that's a faster cache. some caches are faster than others. the instructions are only for if the faster cache of a package not being available in an external repository or in the AUR does not yet exist.

the installation instructions act as a cache. people can read them, which is fast, instead of doing computations that could take a long time. ergo, the developer precomputes how to install the software, and writes it down so future computation on how to install the software can be performed in amortised Ο(1) time

the modification API is to allow the user to have multiple modifications at once. this is the most efficient way to do that.

synthetic division is not dumb. long division is dumb

the crux

the numbers are random?

i have plans that actively contradict death

weird

↉, also known as 0

yeah the synthetic division is much simpler, idek where you could've possibly got those values in the long division from

yay! c: bzzzzzzzzzt

of course! it's all explained on the Wikipedia page for synthetic division

hopefully apioforum uses markdown so that link works

divide 3x³ + 2x² + 4x + 7 by x² + 7x - 2 using long division (hard, extremely complicated. borderline impossible. useless)

do the same division using synthetic division (easy, not at all inconvenient, extremely simple. useful) (i also like useful)

long polynomial division is extremely complicated, i'd say it's more opaque for that reason

indeed! bn + d

oh cool, this is related to synthetic division (the best kind of polynomial division). but i discovered this algorithm myself

there's a faster algorithm

start with n = 1

if it's all zeroes the number is 0

ignore all digits up to and including the first 1 (left-to-right)

when you see a zero, 2n

when you see a one, 2n + 1

so 00000101:

n = 1 (1)01

n = 2 1(0)1

n = 4 + 1 10(1)

n = 5

5

red ඞ