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A problem is well-conditioned if small relative changes in input result in small relative changes in the solution. Otherwise, the problem is ill-conditioned. [3] In other words, a problem is ill-conditioned if its conditions number is "much larger" than 1. The condition number is introduced as a measure of the roundoff errors that can result ...
Since 7 October 2024, Python 3.13 is the latest stable release, and it and, for few more months, 3.12 are the only releases with active support including for bug fixes (as opposed to just for security) and Python 3.9, [55] is the oldest supported version of Python (albeit in the 'security support' phase), due to Python 3.8 reaching end-of-life.
Those p-values are obtained by p = F(X), where F is the assumed distribution of the sample random variable X – often normal. But that assumed F is just an asymptotic approximation, for which the fit will be worst in the tails. Thus you should not be surprised with occasional p-values near 0 or 1, such as 0.
Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
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The problem is in #P, the class of problems that can be defined as counting the number of accepting paths of a polynomial-time non-deterministic Turing machine. The problem is #P-hard, meaning that every other problem in #P has a Turing reduction or polynomial-time counting reduction to it. A counting reduction is a pair of polynomial-time ...