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The reason I want to avoid references is because when I later try to navigate through geometric objects with various relations and constraints on them, my hope is that it will speed that process up. I ...

Yes, in my question the terminology I used appears to make people think I'm talking about actual memory. You are right, I did mean that I do not want to assign it to both, if one is contained within ...

I very much like this approach. This is in line with what I was originally envisioning. I was also inspired to make it so that if we had a LineSegment class, and two line segments overlapped on a line,...

I think I see what you mean. You want to automatically infer when an object has to be on another, without having to declare it explicitly. In your example, since (R is on L) and (P is on R), then (P ...

What do you mean store it separately in different places? Given your classes, its just a pointer to the point class? L.points[P.name] is just a pointer to the actual P class. no duplicated memory. ...

Reference is the minimal way for represent connection between objects (in your case, a line and a point). Well, you may have an array of point objects, and make a line object to contain indexes of its ...

I understand your point perfectly, and it makes sense. I can't say how much more memory having multiple * Point* with the same coordinates, and I don’t know what your program does, but in principle, I ...

Please allow me to elaborate on my question. What I am really after is a way to not have to reference the point multiple times, as that many references seems unnecssary. I would like to make a point ...

"I don't want to "store" it separately in multiple places" - Your current code already stores P in the single place. Both L.points[P.name] and R.points[P.name] refer to that place. ...

click a button in Google sheets that will increment cells that have a number by 1 Buttons can be implemented as drawings in Google Sheets, but they aren't clickable in the mobile Sheets app. The ...

the easiest incrementiation is done by enabling Iterative calculation. for that, go to: File > Settings > Calculation > Iterative calculation > On > Max. ...

I participated in writing many systems intended for banks and insurance companies. In all of them, critical calculations were performed using double variables. However - and this is important - all ...

Yes, Taylor series are generally computationally expensive. If we're limited to a specific group of functions, we can sometimes find a nice enough representation that doesn't explode. If we're talking ...

Performance of numpy.polynomial is fast enough. The code is as follows: from numpy import polynomial as poly def frac_poly_dif(poly_pair): num_poly, den_poly = poly_pair return (num_poly....

Mike Day (Generalising the Fast Reciprocal Square Root Algorithm (2023)) has a really neat attack on this problem. I recommend folks read it if they're interested as it is unusually clear for this ...

So the value should change past every multiple of T/100 where / is the exact division Let T=100*q + r The ith change of bar is when P >= i*q + (i*r)/100 You precompute 100 values i*q+ceil( i*r/100 )...

Here is an implementation that uses the Chudnovsky algorithm with binary splitting. On my computer it is able to calculate a million digits in ~870ms. function floorSqrt(n) { if (n <= Number....

In addition to the CRT, you should also look at [Lucas's Theorem](https://en.wikipedia.org/wiki/Lucas%27s_theorem).

I got this working after a while. Thanks!

Edit: Ok, now I get it. Vector(x, y, z) where x, y, z ∈ {-1, 0, 1} gives you 3^3 - 1 graph nodes (excluding Vector(0, 0, 0)) and you want them all to have edges to their neighbors. What a neighbor ...

"Up-UpRIght is 45 degrees, but Up-UpRightForward is ~54.7 degrees. Likewise going from UpRight-UpRightForward is ~35.3 degrees. I understand that this is normal maths but, for the purposes of ...

I think you can find the row mod 5 and mod 2, then use the Chinese Remainder Theorem to find the result you want.

Check out the cppalliance/int128 library that was released in 2025. Boost.Int128 is a portable implementation of a signed, and an unsigned 128-bit integer and related functionality (e.g. bit counting)...

Here is some C++ code to calculate A000182 using 'memoization' #include <string> #include <sstream> #include <iostream> #include <vector> #include "cRunWatch.h" ...

I have solved the problem. I used the following code to analyze the process: DATA = [] def A000182_analysis(n): result = [1] * n last = 1 for i, k in enumerate(range(1, n), start=1): ...

I'm not familiar with that sequence, but the comments on that OEIS entry mention that this sequence can be derived from full binary trees, which indicated to me that the sequence can probably be ...

I think you cut down your example too much. I at least have no clue what you are actually trying to achieve and what your current solution does. It sounds like you want the diagonal of a unit square ...

I'm not sure I understand what you are actually trying to do here. Is the end goal to include directions while doing pathfinding? i.e. make turning more expensive than going straight ahead in an ...

It sounds like it would be easier to work with polar coordinates, or more specifically, spherical coordinates. r: The length of the vector, presumably 1 in your example. theta: The horizontal ...

Here is the fastest and precise way: (you can also cache b0k and bk0 firstly.) compare(v1, v2) b01 = (cross(v0, v1) >= 0) b12 = (cross(v1, v2) >= 0) b20 = (cross(v2, v0) >= 0) return ...

we would love to help you but the code you provided isn't really explainatory, and the question you gave us isn't much to work with :)

The answer is dependant on what you are trying to observe/show through this chart. As long as you tell the viewer which frequency band you are using inyou computation, it's probably fine. Now, on to ...

See also dsp.stackexchange.com.

It's hard to give suggestions without knowing what package you are using or what kind of calculator you are trying to make. For example, while a dynamic expression parsing package might be useful for ...

This is probably better off on the sister site [stats.se]. It is about data modelling and interpretation - not a programming question.

as stated by @Stef, I was wrong about the topological sorter, but I still think that the underlying graph structure is what you need. Here is an implementation that does what you want: from ...

You are probably right now that I think about it. The topological sorter itself isn't exactly what is needed here, though the data structure might be pretty close to ideal.

In addition to self.line_segments and self_inequalities, you could add two dicts self.smaller and self.greater that maps an item to the list of smaller items, and to the list of greater items. Then, ...

Note that if ineq == (m, n): assert False, f"Inequality {m} < {n} already exists in the registry." can be replaced by assert ineq != (m, n), f"Inequality {m} < {n} already ...

I don't think so? A topological sort gives you one order that respects all given inequalities, but "adds" new inequalities arbitrarily. The OP wants to propagate inequalities transitively ...