bollu/bollu.github.io

code + contents of my website, and programming life

bollu.github.io's Issues

rotas-paths

A Universe of Sorts

http://localhost:8000/rotas-paths.html

Typo: 'seem' should be 'seen'

In https://github.com/bollu/blog/blame/c36782b7dde231d19e71e78c6422c81d599af78e/content/blog/reading-kmett-structs.md#L236.

words-to-know-in-target-language

A Universe of Sorts

https://bollu.github.io/words-to-know-in-target-language.html

Topology computation blog KaTeX double rendering

https://bollu.github.io/topology-is-really-about-computation-part-1.html

All the formulae are rendered twice. This is making the writing very unreadable

hopf-algebras-and-combinatorics

A Universe of Sorts

http://bollu.github.io/hopf-algebras-and-combinatorics.html

Grobner basis is an overkill. It is a system of linear equations

Referring #computing-equivalent-gate-sets-using-grobner-bases.

The problem is a system of linear equations with 2^n - 2 variables a, axorb, axorc, etc. and 2^n - 1 equations (2^n equations with trivial 0 = 0 equation): 1*a + 1*b + 1*axorc + 1*bxorc = 1 (mod 8) for (a, b, c) = (1, 1, 0) etc.
For example n = 3:

A =
[1 0 1 0 1 0]
[0 1 1 0 0 1]
[1 1 0 0 1 1]
[0 0 0 1 1 1]
[1 0 1 1 0 1]
[0 1 1 1 1 0]
[1 1 0 1 0 0]

b = (0, 1, 1, 0, 1, 0, 0, 1)

I know nothing about Sage but I implement this: https://gist.github.com/pcpthm/9bf91ed750cb2b4abc4009475680d908.

Linear equation on integer (not necessary prime) modulo ring can be solved by modified Gaussian eliminations in O(N^3) time where N is size of matrix ~ 2^n. This is still exponential in term of n but considerably faster / less power. Probably specialized algorithm can be implemented via FFT-like or something with O(N^2 * poly(n)) runtime.

Perhaps the matrix can be analyzed to get the idea of general solution.

Website security errors

Hi there,

Followed a Hacker News link to your repo, but I noticed there are security errors on your blog page. Thought you would want to know.

using-the-bound-library

A Universe of Sorts

https://bollu.github.io/using-the-bound-library.html

hairy-ball-theorem-from-sperners-lemma-wip

A Universe of Sorts

http://bollu.github.io/hairy-ball-theorem-from-sperners-lemma-wip.html

J Incunabulum

What is the t variable really tracking?

The t variable is the type of the array. In the Incunabulum there are only 2 types: unboxed, and boxed. See https://www.jsoftware.com/papers/AIOJ/typedefA.htm

How does one create a multi-dimensional array easily?

d=3,2
a=d#~6

What are some interesting programs one can run with this mini-interpreter?

Not any that couldn't be run with any other APL. Imo, the main value of the Incunabulum is just how it works.

word2vec-c-code-implements-gradient-descent-really-weirdly

A Universe of Sorts

http://bollu.github.io/word2vec-c-code-implements-gradient-descent-really-weirdly.html

nilradical-is-intersection-of-all-prime-ideals

A Universe of Sorts

https://bollu.github.io/nilradical-is-intersection-of-all-prime-ideals.html

articles/precision-recall-and-all-that

A Universe of Sorts

https://pixel-druid.com/articles/precision-recall-and-all-that.html

a-hackers-guide-to-numerical-analysis

A Universe of Sorts

http://bollu.github.io/a-hackers-guide-to-numerical-analysis.html

direct-and-inverse-limits

A Universe of Sorts

http://localhost:8000/direct-and-inverse-limits.html

sam-harris-and-jordan-peterson-vancouver-1-todo

A Universe of Sorts

https://bollu.github.io/sam-harris-and-jordan-peterson-vancouver-1-todo.html

J interpreter: meaning of `t`

What is the t variable really tracking?

Each value is either an array of numbers (t==0) or it is an array of boxes (t==1).
So t is the type of the scalars that make up the array.

The monadic box operator < converts a value into a box.

IMO, since I still don't understand all of the code.

simplicial-approximation-maps-can-be-approximated-by-simplicial-maps-todo

A Universe of Sorts

https://bollu.github.io/simplicial-approximation-maps-can-be-approximated-by-simplicial-maps-todo.html

counterexample-to-fundamental-theorem-of-calculus

A Universe of Sorts

https://bollu.github.io/counterexample-to-fundamental-theorem-of-calculus.html

Add a feed?

Hi! I am the editor of Haskell Weekly. An issue from a couple weeks ago (https://haskellweekly.news/issues/92.html) featured your most recent blog post. I would like to be notified when you write a new post, but as far as I can tell your blog does not have a feed. Would you mind adding an Atom or RSS feed? Thanks!

level-set-of-a-continuous-function-must-be-closed

A Universe of Sorts

https://bollu.github.io/level-set-of-a-continuous-function-must-be-closed.html

everything-you-know-about-word2vec-is-wrong

A Universe of Sorts

http://bollu.github.io/everything-you-know-about-word2vec-is-wrong.html

J Incunabulum Disected

https://rickyhan.com/jekyll/update/2020/01/16/j-incunabulum-disected.html

take-at-most-4-letters-from-15-letters

A Universe of Sorts

http://bollu.github.io/take-at-most-4-letters-from-15-letters.html

blazing-fast-math-rendering-on-the-web

A Universe of Sorts

http://bollu.github.io/blazing-fast-math-rendering-on-the-web.html

How does one work with arrays in a linear language?

Given an array of qubits xs: Qubit[], I want to switch to little endian. Due to no-cloning, I can't copy them! I suppose I can use recursion to build up a new "list". But this is not the efficient array version we know and love and want.

The code that I want to work but does not:

function switchEndian(xs: Qubit[]): Unit {
    for(i in 0..Length(xs) - 1) {
        Qubit q = xs[i]; // boom, this does not work!
        xs[i] = xs[Length(xs) - 1 - i]
        xs[Length(xs) - 1 - i] = q;
    }
}

You just need a linear swap function.

function switchEndian(xs: Qubit[]): Unit {
    for(i in 0..Length(xs) - 1) {
        swap(xs[i], xs[Length(xs) - 1 - i]);
    }
}

Merge conflicts are committed into the repository

https://github.com/bollu/bollu.github.io/blob/master/todo.md

Notice that there is <<<<< HEAD things

J interpreter: create a multidimensional array

My theory is that

2 2#~4

should produce a 2x2 matrix. It is only a theory, since I am so far unable to run the interpreter without it crashing. It seems to me that # is the APL "rho" operator and ~ is the APL "iota" operator.

Resume link broken on the main website

This link is 404

architecture-cheat-sheet

A Universe of Sorts

https://bollu.github.io/architecture-cheat-sheet.html