Mathematics

Questions tagged [python]

For mathematical questions about Python; questions purely about the language, syntax, or runtime errors are off-topic here and would likely be better received on Stack Overflow.

971 questions
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How to convert Euler angles to Quaternions and get the same Euler angles back from Quaternions?

I am rotating n 3D shape using Euler angles in the order of XYZ meaning that the object is first rotated along the X axis, then Y and then Z . I want to convert the Euler angle to Quaternion and then get the same Euler angles back from the…
Amir
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Infinite sum of Python for loop

I'm a geometry student. Recently we were doing all kinds of crazy circle stuff, and it occurred to me that I don't know why $\pi r^2$ is the area of a circle. I mean, how do I really know that's true, aside from just taking my teachers + books at…
Ashleigh Basil
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Math for simple 3D coordinate rotation (python)

I'm rotating points from one coordinate system to the other, but drawing a blank how to do this. I've done some reading about Euler angles but after staring at this GIF for a while I just get dizzy. above: from here What I am doing: The new $z$ axis…
uhoh
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Convergence of the complex QR algorithm to Schur decomposition

I study the complex Schur decomposition of a complex matrix $A \in \mathbb{C}^{n \times n}$ , that is: $$ A = U T U^H $$ where $T$ is upper-triangular (the eigenvalues of $A$ appear on its diagonal, and may be complex) and $U$ is unitary $U^H =…
Triceratops
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Why is a simulation of a probability experiment off by a factor of 10?

From a university homework assignment: There are $8$ numbered cells and $12$ indistinct balls. All $12$ balls are randomly divided between all of the $8$ cells. What is the probability that there is not a single empty cell ( $i.e.$ each cell has at…
Shmuel Levinson
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When are $n!+1$ and $(n+2)!+1$ coprime?

For every $n\geq 1$ , $n!+1$ and $(n+1)!+1$ are coprime. I suspected the same would happen for $n!+1$ and $(n+2)!+1$ , but short Python script yielded 3 counterexamples: $\gcd(7!+1,9!+1)=71$ $\gcd(16!+1,18!+1)=61$ $\gcd(61!+1,63!+1)=71$ But up to…
aleph2
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Bouncing Bullet Problem

This is a problem that was presented to me through the google foobar challenge, but my time has since expired and they had decided that I did not complete the problem. I suspect a possible bug on their side, because I passed 9/10 test cases (which…
Kraigolas
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How to solve 5x5 grid with 16 diagonals?

I have a grid 5x5 and I have to fill 16 little squares with a diagonal Rules You cannot place more than 1 diagonal in each square The diagonals cannot touch each other (example bellow) Click here to view the solution But what I seek here is a…
BrunoLM
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tensor product and einsum in numpy

I am trying to understand the einsum function in NumPy. In this documentation , the last example, >>> a = np.arange(60.).reshape(3,4,5) >>> b = np.arange(24.).reshape(4,3,2) >>> np.einsum('ijk,jil->kl', a, b) array([[ 4400., 4730.], [ 4532., 4874.],…
LWZ
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How to reduce matrix into row echelon form in NumPy?

I'm working on a linear algebra homework for a data science class. I'm suppose to make this matrix into row echelon form but I'm stuck. Here's the current output I would like to get rid of -0.75, 0.777, and 1.333 in A[2,0], A[3,0], and A[3,1]…
Ednalyn C. De Dios
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Determine if a number is algebraic.

I recall there is an algorithm involving lattices that would tell me if a given number(approximation) is an algebraic number or not, along with the exact algebraic form of the number. Is there any tool (Gap, Mathematica, python package, etc) that…
ReverseFlowControl
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How many non-diagonalizable $2\times 2$ matrices are there with all entries single-digit strictly positive integers?

I'd like to know how many non-diagonalizable size 2 matrices there are with integer coefficient between 1 and 9 . I built a python program which counts the non-diagonalizable matrices with such coefficients: from sympy import * count = 0 for a in…
anni
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How to perform high precision calculation involving 100s of decimal places?

This is not directly a math question but rather a question on computing error. I am looking for ways to perform calculation involving 100s of decimal places (especially for, but not limited to, this problem statement ) One well known library for…
Nilotpal Sinha
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Doubling Point Formula of Elliptic Curve is Not Working

Let $E$ be an elliptic curve and a point $P = (x, y) \in E,$ from the duplication formula, the x-coordinate of $2P$ is - $$x_{(2P)}=(x^4-b_4*x^2-2*b_6*x-b_8)/(4*x^3+b_2*x^2+2*b_4*x+b_6)$$ The formula is given on page $54$ in book The Arithmetic of…
Consider Non-Trivial Cases
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How many right triangles can be built from points

There are array of points, I need to determine how many right-angled triangles can be built from them. This is a task for both programming and geometry. Because the number of points can be very large, and the time to run the program is limited.…
yoloy
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