two version of R2R are here HEAD master

1 files changed, 1046 insertions, 0 deletions

diff --git a/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py b/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py
new file mode 100644
index 00000000..b32fa955
--- /dev/null
+++ b/.venv/lib/python3.12/site-packages/setuptools/_vendor/more_itertools/recipes.py
@@ -0,0 +1,1046 @@
+"""Imported from the recipes section of the itertools documentation.
+
+All functions taken from the recipes section of the itertools library docs
+[1]_.
+Some backward-compatible usability improvements have been made.
+
+.. [1] http://docs.python.org/library/itertools.html#recipes
+
+"""
+
+import math
+import operator
+
+from collections import deque
+from collections.abc import Sized
+from functools import partial, reduce
+from itertools import (
+    chain,
+    combinations,
+    compress,
+    count,
+    cycle,
+    groupby,
+    islice,
+    product,
+    repeat,
+    starmap,
+    tee,
+    zip_longest,
+)
+from random import randrange, sample, choice
+from sys import hexversion
+
+__all__ = [
+    'all_equal',
+    'batched',
+    'before_and_after',
+    'consume',
+    'convolve',
+    'dotproduct',
+    'first_true',
+    'factor',
+    'flatten',
+    'grouper',
+    'iter_except',
+    'iter_index',
+    'matmul',
+    'ncycles',
+    'nth',
+    'nth_combination',
+    'padnone',
+    'pad_none',
+    'pairwise',
+    'partition',
+    'polynomial_eval',
+    'polynomial_from_roots',
+    'polynomial_derivative',
+    'powerset',
+    'prepend',
+    'quantify',
+    'reshape',
+    'random_combination_with_replacement',
+    'random_combination',
+    'random_permutation',
+    'random_product',
+    'repeatfunc',
+    'roundrobin',
+    'sieve',
+    'sliding_window',
+    'subslices',
+    'sum_of_squares',
+    'tabulate',
+    'tail',
+    'take',
+    'totient',
+    'transpose',
+    'triplewise',
+    'unique',
+    'unique_everseen',
+    'unique_justseen',
+]
+
+_marker = object()
+
+
+# zip with strict is available for Python 3.10+
+try:
+    zip(strict=True)
+except TypeError:
+    _zip_strict = zip
+else:
+    _zip_strict = partial(zip, strict=True)
+
+# math.sumprod is available for Python 3.12+
+_sumprod = getattr(math, 'sumprod', lambda x, y: dotproduct(x, y))
+
+
+def take(n, iterable):
+    """Return first *n* items of the iterable as a list.
+
+        >>> take(3, range(10))
+        [0, 1, 2]
+
+    If there are fewer than *n* items in the iterable, all of them are
+    returned.
+
+        >>> take(10, range(3))
+        [0, 1, 2]
+
+    """
+    return list(islice(iterable, n))
+
+
+def tabulate(function, start=0):
+    """Return an iterator over the results of ``func(start)``,
+    ``func(start + 1)``, ``func(start + 2)``...
+
+    *func* should be a function that accepts one integer argument.
+
+    If *start* is not specified it defaults to 0. It will be incremented each
+    time the iterator is advanced.
+
+        >>> square = lambda x: x ** 2
+        >>> iterator = tabulate(square, -3)
+        >>> take(4, iterator)
+        [9, 4, 1, 0]
+
+    """
+    return map(function, count(start))
+
+
+def tail(n, iterable):
+    """Return an iterator over the last *n* items of *iterable*.
+
+    >>> t = tail(3, 'ABCDEFG')
+    >>> list(t)
+    ['E', 'F', 'G']
+
+    """
+    # If the given iterable has a length, then we can use islice to get its
+    # final elements. Note that if the iterable is not actually Iterable,
+    # either islice or deque will throw a TypeError. This is why we don't
+    # check if it is Iterable.
+    if isinstance(iterable, Sized):
+        yield from islice(iterable, max(0, len(iterable) - n), None)
+    else:
+        yield from iter(deque(iterable, maxlen=n))
+
+
+def consume(iterator, n=None):
+    """Advance *iterable* by *n* steps. If *n* is ``None``, consume it
+    entirely.
+
+    Efficiently exhausts an iterator without returning values. Defaults to
+    consuming the whole iterator, but an optional second argument may be
+    provided to limit consumption.
+
+        >>> i = (x for x in range(10))
+        >>> next(i)
+        0
+        >>> consume(i, 3)
+        >>> next(i)
+        4
+        >>> consume(i)
+        >>> next(i)
+        Traceback (most recent call last):
+          File "<stdin>", line 1, in <module>
+        StopIteration
+
+    If the iterator has fewer items remaining than the provided limit, the
+    whole iterator will be consumed.
+
+        >>> i = (x for x in range(3))
+        >>> consume(i, 5)
+        >>> next(i)
+        Traceback (most recent call last):
+          File "<stdin>", line 1, in <module>
+        StopIteration
+
+    """
+    # Use functions that consume iterators at C speed.
+    if n is None:
+        # feed the entire iterator into a zero-length deque
+        deque(iterator, maxlen=0)
+    else:
+        # advance to the empty slice starting at position n
+        next(islice(iterator, n, n), None)
+
+
+def nth(iterable, n, default=None):
+    """Returns the nth item or a default value.
+
+    >>> l = range(10)
+    >>> nth(l, 3)
+    3
+    >>> nth(l, 20, "zebra")
+    'zebra'
+
+    """
+    return next(islice(iterable, n, None), default)
+
+
+def all_equal(iterable, key=None):
+    """
+    Returns ``True`` if all the elements are equal to each other.
+
+        >>> all_equal('aaaa')
+        True
+        >>> all_equal('aaab')
+        False
+
+    A function that accepts a single argument and returns a transformed version
+    of each input item can be specified with *key*:
+
+        >>> all_equal('AaaA', key=str.casefold)
+        True
+        >>> all_equal([1, 2, 3], key=lambda x: x < 10)
+        True
+
+    """
+    return len(list(islice(groupby(iterable, key), 2))) <= 1
+
+
+def quantify(iterable, pred=bool):
+    """Return the how many times the predicate is true.
+
+    >>> quantify([True, False, True])
+    2
+
+    """
+    return sum(map(pred, iterable))
+
+
+def pad_none(iterable):
+    """Returns the sequence of elements and then returns ``None`` indefinitely.
+
+        >>> take(5, pad_none(range(3)))
+        [0, 1, 2, None, None]
+
+    Useful for emulating the behavior of the built-in :func:`map` function.
+
+    See also :func:`padded`.
+
+    """
+    return chain(iterable, repeat(None))
+
+
+padnone = pad_none
+
+
+def ncycles(iterable, n):
+    """Returns the sequence elements *n* times
+
+    >>> list(ncycles(["a", "b"], 3))
+    ['a', 'b', 'a', 'b', 'a', 'b']
+
+    """
+    return chain.from_iterable(repeat(tuple(iterable), n))
+
+
+def dotproduct(vec1, vec2):
+    """Returns the dot product of the two iterables.
+
+    >>> dotproduct([10, 10], [20, 20])
+    400
+
+    """
+    return sum(map(operator.mul, vec1, vec2))
+
+
+def flatten(listOfLists):
+    """Return an iterator flattening one level of nesting in a list of lists.
+
+        >>> list(flatten([[0, 1], [2, 3]]))
+        [0, 1, 2, 3]
+
+    See also :func:`collapse`, which can flatten multiple levels of nesting.
+
+    """
+    return chain.from_iterable(listOfLists)
+
+
+def repeatfunc(func, times=None, *args):
+    """Call *func* with *args* repeatedly, returning an iterable over the
+    results.
+
+    If *times* is specified, the iterable will terminate after that many
+    repetitions:
+
+        >>> from operator import add
+        >>> times = 4
+        >>> args = 3, 5
+        >>> list(repeatfunc(add, times, *args))
+        [8, 8, 8, 8]
+
+    If *times* is ``None`` the iterable will not terminate:
+
+        >>> from random import randrange
+        >>> times = None
+        >>> args = 1, 11
+        >>> take(6, repeatfunc(randrange, times, *args))  # doctest:+SKIP
+        [2, 4, 8, 1, 8, 4]
+
+    """
+    if times is None:
+        return starmap(func, repeat(args))
+    return starmap(func, repeat(args, times))
+
+
+def _pairwise(iterable):
+    """Returns an iterator of paired items, overlapping, from the original
+
+    >>> take(4, pairwise(count()))
+    [(0, 1), (1, 2), (2, 3), (3, 4)]
+
+    On Python 3.10 and above, this is an alias for :func:`itertools.pairwise`.
+
+    """
+    a, b = tee(iterable)
+    next(b, None)
+    return zip(a, b)
+
+
+try:
+    from itertools import pairwise as itertools_pairwise
+except ImportError:
+    pairwise = _pairwise
+else:
+
+    def pairwise(iterable):
+        return itertools_pairwise(iterable)
+
+    pairwise.__doc__ = _pairwise.__doc__
+
+
+class UnequalIterablesError(ValueError):
+    def __init__(self, details=None):
+        msg = 'Iterables have different lengths'
+        if details is not None:
+            msg += (': index 0 has length {}; index {} has length {}').format(
+                *details
+            )
+
+        super().__init__(msg)
+
+
+def _zip_equal_generator(iterables):
+    for combo in zip_longest(*iterables, fillvalue=_marker):
+        for val in combo:
+            if val is _marker:
+                raise UnequalIterablesError()
+        yield combo
+
+
+def _zip_equal(*iterables):
+    # Check whether the iterables are all the same size.
+    try:
+        first_size = len(iterables[0])
+        for i, it in enumerate(iterables[1:], 1):
+            size = len(it)
+            if size != first_size:
+                raise UnequalIterablesError(details=(first_size, i, size))
+        # All sizes are equal, we can use the built-in zip.
+        return zip(*iterables)
+    # If any one of the iterables didn't have a length, start reading
+    # them until one runs out.
+    except TypeError:
+        return _zip_equal_generator(iterables)
+
+
+def grouper(iterable, n, incomplete='fill', fillvalue=None):
+    """Group elements from *iterable* into fixed-length groups of length *n*.
+
+    >>> list(grouper('ABCDEF', 3))
+    [('A', 'B', 'C'), ('D', 'E', 'F')]
+
+    The keyword arguments *incomplete* and *fillvalue* control what happens for
+    iterables whose length is not a multiple of *n*.
+
+    When *incomplete* is `'fill'`, the last group will contain instances of
+    *fillvalue*.
+
+    >>> list(grouper('ABCDEFG', 3, incomplete='fill', fillvalue='x'))
+    [('A', 'B', 'C'), ('D', 'E', 'F'), ('G', 'x', 'x')]
+
+    When *incomplete* is `'ignore'`, the last group will not be emitted.
+
+    >>> list(grouper('ABCDEFG', 3, incomplete='ignore', fillvalue='x'))
+    [('A', 'B', 'C'), ('D', 'E', 'F')]
+
+    When *incomplete* is `'strict'`, a subclass of `ValueError` will be raised.
+
+    >>> it = grouper('ABCDEFG', 3, incomplete='strict')
+    >>> list(it)  # doctest: +IGNORE_EXCEPTION_DETAIL
+    Traceback (most recent call last):
+    ...
+    UnequalIterablesError
+
+    """
+    args = [iter(iterable)] * n
+    if incomplete == 'fill':
+        return zip_longest(*args, fillvalue=fillvalue)
+    if incomplete == 'strict':
+        return _zip_equal(*args)
+    if incomplete == 'ignore':
+        return zip(*args)
+    else:
+        raise ValueError('Expected fill, strict, or ignore')
+
+
+def roundrobin(*iterables):
+    """Yields an item from each iterable, alternating between them.
+
+        >>> list(roundrobin('ABC', 'D', 'EF'))
+        ['A', 'D', 'E', 'B', 'F', 'C']
+
+    This function produces the same output as :func:`interleave_longest`, but
+    may perform better for some inputs (in particular when the number of
+    iterables is small).
+
+    """
+    # Algorithm credited to George Sakkis
+    iterators = map(iter, iterables)
+    for num_active in range(len(iterables), 0, -1):
+        iterators = cycle(islice(iterators, num_active))
+        yield from map(next, iterators)
+
+
+def partition(pred, iterable):
+    """
+    Returns a 2-tuple of iterables derived from the input iterable.
+    The first yields the items that have ``pred(item) == False``.
+    The second yields the items that have ``pred(item) == True``.
+
+        >>> is_odd = lambda x: x % 2 != 0
+        >>> iterable = range(10)
+        >>> even_items, odd_items = partition(is_odd, iterable)
+        >>> list(even_items), list(odd_items)
+        ([0, 2, 4, 6, 8], [1, 3, 5, 7, 9])
+
+    If *pred* is None, :func:`bool` is used.
+
+        >>> iterable = [0, 1, False, True, '', ' ']
+        >>> false_items, true_items = partition(None, iterable)
+        >>> list(false_items), list(true_items)
+        ([0, False, ''], [1, True, ' '])
+
+    """
+    if pred is None:
+        pred = bool
+
+    t1, t2, p = tee(iterable, 3)
+    p1, p2 = tee(map(pred, p))
+    return (compress(t1, map(operator.not_, p1)), compress(t2, p2))
+
+
+def powerset(iterable):
+    """Yields all possible subsets of the iterable.
+
+        >>> list(powerset([1, 2, 3]))
+        [(), (1,), (2,), (3,), (1, 2), (1, 3), (2, 3), (1, 2, 3)]
+
+    :func:`powerset` will operate on iterables that aren't :class:`set`
+    instances, so repeated elements in the input will produce repeated elements
+    in the output.
+
+        >>> seq = [1, 1, 0]
+        >>> list(powerset(seq))
+        [(), (1,), (1,), (0,), (1, 1), (1, 0), (1, 0), (1, 1, 0)]
+
+    For a variant that efficiently yields actual :class:`set` instances, see
+    :func:`powerset_of_sets`.
+    """
+    s = list(iterable)
+    return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))
+
+
+def unique_everseen(iterable, key=None):
+    """
+    Yield unique elements, preserving order.
+
+        >>> list(unique_everseen('AAAABBBCCDAABBB'))
+        ['A', 'B', 'C', 'D']
+        >>> list(unique_everseen('ABBCcAD', str.lower))
+        ['A', 'B', 'C', 'D']
+
+    Sequences with a mix of hashable and unhashable items can be used.
+    The function will be slower (i.e., `O(n^2)`) for unhashable items.
+
+    Remember that ``list`` objects are unhashable - you can use the *key*
+    parameter to transform the list to a tuple (which is hashable) to
+    avoid a slowdown.
+
+        >>> iterable = ([1, 2], [2, 3], [1, 2])
+        >>> list(unique_everseen(iterable))  # Slow
+        [[1, 2], [2, 3]]
+        >>> list(unique_everseen(iterable, key=tuple))  # Faster
+        [[1, 2], [2, 3]]
+
+    Similarly, you may want to convert unhashable ``set`` objects with
+    ``key=frozenset``. For ``dict`` objects,
+    ``key=lambda x: frozenset(x.items())`` can be used.
+
+    """
+    seenset = set()
+    seenset_add = seenset.add
+    seenlist = []
+    seenlist_add = seenlist.append
+    use_key = key is not None
+
+    for element in iterable:
+        k = key(element) if use_key else element
+        try:
+            if k not in seenset:
+                seenset_add(k)
+                yield element
+        except TypeError:
+            if k not in seenlist:
+                seenlist_add(k)
+                yield element
+
+
+def unique_justseen(iterable, key=None):
+    """Yields elements in order, ignoring serial duplicates
+
+    >>> list(unique_justseen('AAAABBBCCDAABBB'))
+    ['A', 'B', 'C', 'D', 'A', 'B']
+    >>> list(unique_justseen('ABBCcAD', str.lower))
+    ['A', 'B', 'C', 'A', 'D']
+
+    """
+    if key is None:
+        return map(operator.itemgetter(0), groupby(iterable))
+
+    return map(next, map(operator.itemgetter(1), groupby(iterable, key)))
+
+
+def unique(iterable, key=None, reverse=False):
+    """Yields unique elements in sorted order.
+
+    >>> list(unique([[1, 2], [3, 4], [1, 2]]))
+    [[1, 2], [3, 4]]
+
+    *key* and *reverse* are passed to :func:`sorted`.
+
+    >>> list(unique('ABBcCAD', str.casefold))
+    ['A', 'B', 'c', 'D']
+    >>> list(unique('ABBcCAD', str.casefold, reverse=True))
+    ['D', 'c', 'B', 'A']
+
+    The elements in *iterable* need not be hashable, but they must be
+    comparable for sorting to work.
+    """
+    return unique_justseen(sorted(iterable, key=key, reverse=reverse), key=key)
+
+
+def iter_except(func, exception, first=None):
+    """Yields results from a function repeatedly until an exception is raised.
+
+    Converts a call-until-exception interface to an iterator interface.
+    Like ``iter(func, sentinel)``, but uses an exception instead of a sentinel
+    to end the loop.
+
+        >>> l = [0, 1, 2]
+        >>> list(iter_except(l.pop, IndexError))
+        [2, 1, 0]
+
+    Multiple exceptions can be specified as a stopping condition:
+
+        >>> l = [1, 2, 3, '...', 4, 5, 6]
+        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
+        [7, 6, 5]
+        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
+        [4, 3, 2]
+        >>> list(iter_except(lambda: 1 + l.pop(), (IndexError, TypeError)))
+        []
+
+    """
+    try:
+        if first is not None:
+            yield first()
+        while 1:
+            yield func()
+    except exception:
+        pass
+
+
+def first_true(iterable, default=None, pred=None):
+    """
+    Returns the first true value in the iterable.
+
+    If no true value is found, returns *default*
+
+    If *pred* is not None, returns the first item for which
+    ``pred(item) == True`` .
+
+        >>> first_true(range(10))
+        1
+        >>> first_true(range(10), pred=lambda x: x > 5)
+        6
+        >>> first_true(range(10), default='missing', pred=lambda x: x > 9)
+        'missing'
+
+    """
+    return next(filter(pred, iterable), default)
+
+
+def random_product(*args, repeat=1):
+    """Draw an item at random from each of the input iterables.
+
+        >>> random_product('abc', range(4), 'XYZ')  # doctest:+SKIP
+        ('c', 3, 'Z')
+
+    If *repeat* is provided as a keyword argument, that many items will be
+    drawn from each iterable.
+
+        >>> random_product('abcd', range(4), repeat=2)  # doctest:+SKIP
+        ('a', 2, 'd', 3)
+
+    This equivalent to taking a random selection from
+    ``itertools.product(*args, **kwarg)``.
+
+    """
+    pools = [tuple(pool) for pool in args] * repeat
+    return tuple(choice(pool) for pool in pools)
+
+
+def random_permutation(iterable, r=None):
+    """Return a random *r* length permutation of the elements in *iterable*.
+
+    If *r* is not specified or is ``None``, then *r* defaults to the length of
+    *iterable*.
+
+        >>> random_permutation(range(5))  # doctest:+SKIP
+        (3, 4, 0, 1, 2)
+
+    This equivalent to taking a random selection from
+    ``itertools.permutations(iterable, r)``.
+
+    """
+    pool = tuple(iterable)
+    r = len(pool) if r is None else r
+    return tuple(sample(pool, r))
+
+
+def random_combination(iterable, r):
+    """Return a random *r* length subsequence of the elements in *iterable*.
+
+        >>> random_combination(range(5), 3)  # doctest:+SKIP
+        (2, 3, 4)
+
+    This equivalent to taking a random selection from
+    ``itertools.combinations(iterable, r)``.
+
+    """
+    pool = tuple(iterable)
+    n = len(pool)
+    indices = sorted(sample(range(n), r))
+    return tuple(pool[i] for i in indices)
+
+
+def random_combination_with_replacement(iterable, r):
+    """Return a random *r* length subsequence of elements in *iterable*,
+    allowing individual elements to be repeated.
+
+        >>> random_combination_with_replacement(range(3), 5) # doctest:+SKIP
+        (0, 0, 1, 2, 2)
+
+    This equivalent to taking a random selection from
+    ``itertools.combinations_with_replacement(iterable, r)``.
+
+    """
+    pool = tuple(iterable)
+    n = len(pool)
+    indices = sorted(randrange(n) for i in range(r))
+    return tuple(pool[i] for i in indices)
+
+
+def nth_combination(iterable, r, index):
+    """Equivalent to ``list(combinations(iterable, r))[index]``.
+
+    The subsequences of *iterable* that are of length *r* can be ordered
+    lexicographically. :func:`nth_combination` computes the subsequence at
+    sort position *index* directly, without computing the previous
+    subsequences.
+
+        >>> nth_combination(range(5), 3, 5)
+        (0, 3, 4)
+
+    ``ValueError`` will be raised If *r* is negative or greater than the length
+    of *iterable*.
+    ``IndexError`` will be raised if the given *index* is invalid.
+    """
+    pool = tuple(iterable)
+    n = len(pool)
+    if (r < 0) or (r > n):
+        raise ValueError
+
+    c = 1
+    k = min(r, n - r)
+    for i in range(1, k + 1):
+        c = c * (n - k + i) // i
+
+    if index < 0:
+        index += c
+
+    if (index < 0) or (index >= c):
+        raise IndexError
+
+    result = []
+    while r:
+        c, n, r = c * r // n, n - 1, r - 1
+        while index >= c:
+            index -= c
+            c, n = c * (n - r) // n, n - 1
+        result.append(pool[-1 - n])
+
+    return tuple(result)
+
+
+def prepend(value, iterator):
+    """Yield *value*, followed by the elements in *iterator*.
+
+        >>> value = '0'
+        >>> iterator = ['1', '2', '3']
+        >>> list(prepend(value, iterator))
+        ['0', '1', '2', '3']
+
+    To prepend multiple values, see :func:`itertools.chain`
+    or :func:`value_chain`.
+
+    """
+    return chain([value], iterator)
+
+
+def convolve(signal, kernel):
+    """Convolve the iterable *signal* with the iterable *kernel*.
+
+        >>> signal = (1, 2, 3, 4, 5)
+        >>> kernel = [3, 2, 1]
+        >>> list(convolve(signal, kernel))
+        [3, 8, 14, 20, 26, 14, 5]
+
+    Note: the input arguments are not interchangeable, as the *kernel*
+    is immediately consumed and stored.
+
+    """
+    # This implementation intentionally doesn't match the one in the itertools
+    # documentation.
+    kernel = tuple(kernel)[::-1]
+    n = len(kernel)
+    window = deque([0], maxlen=n) * n
+    for x in chain(signal, repeat(0, n - 1)):
+        window.append(x)
+        yield _sumprod(kernel, window)
+
+
+def before_and_after(predicate, it):
+    """A variant of :func:`takewhile` that allows complete access to the
+    remainder of the iterator.
+
+         >>> it = iter('ABCdEfGhI')
+         >>> all_upper, remainder = before_and_after(str.isupper, it)
+         >>> ''.join(all_upper)
+         'ABC'
+         >>> ''.join(remainder) # takewhile() would lose the 'd'
+         'dEfGhI'
+
+    Note that the first iterator must be fully consumed before the second
+    iterator can generate valid results.
+    """
+    it = iter(it)
+    transition = []
+
+    def true_iterator():
+        for elem in it:
+            if predicate(elem):
+                yield elem
+            else:
+                transition.append(elem)
+                return
+
+    # Note: this is different from itertools recipes to allow nesting
+    # before_and_after remainders into before_and_after again. See tests
+    # for an example.
+    remainder_iterator = chain(transition, it)
+
+    return true_iterator(), remainder_iterator
+
+
+def triplewise(iterable):
+    """Return overlapping triplets from *iterable*.
+
+    >>> list(triplewise('ABCDE'))
+    [('A', 'B', 'C'), ('B', 'C', 'D'), ('C', 'D', 'E')]
+
+    """
+    for (a, _), (b, c) in pairwise(pairwise(iterable)):
+        yield a, b, c
+
+
+def sliding_window(iterable, n):
+    """Return a sliding window of width *n* over *iterable*.
+
+        >>> list(sliding_window(range(6), 4))
+        [(0, 1, 2, 3), (1, 2, 3, 4), (2, 3, 4, 5)]
+
+    If *iterable* has fewer than *n* items, then nothing is yielded:
+
+        >>> list(sliding_window(range(3), 4))
+        []
+
+    For a variant with more features, see :func:`windowed`.
+    """
+    it = iter(iterable)
+    window = deque(islice(it, n - 1), maxlen=n)
+    for x in it:
+        window.append(x)
+        yield tuple(window)
+
+
+def subslices(iterable):
+    """Return all contiguous non-empty subslices of *iterable*.
+
+        >>> list(subslices('ABC'))
+        [['A'], ['A', 'B'], ['A', 'B', 'C'], ['B'], ['B', 'C'], ['C']]
+
+    This is similar to :func:`substrings`, but emits items in a different
+    order.
+    """
+    seq = list(iterable)
+    slices = starmap(slice, combinations(range(len(seq) + 1), 2))
+    return map(operator.getitem, repeat(seq), slices)
+
+
+def polynomial_from_roots(roots):
+    """Compute a polynomial's coefficients from its roots.
+
+    >>> roots = [5, -4, 3]  # (x - 5) * (x + 4) * (x - 3)
+    >>> polynomial_from_roots(roots)  # x^3 - 4 * x^2 - 17 * x + 60
+    [1, -4, -17, 60]
+    """
+    factors = zip(repeat(1), map(operator.neg, roots))
+    return list(reduce(convolve, factors, [1]))
+
+
+def iter_index(iterable, value, start=0, stop=None):
+    """Yield the index of each place in *iterable* that *value* occurs,
+    beginning with index *start* and ending before index *stop*.
+
+
+    >>> list(iter_index('AABCADEAF', 'A'))
+    [0, 1, 4, 7]
+    >>> list(iter_index('AABCADEAF', 'A', 1))  # start index is inclusive
+    [1, 4, 7]
+    >>> list(iter_index('AABCADEAF', 'A', 1, 7))  # stop index is not inclusive
+    [1, 4]
+
+    The behavior for non-scalar *values* matches the built-in Python types.
+
+    >>> list(iter_index('ABCDABCD', 'AB'))
+    [0, 4]
+    >>> list(iter_index([0, 1, 2, 3, 0, 1, 2, 3], [0, 1]))
+    []
+    >>> list(iter_index([[0, 1], [2, 3], [0, 1], [2, 3]], [0, 1]))
+    [0, 2]
+
+    See :func:`locate` for a more general means of finding the indexes
+    associated with particular values.
+
+    """
+    seq_index = getattr(iterable, 'index', None)
+    if seq_index is None:
+        # Slow path for general iterables
+        it = islice(iterable, start, stop)
+        for i, element in enumerate(it, start):
+            if element is value or element == value:
+                yield i
+    else:
+        # Fast path for sequences
+        stop = len(iterable) if stop is None else stop
+        i = start - 1
+        try:
+            while True:
+                yield (i := seq_index(value, i + 1, stop))
+        except ValueError:
+            pass
+
+
+def sieve(n):
+    """Yield the primes less than n.
+
+    >>> list(sieve(30))
+    [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
+    """
+    if n > 2:
+        yield 2
+    start = 3
+    data = bytearray((0, 1)) * (n // 2)
+    limit = math.isqrt(n) + 1
+    for p in iter_index(data, 1, start, limit):
+        yield from iter_index(data, 1, start, p * p)
+        data[p * p : n : p + p] = bytes(len(range(p * p, n, p + p)))
+        start = p * p
+    yield from iter_index(data, 1, start)
+
+
+def _batched(iterable, n, *, strict=False):
+    """Batch data into tuples of length *n*. If the number of items in
+    *iterable* is not divisible by *n*:
+    * The last batch will be shorter if *strict* is ``False``.
+    * :exc:`ValueError` will be raised if *strict* is ``True``.
+
+    >>> list(batched('ABCDEFG', 3))
+    [('A', 'B', 'C'), ('D', 'E', 'F'), ('G',)]
+
+    On Python 3.13 and above, this is an alias for :func:`itertools.batched`.
+    """
+    if n < 1:
+        raise ValueError('n must be at least one')
+    it = iter(iterable)
+    while batch := tuple(islice(it, n)):
+        if strict and len(batch) != n:
+            raise ValueError('batched(): incomplete batch')
+        yield batch
+
+
+if hexversion >= 0x30D00A2:
+    from itertools import batched as itertools_batched
+
+    def batched(iterable, n, *, strict=False):
+        return itertools_batched(iterable, n, strict=strict)
+
+else:
+    batched = _batched
+
+    batched.__doc__ = _batched.__doc__
+
+
+def transpose(it):
+    """Swap the rows and columns of the input matrix.
+
+    >>> list(transpose([(1, 2, 3), (11, 22, 33)]))
+    [(1, 11), (2, 22), (3, 33)]
+
+    The caller should ensure that the dimensions of the input are compatible.
+    If the input is empty, no output will be produced.
+    """
+    return _zip_strict(*it)
+
+
+def reshape(matrix, cols):
+    """Reshape the 2-D input *matrix* to have a column count given by *cols*.
+
+    >>> matrix = [(0, 1), (2, 3), (4, 5)]
+    >>> cols = 3
+    >>> list(reshape(matrix, cols))
+    [(0, 1, 2), (3, 4, 5)]
+    """
+    return batched(chain.from_iterable(matrix), cols)
+
+
+def matmul(m1, m2):
+    """Multiply two matrices.
+
+    >>> list(matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]))
+    [(49, 80), (41, 60)]
+
+    The caller should ensure that the dimensions of the input matrices are
+    compatible with each other.
+    """
+    n = len(m2[0])
+    return batched(starmap(_sumprod, product(m1, transpose(m2))), n)
+
+
+def factor(n):
+    """Yield the prime factors of n.
+
+    >>> list(factor(360))
+    [2, 2, 2, 3, 3, 5]
+    """
+    for prime in sieve(math.isqrt(n) + 1):
+        while not n % prime:
+            yield prime
+            n //= prime
+            if n == 1:
+                return
+    if n > 1:
+        yield n
+
+
+def polynomial_eval(coefficients, x):
+    """Evaluate a polynomial at a specific value.
+
+    Example: evaluating x^3 - 4 * x^2 - 17 * x + 60 at x = 2.5:
+
+    >>> coefficients = [1, -4, -17, 60]
+    >>> x = 2.5
+    >>> polynomial_eval(coefficients, x)
+    8.125
+    """
+    n = len(coefficients)
+    if n == 0:
+        return x * 0  # coerce zero to the type of x
+    powers = map(pow, repeat(x), reversed(range(n)))
+    return _sumprod(coefficients, powers)
+
+
+def sum_of_squares(it):
+    """Return the sum of the squares of the input values.
+
+    >>> sum_of_squares([10, 20, 30])
+    1400
+    """
+    return _sumprod(*tee(it))
+
+
+def polynomial_derivative(coefficients):
+    """Compute the first derivative of a polynomial.
+
+    Example: evaluating the derivative of x^3 - 4 * x^2 - 17 * x + 60
+
+    >>> coefficients = [1, -4, -17, 60]
+    >>> derivative_coefficients = polynomial_derivative(coefficients)
+    >>> derivative_coefficients
+    [3, -8, -17]
+    """
+    n = len(coefficients)
+    powers = reversed(range(1, n))
+    return list(map(operator.mul, coefficients, powers))
+
+
+def totient(n):
+    """Return the count of natural numbers up to *n* that are coprime with *n*.
+
+    >>> totient(9)
+    6
+    >>> totient(12)
+    4
+    """
+    # The itertools docs use unique_justseen instead of set; see
+    # https://github.com/more-itertools/more-itertools/issues/823
+    for p in set(factor(n)):
+        n = n // p * (p - 1)
+
+    return n