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Search - "factoring"
My Lazy Habits:
1. Not testing my own code thoroughly... cuz fuck that. That's the tester's/QA's job.
2. I create slack commands to get certain things done, so I dont have to get up and open my laptop each time I receive a ticket.
3. Ask more time for development that I actually need so I can fit in couple naps here and there.
4. Falsely claiming that I am busy when someone invites me over meet or a phone call. Like just text me.
5. Factoring my laziness in when I design features LOL.1
The Zen Of Ripping Off Airtable:
(patterned after The Zen Of Python. For all those shamelessly copying airtables basic functionality)
*Columns can be *reordered* for visual priority and ease of use.
* Rows are purely presentational, and mostly for grouping and formatting.
* Data cells are objects in their own right, so they can control their own rendering, and formatting.
* Columns (as objects) are where linkages and other column specific data are stored.
* Rows (as objects) are where row specific data (full-row formatting) are stored.
* Rows are views or references *into* columns which hold references to the actual data cells
* Tables are meant for managing and structuring *small* amounts of data (less than 10k rows) per table.
* Just as you might do "=A1:A5" to reference a cell range in google or excel, you might do "opt(table1:columnN)" in a column header to create a 'type' for the cells in that column.
* An enumeration is a table with a single column, useful for doing the equivalent of airtables options and tags. You will never be able to decide if it should be stored on a specific column, on a specific table for ease of reuse, or separately where it and its brothers will visually clutter your list of tables. Take a shot if you are here.
* Typing or linking a column should be accomplishable first through a command-driven type language, held in column headers and cells as text.
* Take a shot if you somehow ended up creating any of the following: an FSM, a custom regex parser, a new programming language.
* A good structuring system gives us options or tags (multiple select), selections (single select), and many other datatypes and should be first, programmatically available through a simple command-driven language like how commands are done in datacells in excel or google sheets.
* Columns are a means to organize data cells, and set constraints and formatting on an entire range.
* Row height, can be overridden by the settings of a cell. If a cell overrides the row and column render/graphics settings, then it must be drawn last--drawing over the default grid.
* The header of a column is itself a datacell.
* Columns have no order among themselves. Order is purely presentational, and stored on the table itself.
* The last statement is because this allows us to pluck individual columns out of tables for specialized views.
*Very* fast scrolling on large datasets, with row and cell height variability is complicated. Thinking about it makes me want to drink. You should drink too before you embark on implementing it.
* Wherever possible, don't use a database.
If you're thinking about using a database, see the previous koan.
* If you use a database, expect to pick and choose among column-oriented stores, and json, while factoring for platform support, api support, whether you want your front-end users to be forced to install and setup a full database,
and if not, what file-based .so or .dll database engine is out there that also supports video, audio, images, and custom types.
* For each time you ignore one of these nuggets of wisdom, take a shot, question your sanity, quit halfway, and then write another koan about what you learned.
* If you do not have liquor on hand, for each time you would take a shot, spank yourself on the ass. For those who think this is a reward, for each time you would spank yourself on the ass, instead *don't* spank yourself on the ass.
* Take a sip if you *definitely* wildly misused terms from OOP, MVP, and spreadsheets.5
Looking for someone to test a new factorization script I wrote.
Tested against a set of products from all primes under 1000. Worked even on numbers up to 87954921289
Worked for about 66% of the products tested.
Obviously I'm cheating a little bit because I'm checking for four conditions n%a == 0, n%a == 1, n%b == 0, and n%b == 1
It appears it is possible to generate the series from just the product, and then factor each result. The last factor in each each set of factors becomes x, and we do p%x and check for zero.
if it works, we've found our answer.
Kind of wonky but basically what its doing is taking p, tacking on a 0 to the right, and then tacking p to the right of *that*.
So if you had a product like
The starting number we look at is
The middle digit becomes i, and the unit digit becomes j.
Don't know why it works more often then not, and don't know if it would really be any faster.
Just think it's cool.9
For any product of two non-trivial primes, it is *always* possible to get the quotient of its factors b/a derived solely from the product of those factors, *without* first factoring the product (p).
So I made a couple slight modifications to the formula in the previous post and got some pretty cool results.
The original post is here:
The default transformation from p, to the new product (call it p2) leads to *very* large products (even for products of the first 100 primes).
Take for example
a = 6229, b = 10477, p = a*b = 65261233
While the new product the formula generates, has a factor tree that contains our factor (a), the product is huge.
So huge I put the whole number in a pastebin here:
Now, that number DOES contain our example factor 6229. I demonstrated that in the prior post.
But first, it's huge, 2972 digits long, and second, many of its factors are huge too.
Right from the get go I had hunch, and did (p2 mod p) and the result was surprisingly small, much closer to the original product. Then just to see what happens I subtracted this result from the original product.
The modification looks like this:
The result is '49856916'
Thats within the ballpark of our original product.
And then I factored it.
1, 2, 3, 4, 6, 12, 23, 29, 46, 58, 69, 87, 92, 116, 138, 174, 276, 348, 667, 1334, 2001, 2668, 4002, 6229, 8004, 12458, 18687, 24916, 37374, 74748, 143267, 180641, 286534, 361282, 429801, 541923, 573068, 722564, 859602, 1083846, 1719204, 2167692, 4154743, 8309486, 12464229, 16618972, 24928458, 49856916
Well damn. It's not a-smooth or b-smooth (where 'smoothness' is defined as 'all factors are beneath some number n')
but this is far more approachable than just factoring the original product.
It still requires a value of i equal to
i = floor(a/2)
But the results are actually factorable now if this works for other products.
I rewrote the script and tested on a couple million products and added decimal support, and I'm happy to report it works.
Script is posted here if you want to test it yourself:
What I'll do next is probably add some basic factorization of trivial primes
(say the first 100), and then figure out the average number of factors in each derived product.
I'm also still working on getting to values of i < a/2, but only having sporadic success.
It also means *very* large numbers (either a subset of them or universally) with *lots* of factors may be reducible to unique products with just two non-trivial factors, but thats a big question mark for now.
@scor if you want to take a look.5