA', 'BAC']
      >>> list(RingSeq('').rotations_and_reflections())
      []

    Returns:
      The sequence and its rotations, and their reflections
    """
    return rotations_and_reflections(self.underlying)

slice_o(start, end, step=1)

Selects an interval of elements.

Examples:

>>> RingSeq('ABC').slice_o(-1, 5)
'CABCAB'
>>> 'ABC'[-1:5]
'C'
>>> RingSeq('ABC').slice_o(-1, 5, 2)
'CBA'
>>> 'ABC'[-1:5:2]
'C'
Notes

Given the definition of circular sequence, a slice can contain more elements than the sequence itself. As shown in the examples, behaves differently from standard methods [i:j] and [i:j:k].

Parameters:

Name Type Description Default
start IndexO

circular index where the slice starts

 required
end IndexO

circular index where the slice ends

 required
step int

number of steps for filtering

 1

Returns:

Type Description
Seq

The sliced sequence, with only the first element every each step

Raises:

Type Description
ValueError

An error occurs if slice step is zero.
Source code in src/ring_seq/RingSeq.py 
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def slice_o(self, start: IndexO, end: IndexO, step: int = 1) -> Seq:
    """Selects an interval of elements.

    Examples:
      >>> RingSeq('ABC').slice_o(-1, 5)
      'CABCAB'
      >>> 'ABC'[-1:5]
      'C'
      >>> RingSeq('ABC').slice_o(-1, 5, 2)
      'CBA'
      >>> 'ABC'[-1:5:2]
      'C'

    Notes:
      Given the definition of circular sequence, a slice can contain more elements than the sequence itself.
      As shown in the examples, behaves differently from standard methods `[i:j]` and `[i:j:k]`.

    Args:
      start: circular index where the slice starts
      end: circular index where the slice ends
      step: number of steps for filtering

    Returns:
      The sliced sequence, with only the first element every each step

    Raises:
      ValueError: An error occurs if slice step is zero.
    """
    return slice_o(self.underlying, start, end, step)

start_at(i)

Rotates the sequence to start at some circular index.

Examples:

>>> RingSeq('ABC').start_at(1)
'BCA'
Notes

Is equivalent to rotate_left.

Parameters:

Name Type Description Default
i IndexO

circular index where the sequence starts

 required

Returns:

Type Description
Seq

The rotated sequence
Source code in src/ring_seq/RingSeq.py 
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def start_at(self, i: IndexO) -> Seq:
    """Rotates the sequence to start at some circular index.

    Examples:
      >>> RingSeq('ABC').start_at(1)
      'BCA'

    Notes:
      Is equivalent to `rotate_left`.

    Args:
      i: circular index where the sequence starts

    Returns:
      The rotated sequence
    """
    return start_at(self.underlying, i)

symmetry()

Computes the order of reflectional (mirror) symmetry possessed by this circular sequence.

Examples:

>>> RingSeq('-|--|--|--|-').symmetry()
4
>>> RingSeq('-|+-|+-|+-|+').symmetry()
0
Notes

Reflectional symmetry is always lower or equal than rotational symmetry.

Returns:

Type Description
int

The reflectional (mirror) symmetry order, that is the number >= 0 of reflections
int

in which a circular sequence looks exactly the same
Source code in src/ring_seq/RingSeq.py 
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def symmetry(self) -> int:
    """Computes the order of reflectional (mirror) symmetry possessed by this circular sequence.

    Examples:
      >>> RingSeq('-|--|--|--|-').symmetry()
      4
      >>> RingSeq('-|+-|+-|+-|+').symmetry()
      0

    Notes:
      Reflectional symmetry is always lower or equal than rotational symmetry.

    Returns:
      The reflectional (mirror) symmetry order, that is the number >= 0 of reflections
      in which a circular sequence looks exactly the same
    """
    return symmetry(self.underlying)

symmetry_indices()

Finds the indices of each element of this circular sequence close to an axis of reflectional symmetry.

Examples:

>>> RingSeq('-|--|--|--|-').symmetry_indices()
[1, 4, 7, 10]
>>> RingSeq('-|+-|+-|+-|+').symmetry_indices()
[]

Returns:

Type Description
list[Index]

The indices of each element close to an axis of reflectional symmetry,
list[Index]

that is a line of symmetry that splits the sequence in two identical halves
Source code in src/ring_seq/RingSeq.py 
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def symmetry_indices(self) -> list[Index]:
    """Finds the indices of each element of this circular sequence close to an axis of reflectional symmetry.

    Examples:
      >>> RingSeq('-|--|--|--|-').symmetry_indices()
      [1, 4, 7, 10]
      >>> RingSeq('-|+-|+-|+-|+').symmetry_indices()
      []

    Returns:
      The indices of each element close to an axis of reflectional symmetry,
      that is a line of symmetry that splits the sequence in two identical halves
    """
    return symmetry_indices(self.underlying)