This is an example of an ordered pair. We use essential cookies to perform essential website functions, e.g. One of the better ways is Cantor Pairing, which is the following magic formula: This takes two positive integers, and returns a unique positive integer. carefully: You want to track pairs of integer values but the protocol, schema or API will Learn more. Nothing really special about it. When we apply the pairing function to and we often denote the resulting number as . Usage. By using this website, you agree to our Cookie Policy. 3 way of plotting the Cantor function (devil's staircase) using LaTeX. But there do exist practical limits on the size of inputs. Examples. share | cite | improve this answer | follow | edited Mar 9 '13 at 4:23. answered Mar 9 '13 at 4:16. I was told once that there is a theory consisting of just a pairing function that is stable, although I cannot find a reference for it. Value. modified to accommodate a collection. For example, you could perform the pair algebra using numexpr to gain big speedups over any numpy manipulation and tuple data types to achieve the same effect. Explanation and JS implementation here: Clone with Git or checkout with SVN using the repository’s web address. Install $ pip install pairing Usage from pairing import pair, depair pair(22, 33) # 1573 pair(33, 22) # 1562 depair(1573) # (22, 33) depair(1562) # (33, 32) When (not) to use this. Pass any two positive integers and get a unique integer back. You may implement whatever bijective function you wish, so long as it is proven to be bijective for all possible inputs. Noticed that we specified safe=False which allows these sorts of errors to pass without warning. This function is the inverse to the Cantor pairing function. It is helpful to define some intermediate values in the calculation: You have tuples as a result of element-wise array operations and want to store additions, one multiplication, and a single right shift (to get the $\tfrac12$). Recognizing functions from verbal description word problem. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. The formula for calculating mod is a mod b = a - b[a/b]. You can then map the row to an X axis, the column to an Y axis. dict.cc English-German Dictionary: Translation for Cantor pairing function. According to wikipedia, it is a computable bijection. The pairing function can be understood as an ordering of the points in the plane. Learn more, We use analytics cookies to understand how you use our websites so we can make them better, e.g. Pairing functions arise naturally in the demonstration that the cardinalities of the rationals and the nonnegative integers are the same, i.e.,, where is known as aleph-0, originally due to Georg Cantor. they're used to log you in. This is a python implementation of the Cantor pairing function and provides two functions, pair and depair. context should be reserved as a hack of last resort when the system can not be Given two points 8u,v< and 8x,y<, the point 8u,v< occurs at or before 8x,y< if and only if PairOrderedQ@8u,v<,8x,y

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