Questions tagged [programming]
For mathematical questions related to programming, and questions where a computer-aided solution is strongly suggested. A strong connection with a mathematical topic is needed to make programming questions on-topic. This should not be the only tag. Consider also using the tags (algorithms), (numerical-methods), or (linear-programming).
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Software Tools that allow you to do symbolic Ricci Calculus / Tensor Notation?
Here are some examples of problems that I want to be able to solve for symbolically:
Let $R = \sqrt{x_k x_k}$. Calculate $\displaystyle{\partial R \over \partial x_i}$ and $\displaystyle{\partial^2 R ...
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Given a 3D camera and a horizontal plane both at the origin, how can I determine the pitch of the camera to view the plane N units below the horizon?
Given a 480px x 480px screen, and a 3D camera at the origin, with a horizontal plane on the X-Z axis that cuts through it (seen as a horizontal line through the center of the screen), how can I ...
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Cubic polynomials over finite fields
I was watching an introduction video on "Tangent conics and tangent quadrics" by Prof. Norbert Wildberger , where the following Taylor polynomial was introduced:
$$p_r(x) = (a+br+cr^2 + dr^3)...
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Is it fair to say that Martin Löf Type Theory is doing the same for maths as what type theory did for programming languages?
Let me clarify what I mean.
I am currently writing a dissertation on ML/Homotopy type theory as someone who is more of a theoretical computer scientist than an Algebraist. My dissertation is focused ...
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Oscillations in Newton's fractal
I'm working on a program that draws Newton's fractal for a given polynomial. Newton's fractal is a fractal derived from Newton's root-finding method, which given some initial guess $x_0$ and function $...
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Groups, Algorithms and Programming (GAP 4) lack of functions
I am a newbie in using of GAP. To learn it I downloaded a book "Groups, Algorithms and Programming" (subtitle GAP 3.4.4 of 20 Dec. 1995, gap3-jm of 19 Feb. 2018) and also Reference Manual of ...
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Constructing a semidirect product in GAP using characters
I have a finite group $G$ and an elementary abelian group $E(p^h)$ where $p\not \mid |G|$. I just want to construct via GAP the semidirect product $E(p^h):G$ given by a character $\chi$ of $G$, not ...
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Calculate probability of flipping coins with probabilities dependent on previous results
Let's say I have a biased coin that has a probability of 0.2 for heads and 0.8 for tails. If you flip it 6 times without getting a heads however, the probability of heads increases by 0.2 per non-...
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Is there always a natural transformation between endofunctors in the same category?
I'm trying to get a deeper intuition about natural transformations. More specifically, I'm trying to port the concepts of Category Theory to programming (Julia programming in this case, which requires ...
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Turning Haskell self-recursion into a mathematical formula
I have a Haskell function, which uses self-recursion to a limit
stock 0 = 0
stock n = (n*3) + (stock (n-1))
however, I somehow have to turn this function into ...
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How to make anything higher and lower to a base value equal to eachother.
So currently I am making a system for a game that works something like this.
You have Value A/Turquoise, which is 1
You have Value B/Orange, which is 0.5
I first move Value A decimal point 2 times to ...
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Prove: if a solution exists for LP and a feasible integer solution then there exists a solution to IP
If a solution exists for an optimization problem in LP and if there is a feasible integer solution then there exists a solution to the corresponding integer programming problem.
This is the basic ...
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Accuracy of the Crank-Nicolson method for non-linear, inhomogeneous heat equation
I am currently coding a solution to the following PDE:
$\frac{\partial T }{\partial t} =\frac{\partial}{\partial \theta}(A(\theta ,\phi )\frac{\partial T }{\partial \theta}) +\frac{\partial }{\partial ...
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Calculating this integral along a Bezier curve in code
I'm doing some graphics code work and need to solve this integral in code:
$$
\int_{0}^{1} f(P(t)) dt
$$
Where $P(t)$ is a quadratic or cubic Bezier curve, and $f(p)$ ($p$ is a point) is defined as:
$$...
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Is there any way to find the number of real roots of a polynomial computationally?
I'm creating a program to find the real roots of any given polynomial. It takes a user given polynomial as input and tries to find its roots. As an aid, mainly to check if I've missed any after the ...
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