OtjFddlmZddlmZmZddlmZd dZd dZ d dZdS) ) defaultdict)multisetis_palindromic)as_int Nc t|}t|}|dkrtdt|g}}||kr.t||\}}||||k.||||dkr| n||t |dz }|0||krtd|d|d||krdg||z z|dd<|S) a Return a list of the digits of ``n`` in base ``b``. The first element in the list is ``b`` (or ``-b`` if ``n`` is negative). Examples ======== >>> from sympy.ntheory.digits import digits >>> digits(35) [10, 3, 5] If the number is negative, the negative sign will be placed on the base (which is the first element in the returned list): >>> digits(-35) [-10, 3, 5] Bases other than 10 (and greater than 1) can be selected with ``b``: >>> digits(27, b=2) [2, 1, 1, 0, 1, 1] Use the ``digits`` keyword if a certain number of digits is desired: >>> digits(35, digits=4) [10, 0, 0, 3, 5] Parameters ========== n: integer The number whose digits are returned. b: integer The base in which digits are computed. digits: integer (or None for all digits) The number of digits to be returned (padded with zeros, if necessary). See Also ======== sympy.core.intfunc.num_digits, count_digits zb must be greater than 1rNzFor z , at least z digits are needed.)r ValueErrorabsdivmodappendreverselen)nbdigitsxyrndigs R/var/www/html/CA-Chatbot/venv/lib/python3.11/site-packages/sympy/ntheory/digits.pyrrs\ q Aq A1uu34441vvr11ff!Q<>> from sympy.ntheory import count_digits >>> count_digits(1111339) {1: 4, 3: 2, 9: 1} The digits returned are always represented in base-10 but the number itself can be entered in any format that is understood by Python; the base of the number can also be given if it is different than 10: >>> n = 0xFA; n 250 >>> count_digits(_) {0: 1, 2: 1, 5: 1} >>> count_digits(n, 16) {10: 1, 15: 1} The default dictionary will return a 0 for any digit that did not appear in the number. For example, which digits appear 7 times in ``77!``: >>> from sympy import factorial >>> c77 = count_digits(factorial(77)) >>> [i for i in range(10) if c77[i] == 7] [1, 3, 7, 9] See Also ======== sympy.core.intfunc.num_digits, digits )rintrritemspop)rrrvs r count_digitsrKs[N S(6!Q<<006688 9 9BbBFF1IIIbffaRjj Irc>tt||dS)areturn True if ``n`` is the same when read from left to right or right to left in the given base, ``b``. Examples ======== >>> from sympy.ntheory import is_palindromic >>> all(is_palindromic(i) for i in (-11, 1, 22, 121)) True The second argument allows you to test numbers in other bases. For example, 88 is palindromic in base-10 but not in base-8: >>> is_palindromic(88, 8) False On the other hand, a number can be palindromic in base-8 but not in base-10: >>> 0o121, is_palindromic(0o121) (81, False) Or it might be palindromic in both bases: >>> oct(121), is_palindromic(121, 8) and is_palindromic(121) ('0o171', True) r ) _palindromicr)rrs rrrws> q! a ( ((r)rN)r) collectionsrsympy.utilities.iterablesrrr!sympy.utilities.miscrrrrrr&s######NNNNNNNN''''''AAAAH))))X))))))r