18 votes

Optimize search for rational numbers on unit circle?

This method is called the Stereographic approach and can be used to generate arbitary rational triples without needing brute force searching. I was fortunate to have learned this trick off Minhyong ...
  • 21.7k
18 votes

Optimize search for rational numbers on unit circle?

This is a compiled program to find all Pythagorean triples $(a,b,c)$ with $a^2 + b^2 = c^2$ and $a \leq b$ and where c lies between ...
12 votes
Accepted

Memory leak with Mathematica Graph functions

Here is another possible way to eliminate the impact of history, etc. The following code aborts on my machine after printing to the console three times. ...
  • 4,753
12 votes
Accepted

NDSolve very slow on 2D heat equation

The simplest solution I find is, add SolveDelayed -> True to NDSolve: ...
  • 58.5k
12 votes
Accepted

Speed up replacement of very large alternatives expression

Use threaded rules instead of alternatives: instead of 1 | 2 -> 0 use {1 -> 0, 2 -> 0}. Combined with a ...
  • 40.1k
11 votes

What is a good way to compute successive primorials with Mathematica?

Mathematica code is already provided in the The On-Line Encyclopedia of Integer Sequences, here http://oeis.org/A002110 oeis Sol 1 ...
  • 33k
8 votes
Accepted

Optimize search for rational numbers on unit circle?

This is not the fastest solution in the world for finding rational points on the unit circle (takes 4.3 seconds on my laptop for denominators up to 100000), but at least it's short: ...
  • 16.2k
8 votes

NDSolve very slow on 2D heat equation

Try FiniteElement method with NeumannValue instead of derivative-bc: ...
7 votes

What is a good way to compute successive primorials with Mathematica?

Luckily Prime is Listable and we can make an elegant solution with FoldList: ...
  • 7,754
5 votes

What is a good way to compute successive primorials with Mathematica?

Not sure if the following is considered a good way, but at least it gave results in realistic time frames and did not crash anything. Create the list of primes and then multiply the elements of the ...
  • 9,067
5 votes
Accepted

RegionIntersection runs for a very long time and then aborts without returning a result

Edit $Version 13.2.0 for Microsoft Windows (64-bit) (November 18, 2022) ...
  • 49.1k
5 votes

Optimize search for rational numbers on unit circle?

As mentioned above, we may search for Phytogorean triples: n1^2+n2^2==n3^2. To simplify, we may restrict the search to the first quadrant, as all the other solutions are mirror images, mirrored at the ...
  • 35.3k
5 votes

improving efficiency of a code

In addition to what Syed already pointed out, you can speed up the search for the restricted set of edges by using a SparseArray and by using ...
4 votes

How to gather functions which intersect at the same point?

This goes through all $2^n -n -1$ subsets of length 2 or more. An overkill that allows very simple code, but it's not practical for large $n$. See other answer(s). ...
  • 33k
4 votes

Why does `MemoryInUse` keep increasing?

Explanation At least on my system, the slope Mean@Differences@ml is equal to $16$ bytes, which is equal to ...
  • 33k
4 votes
Accepted

improving efficiency of a code

...
  • 25k
4 votes

Speed up replacement of very large alternatives expression

v2 is not as fast as Roman's v1 ...
  • 30.3k
3 votes

Give a element rank list of a list

Not sure if this simplification helps: ordinalScale[list_] := AssociationThread[Sort@list, Range@Length@list] /@ list
2 votes

Bugs with computational geometry: versions 12.2 vs 13.2

If simple polygons are given by lists of their vertices, then the fastest and most reliable way to check their intersection is: ...
  • 623
2 votes

How to gather functions which intersect at the same point?

This goes only through all $(n^2-n)/2$ Subsets[func, {2}] as suggested by @Syed. For $n=100$ that is only $4950$ cases. It calculates the intersection points of ...
  • 33k
2 votes
Accepted

NIntegrate: slow convergence error and speed efficiency

If we change the method of integration, we can obtain the NNt[1,1] which we see in the screenshot without any errors. The method is ...
  • 9,067
1 vote

Quickly summing matrix elements

One possibility is to use TensorContract/TensorProduct, but you need to also use Inactive to ...
  • 126k
1 vote

Efficient memory usage while building a large sparse matrix

Even though you have shared no details about f, as others have mentioned, I think I understand your problem. Consider this (note that ...
  • 4,753
1 vote
Accepted

How to refer to calling notebook instead of my personal include? / detector for high-memory-usage cells

The issue is that the default values EvaluationNotebook[] and EvaluationCell[] are evaluated when the function is defined, not ...
  • 29.9k

Only top scored, non community-wiki answers of a minimum length are eligible