Tetration may be thought of as the next operator after exponentiation: where $x \times n$ can be written as the sum $x+x+x+\cdots + x$ with $n$ terms, and $x^n$ is the multiplication of $n$ factors: $x\cdot x \cdot x \cdots x$, the expression written $^nx$ is equal to the repeated exponentiation involving $n$ occurences of $x$:$$^nx = x^{x ...

1 day ago · math — Mathematical functions¶ This module provides access to the mathematical functions defined by the C standard. These functions cannot be used with complex numbers; use the functions of the same name from the cmath module …

Jun 8, 2015 · To be clear, a^^b is not the same thing as a^b, it is the exponential tower a^ (a^ (a^...^a)) where there are b copies of a, also known as tetration. Let T (a,b) = a^^b so T (a,1) = a and T (a,b) = a^T (a,b-1). To compute T (a,b) mod m = a^T (a,b-1) mod m, we want to compute a power of a mod m with an extremely large exponent.

hyperop is a small library for representing really, really, ridiculously large numbers in pure python. It does so using hyperoperations. Hyperoperation 0, H0 is the successor function, H0(None, 4) = 5; H1 is addition, H1(2,4) = 2 + (1+1+1+1) = 6

Jan 29, 2024 · Define the tetration number. Define the function find_tetranum, which accepts the base number and the tetration number as input. If the tetration number is greater than or equal to 2 then define the number as the base number times itself.

Jun 2, 2023 · This is the python code I've made to easily calculate tetration using my method. It calculates x^^ (a+bi) for all a, b real (except a whole and below -2) and for all x greater that e^-e. It might not be 100% precise, and maybe some mistakes, but it overall works.

Dec 8, 2016 · With tetration, if the final answer is d digits, then all intermediate results are O (log d) digits, as opposed to O (d) digits with exponentiation. Because the intermediate results for tetration are so small compared to the final result, there's no savings to …

Oct 15, 2024 · Here are two Python functions to compute tetration. The first function uses recursion, and the second one uses iteration. In both functions, we added a check for n = 0 at the beginning.

Jun 16, 2024 · This python module let's you tetrate in your python code: both recursively (tetrate(num, tet_by)) and iteratively (tetrate_iteration(num_ tet_by)) (!!RECURSIVE METHOD …

Sep 20, 2023 · I’m trying to make a tetration calculator, where python repeatedly takes the exponent of the base number one less time than the height number. The last 2 lines have multiple errors, and I have no idea what I’m supposed to do to fix it.