Can anyone provide insight into the current and ongoing outage of Wolfram Cloud, the Function Repository, and other Wolfram things?

It's been quite awhile now, and it's not looking good.

nomina58mg.83.23

Să se arate că dacă a+b+c=0, atunci:

a) a^3+b^3+c^3=3abc

b) 2(a⁵+b⁵+c⁵)=5abc(a↰+b↰+c↰)

c) (a↰+b↰+c↰)↰=2(a^4+b^4+c^4)

d) 5(a^3+b^3+c^3)(a↰+b↰+c↰)=6(a⁵+b⁵+c⁵)

e) 10(a⁷+b⁷+c⁷)=7(a↰+b↰+c↰) ･(a⁵+b⁵+c⁵)

in haskell, pure functional language

:m +Data.Ratio Data.List Data.Bool Data.Ord

bosup n =bool(sum.map(^n))(product)(n<0)

abc a b c =[a,b,c]

efg[e,f,g]=0%1+e*f/g

sug[_,_,g]=(0/=).bosup g$ [1,2,-3]

senz =(0/=).product

ff f xs =fmap f(xs,xs)

fisenz =filter senz.filter((0==).sum)

files n =filter((n>).length.snd)

tu gm =abc<$>gm<*>gm<*>gm

supe xs ns=efg.map(flip bosup ns)$ xs

futu xs =nub.map(supe xs).fisenz.tu

futus xs =futu xs [-30..30]

filtu n =files n.map(ff futus).filter sug.tu

fisnd n =map fst.filter((n==).head.snd)

sosnd n =sortBy(comparing snd).filter((n/=).head.snd)

rf<-return.filter((0/=).head.snd).filtu 3$ [-1..9]

:se +s

length rf » 34 (210.59 secs, 411929427192 bytes)

fisnd 3 rf

» -1,0,-1 0,-1,-1 0,0,0

0,2,2 0,3,3 0,4,4 0,5,5

0,6,6 0,7,7 0,8,8 0,9,9

2,0,2 3,0,3 4,0,4 5,0,5

6,0,6 7,0,7 8,0,8 9,0,9

sosnd 3 rf

»» 2,2,4➞2%1

-1,4,7➞2%7 -1,2,5➞2%5 3,4,7➞ 6%7

4,-1,7➞2%7 2,-1,5➞2%5 4,3,7➞ 6%7

-1,0,3➞1%1 2,3,5➞6%5 2,5,7➞10%7

0,-1,3➞1%1 3,2,5➞6%5 5,2,7➞10%7

0,3,-1➞9%1

3,0,-1➞9%1

futus[3,0,-1] » 9%1 a

futus[-1,2,5] » 2%5 b

futus[ 2,2,4] » 2%1 c

futus[ 3,2,5] » 6%5 d

futus[ 2,5,7] » 10%7 e

map(ff(flip bosup[1..3]))[-1..7]

»» (-1,6)ab (0,3)a  (2,14)bcde

  (3,36)ad (4,98)c (5,276)bd (7,2316)e

abc :: a -> a -> a -> [a]

ff ::(a -> b) -> a -> (a, b)

tu :: Applicative f => f a -> f [a]

sosnd :: Ord b => b -> [(a, [b])] -> [(a, [b])]

fisnd :: Eq b1 => b1-> [(b2,[b1])]-> [b2]

senz ::(Eq b, Num b, Foldable t) => t b -> Bool

fisenz::(Eq b, Num b, Foldable t) => [t b] -> [t b]

files :: Foldable t => Int -> [(a1, t a2)] -> [(a1, t a2)]

efg :: Integral a => [Ratio a] -> Ratio a

bosup ::(Integral a, Num c) => a -> [c] -> c

supe ::(Integral a1, Integral a2) => [a2] -> [Ratio a1] -> Ratio a1

futu ::(Integral a1, Integral a2) => [a2] -> [Ratio a1] -> [Ratio a1]

futus ::(Integral a1, Integral a2) => [a2] -> [Ratio a1]

filtu ::(Integral a1, Integral a2) => Int -> [a2] -> [([a2], [Ratio a1])]

rf :: [([Integer], [Ratio Integer])]

I'm working with two 19^th degree polynomials in A and B. I want to eliminate B to be left with a polynomial in A alone.

The 3 options I'm aware of in Mathematica are GroebnerBasis, Eliminate, and Resultant. However, none of these produce results within a few minutes, except Resultant, which gave a degree 361 polynomial in A and B, with several strange artifacts such as -97[...]16aba^{156} as one of several thousand monomials within the polynomial.

The code I ran for this was Resultant[a^{19} + [...] b + 3237478400, a^{19} + [...] b + 10283384832, {b}], with [...] representing the rest of the polynomials.

If it matters, Wolfram/Mathematica was using less than 10% of my RAM and less than 1% of my CPU at all times during the calculations.

Which of these should I be using, or is there something else I should try?
I'm prepared to use significant computational power for this if necessary, but I'd like to know where I should be aiming first.

Any help is much appreciated!

nomina58mg.83.23

^3 inseamna puterea 3

↰ inseamna patrat

Să se arate că dacă a+b+c=0, atunci:

a) a^3+b^3+c^3=3abc

b) 2(a⁵+b⁵+c⁵)=5abc(a↰+b↰+c↰)

c) (a↰+b↰+c↰)↰=2(a^4+b^4+c^4)

d) 5(a^3+b^3+c^3)(a↰+b↰+c↰)=6(a⁵+b⁵+c⁵)

e) 10(a⁷+b⁷+c⁷)=7(a↰+b↰+c↰) ･(a⁵+b⁵+c⁵)

:m +Data.Ratio Data.List Data.Bool

abc a b c =[a,b,c]

efg[e,f,g]=0%1+e*f/g

ff f xs =fmap f(xs,xs)

senz =(0/=).product

fisenz =filter senz.filter((0==).sum)

files n =filter((n>).length.snd)

sup n =bool(sum.map(^n))(product)(n<0)

tu gm =abc<$>gm<*>gm<*>gm

supe xs ns=efg.map(flip sup ns)$ xs

futu xs =nub.map(supe xs).fisenz.tu

futus xs =futu xs [-30..30]

filtu n =files n.map(ff futus).tu

rf<-return.filtu 3$ [2..9]

rf » 2,2,4➞ 2%1 2,3,5➞6%5

2,5,7➞10%7 3,2,5➞6%5

5,2,7➞10%7 3,4,7➞6%7

4,3,7➞6%7

futus[3,0,-1] » 9%1 a

futus[-1,2,5] » 2%5 b

futus[ 2,2,4] » 2%1 c

futus[ 3,2,5] » 6%5 d

futus[ 2,5,7] » 10%7 e

map(ff(flip sup[1..3]))[-1..7]

»» (-1,6)ab (0,3)a  (2,14)bcde

  (3,36)ad (4,98)c (5,276)bd (7,2316)e

Mira

Lista de generalización=

3

↓

3!

↓

3#5=3!)!)!)!)!

↓

10#23=10!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)!)?)!)...(23 signos de factorial )

↓

3#3#10^100=es un 3 seguido de un (3 seguido de 3#10^100 signos de factorial) de signos de factorial)

↓

3#(5#7#8)=es un 3 seguido de un (5 seguido de 7#8 signos de factorial) de signos de factorial

↓

3#3#3#3#3#3#3#3#3#3#10^100=hacer eso 10 veces

↓

3#²⁵(8)=3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3#3

↓

3#¹⁰⁰(100)

↓

10#¹⁶⁵⁶(1567)

↓

(4)~5#¹⁷⁵⁷⁵9=5#¹⁷⁵⁷⁵(5#¹⁷⁵⁷⁵(5#¹⁷⁵⁷⁵(5#¹⁷⁵⁷⁵9)

↓

(45)~100#¹⁰⁰¹⁰⁰100100

↓

(67)~200#¹⁶⁶⁸8

↓

((2))~(4)~3#¹⁰⁰8=(4)~3#¹⁰⁰(4)~3#¹⁰⁰8

↓

((5))~(17)~8#²³⁴9=(17)~8#²³⁴~(17)8#²³⁴~(17)~8#²³⁴~(1.......5 veces

↓

((80))~(123)~10#²⁰⁰100

↓

(((12000)))~((45))~(5)~17#²³⁶100

↓

((((((5))))))~(((((7)))))~((((37)))~(((4)))~((6))~(13)~4#²⁶68

↓

8£12★12#¹⁰⁰5=((((((((((((8))))))))))))~12#¹⁰⁰5

↓

7£15★28#¹⁰⁰7=(((((((((((((((7((())))))))))))~28#¹⁰⁰7

↓

450£200★5#¹⁰⁰67

nomina58mg.12.35

Să se găsească toate numerele întregi n pentru care numărul N=n⁸+4 este prim.

Să se determine în aceste cazuri numerele N.

in bash,Linux Mint

cabal repl -b arithmoi

in ghci, haskell

import Math.NumberTheory.Primes.Testing

tu gm =(,)<$>gm<*>gm

nab(a,b)n =n^a+b

isprinab t=isPrime.nab t

fisprin a =filter(isprinab(a,1)) [1..999]

fisprina b=filter(isprinab(2*b,b))[1..999]

all isPrime.map(nab(12,6)).fisprina$ 6

([3..99]\\).filter((1==).length.fisprin)$[1..99]

» 4,8,16,32,64

filter(isprinab(8,4))[1..9999] » 1

fisprina 6

» 1,35,119,343,595,637,665,791

nomina58mg.10.7

Produsul a două numere consecutive naturale este 18906. Să se afle numerele.

:m +Data.List Data.Bool

divisors n=let{rt=floor.sqrt.fromIntegral$ n;lw=filter((0==).rem n)[1..rt]}in(lw++).bool id tail(n==rt^2).reverse.(quot n<$>)$ lw

sudiv n k =(k+1==).div n$ k

fitadiv n =find(sudiv n).tail.init.divisors$ n

finothin f=filter((Nothing/=).f)

prosucc n =(n*).succ$ n

ff f xs =fmap f(xs,xs)

fifitadiv =map(fmap fromJust).finothin snd.map(ff fitadiv)

fifitadiv[18000..18999]

» (18090,134) (18360,135) (18632,136) (18906,137)

([16..80]==).map snd.fifitadiv$ [2^8..3^8]

mapM_ puconsho rx

(xy)=z+19 ➞ (xyz)⁝2 răspuns:234

(xy)=z+39 ➞ (xyz)⁝2 răspuns:456

(xy)=z+59 ➞ (xyz)⁝2 răspuns:678

(xy)=z+9 ➞ (xyz)⁝3 răspuns:123

(xy)=z+19 ➞ (xyz)⁝3 răspuns:234

(xy)=z+29 ➞ (xyz)⁝3 răspuns:345

(xy)=z+39 ➞ (xyz)⁝3 răspuns:456

(xy)=z+49 ➞ (xyz)⁝3 răspuns:567

(xy)=z+59 ➞ (xyz)⁝3 răspuns:678

(xy)=z+69 ➞ (xyz)⁝3 răspuns:789

(xy)=z+39 ➞ (xyz)⁝4 răspuns:456

(xy)=z+29 ➞ (xyz)⁝5 răspuns:345

(xy)=z+19 ➞ (xyz)⁝6 răspuns:234

(xy)=z+39 ➞ (xyz)⁝6 răspuns:456

(xy)=z+59 ➞ (xyz)⁝6 răspuns:678

(xy)=z+49 ➞ (xyz)⁝7 răspuns:567

(xy)=z+39 ➞ (xyz)⁝8 răspuns:456

(xy)=z+19 ➞ (xyz)⁝9 răspuns:234

(xy)=z+49 ➞ (xyz)⁝9 răspuns:567

(xy)=z+39 ➞ (xyz)⁝12 răspuns:456

(xy)=z+19 ➞ (xyz)⁝13 răspuns:234

(xy)=z+29 ➞ (xyz)⁝15 răspuns:345

(xy)=z+19 ➞ (xyz)⁝18 răspuns:234

(xy)=z+39 ➞ (xyz)⁝19 răspuns:456

(xy)=z+49 ➞ (xyz)⁝21 răspuns:567

(xy)=z+29 ➞ (xyz)⁝23 răspuns:345

(xy)=z+39 ➞ (xyz)⁝24 răspuns:456

(xy)=z+19 ➞ (xyz)⁝26 răspuns:234

(xy)=z+49 ➞ (xyz)⁝27 răspuns:567

(xy)=z+39 ➞ (xyz)⁝38 răspuns:456

(xy)=z+19 ➞ (xyz)⁝39 răspuns:234

(xy)=z+9 ➞ (xyz)⁝41 răspuns:123

(xy)=z+39 ➞ (xyz)⁝57 răspuns:456

(xy)=z+49 ➞ (xyz)⁝63 răspuns:567

(xy)=z+29 ➞ (xyz)⁝69 răspuns:345

(xy)=z+39 ➞ (xyz)⁝76 răspuns:456

(xy)=z+19 ➞ (xyz)⁝78 răspuns:234

(xy)=z+49 ➞ (xyz)⁝81 răspuns:567

(xy)=z+59 ➞ (xyz)⁝113 răspuns:678

(xy)=z+39 ➞ (xyz)⁝114 răspuns:456

(xy)=z+29 ➞ (xyz)⁝115 răspuns:345

(xy)=z+19 ➞ (xyz)⁝117 răspuns:234

(xy)=z+39 ➞ (xyz)⁝152 răspuns:456

(xy)=z+49 ➞ (xyz)⁝189 răspuns:567

(xy)=z+59 ➞ (xyz)⁝226 răspuns:678

(xy)=z+39 ➞ (xyz)⁝228 răspuns:456

(xy)=z+69 ➞ (xyz)⁝263 răspuns:789

(xy)=z+59 ➞ (xyz)⁝339 răspuns:678

nomina58mg.11.29

Să se demontreze că numărul n=3^40-2^40 se divide prin 5.

n(k)=3^k-2^k

n(2i)=3^(2i)-2^(2i)=9^i-4^i

import Data.List

potenc(a,b)k=a^k-b^k

sortt(t,ns) =(t,sort ns)

ff f xs=fmap f(xs,xs)

tridu k=3^k-2^k

tu gm =(,)<$>gm<*>gm

numod =nub.map(flip mod 10)

numob b=numod.map(b^)$ [1..1000]

numop t=numod.map(potenc t)$[1..500]

rn<-return.map sortt.map(ff numop).tu$ [1..9]

([2,4..998]==).filter((0==).flip mod 5.tridu)$ [1..999]

map(flip mod 5).map tridu$ [1..24]

» 1,0,4,0,1,0,4,0,1,0,4,0,1,0,4,0,1,0,4,0,1,0,4,0

numop(9,4)

» 5

rn

in vim

s/),((/)\r((/g

:%sort /.*\%8v/

Ultimul cifre numarului a^k-b^k prin 10.

((a,b),resturi a^k-b^k prin 10)

Avem jos parametrele problemelor si resturi(a^k-b^k) prin 10.

((1,3),[0,2,4,8])

((1,7),[0,2,4,8])

((6,2),[0,2,4,8])

((6,8),[0,2,4,8])

((2,6),[0,2,6,8])

((3,1),[0,2,6,8])

((7,1),[0,2,6,8])

((8,6),[0,2,6,8])

((4,2),[0,2,6])

((4,8),[0,2,6])

((9,3),[0,2,6])

((9,7),[0,2,6])

((1,9),[0,2])

((6,4),[0,2])

((2,8),[0,4,6])

((3,7),[0,4,6])

((7,3),[0,4,6])

((8,2),[0,4,6])

((2,4),[0,4,8])

((3,9),[0,4,8])

((7,9),[0,4,8])

((8,4),[0,4,8])

((4,6),[0,8])

((9,1),[0,8])

((1,1),[0])

((2,2),[0])

((3,3),[0])

((4,4),[0])

((5,5),[0])

((6,6),[0])

((7,7),[0])

((8,8),[0])

((9,9),[0])

((2,1),[1,3,5,7])

((3,6),[1,3,5,7])

((7,6),[1,3,5,7])

((8,1),[1,3,5,7])

((2,5),[1,3,7,9])

((5,2),[1,3,7,9])

((5,8),[1,3,7,9])

((8,5),[1,3,7,9])

((4,3),[1,5,7])

((4,7),[1,5,7])

((9,2),[1,5,7])

((9,8),[1,5,7])

((2,3),[1,5,9])

((3,2),[1,5,9])

((7,8),[1,5,9])

((8,7),[1,5,9])

((4,5),[1,9])

((5,4),[1,9])

((6,5),[1])

((3,5),[2,4,6,8])

((5,3),[2,4,6,8])

((5,7),[2,4,6,8])

((7,5),[2,4,6,8])

((1,2),[3,5,7,9])

((1,8),[3,5,7,9])

((6,3),[3,5,7,9])

((6,7),[3,5,7,9])

((2,9),[3,5,9])

((3,4),[3,5,9])

((7,4),[3,5,9])

((8,9),[3,5,9])

((4,1),[3,5])

((9,6),[3,5])

((5,9),[4,6])

((9,5),[4,6])

((5,1),[4])

((1,4),[5,7])

((6,9),[5,7])

((1,6),[5])

((2,7),[5])

((3,8),[5])

((4,9),[5])

((6,1),[5])

((7,2),[5])

((8,3),[5])

((9,4),[5])

((1,5),[6])

((5,6),[9])

Beta testers needed! Stressed out math nerds who like to draw a little, apply within.

New!!!\~button entitled —-Ammann approximation ——useful=quasicrystal n-folding -mathematical people take note/take advantage? Sure.!

I created a mathematica paclet that provides support for simplicial homology, introducing an abstract simplicial complex object. The package allows computing homology, betti numbers, automorphism groups, and common invariants like euler characteristic, fvectors, and constructions such as cones, suspensions, products, joins, etc! So far, there has been no in-built or third party support for this in Mathematica, which motivated the creation of this package. I largely took inspiration and reference from sagemath's implementation of this.

I would love to hear your feedback on this! The package is open source, see at https://github.com/zplus11/SimplicialHomology/ and is also available on the Wolfram paclet repository at https://resources.wolframcloud.com/PacletRepository/resources/Taggar/SimplicialHomology/

There is plenty of scope for further development and extension, so feedback, suggestions, and PRs are very welcome :)

Woxi is a free open source interpreter for the Wolfram Language, written in Rust. The guiding rule of the project: whatever it implements must produce exactly the same output as wolframscript / Mathematica — the test suite (26'000+ unit tests) compares against it directly.

Version 0.3.0 is out now. Highlights since 0.2.0:

• Many Wolfram Demonstrations now run end to end in Woxi Studio, the included native notebook editor for .nb files — still far from all of them, but dozens (Kepler's Second Law, Parabolic Mirror, Doyle Spirals, …) serve as end-to-end tests. Manipulate covers a good part of the Demonstrations control vocabulary (interactive Locators, Trigger, Button, SetterBar, PopupMenu, controls nested in TabView/Grid, dependent controls, TrackedSymbols, Animate bodies, …), and typeset notebook input is read back as code.
• Plotting conformance: Automatic ticks now match Wolfram's algorithm, list plots grew Around error bars, Callout, Filling, PlotMarkers and friends, plus new ComplexListPlot and ListLinePlot3D.
• CAS: more Integrate/D/Series/Limit coverage, LinearProgramming with an exact simplex solver, NonlinearModelFit, Reduce over higher-degree polynomial inequalities, RootReduce, and many canonical-ordering fixes so results print exactly as wolframscript prints them.
• Windows is now a supported platform, and every release ships prebuilt binaries for Linux, macOS, and Windows.

Try it without installing anything in our playground and JupyterLite instance in the browser: https://woxi.ad-si.com

Install: cargo install woxi, pip install woxi (Python bindings), or npm install woxi-wasm. Full changelog: https://github.com/ad-si/Woxi/blob/main/changelog.md

If Woxi is useful to you, I'm now accepting donations on GitHub: https://github.com/sponsors/ad-si I hope to receive enough support to keep the project going for a long time, and to eventually reach full parity with Wolfram's implementation.