#polynomials — Public Fediverse posts

Alright, future engineers!
**Synthetic Division** is a shortcut to divide a polynomial by a linear factor `(x-k)`.
Ex: `(x^3 - x^2 + x - 1) / (x-1)` use `k=1`.
Pro-Tip: ONLY works if the divisor is `(x-k)`! Not for `x^2+1` or higher powers.
#Polynomials #Algebra #STEM #StudyNotes

🤓 Ah yes, the riveting tale of #Lagrange Interpolating Polynomials—a math nerd’s wet dream! 📈 Just what the internet needs: *another* 5000-word novel on fitting curves to dots! 🤯 Because who doesn’t love a good bedtime story about polynomial coefficients? 🙄
https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/ #mathnerd #mathstories #polynomials #datafitting #curvefitting #HackerNews #ngated

@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true

🤓 Ah yes, the riveting tale of #Lagrange Interpolating Polynomials—a math nerd’s wet dream! 📈 Just what the internet needs: *another* 5000-word novel on fitting curves to dots! 🤯 Because who doesn’t love a good bedtime story about polynomial coefficients? 🙄
https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/ #mathnerd #mathstories #polynomials #datafitting #curvefitting #HackerNews #ngated

🤓 Ah yes, the riveting tale of #Lagrange Interpolating Polynomials—a math nerd’s wet dream! 📈 Just what the internet needs: *another* 5000-word novel on fitting curves to dots! 🤯 Because who doesn’t love a good bedtime story about polynomial coefficients? 🙄
https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/ #mathnerd #mathstories #polynomials #datafitting #curvefitting #HackerNews #ngated

🤓 Ah yes, the riveting tale of #Lagrange Interpolating Polynomials—a math nerd’s wet dream! 📈 Just what the internet needs: *another* 5000-word novel on fitting curves to dots! 🤯 Because who doesn’t love a good bedtime story about polynomial coefficients? 🙄
https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/ #mathnerd #mathstories #polynomials #datafitting #curvefitting #HackerNews #ngated

Alright, future engineers!
**Factoring** breaks down a polynomial into a product of simpler expressions.
Ex: `x^2 + 5x + 6 = (x+2)(x+3)`
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Factoring** breaks a polynomial into simpler expressions (factors) that multiply to it. Ex: `x^2+5x+6 = (x+2)(x+3)`. Pro-Tip: Always look for a Greatest Common Factor (GCF) first!

#Algebra #Polynomials #STEM #StudyNotes

I've been making plots of the sets of roots of some polynomials. They look more interesting than I'd expected! And I've been making sounds from them, too. I have a bunch on this page of my website (I'll probably be adding more). Click on the images to embiggen them, and if you're in a hurry, the last sound on the page is the most catchy. https://www.madandmoonly.com/doctormatt/sound/littlewoodPolynomials/

#mathematics #math #maths #polynomials #sonification #illustration #sound

Notes on Lagrange Interpolating Polynomials

https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/

#HackerNews #LagrangeInterpolate #Polynomials #Math #Education #DataScience #Algorithms

#Noisevember! I revisited the Littlewood polynomial sound from day 2 of Noisevember. I thought to investigate a different sort of polynomial. Here, instead of polynomials with coefficients all ±1, the polynomials have coefficient ±1/(n+1) on the x^n term. As before, all roots of all such 15th degree polynomials are considered. (I really should create a gallery of these root plots so we can easily compare them.) Along the way, I realized I was making an error with the way I created "random" stereo that introduced a bunch of unneeded noise. So that's something! I'll have to go back and replace the Littlewood polynomial sound. https://soundcloud.com/matthew-m-conroy/out-keep1

Here's a plot of the roots (essentially the spectrogram of the sound).

#noise #sound #audio #math #maths #mathematics #polynomials #roots

Hi fam, have a fulfilling weekend! Some joker marked my account, e.g. this post about #polynomials & #calculus, which is a textbook example of #inclusion, as spam. This is incredibly unfair; So I'm asking you to share this: bsky.app/profile/paul... (w #ALText) as a protest. #education #mathematics

RE: https://bsky.app/profile/did:plc:omyr27fmzj3phbagch4sqyub/post/3lbwoytxzo22d

Convolutions, Polynomials and Flipped Kernels

https://eli.thegreenplace.net/2025/convolutions-polynomials-and-flipped-kernels/

#HackerNews #Convolutions #Polynomials #FlippedKernels #MachineLearning #DataScience

**A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode**

“_....the hyper-Catalan numbers 𝐶𝐦 count the number of subdivisions of a polygon into a given number of triangles, quadrilaterals, pentagons, etc. (its type 𝐦), and we show that their generating series solves a polynomial equation of a particular geometric form. This solution is straightforwardly extended to solve the general univariate polynomial equation._”

Wildberger, N. J. and Rubine, D. (2025) ‘A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode’, The American Mathematical Monthly, pp. 1–20. doi: https://doi.org/10.1080/00029890.2025.2460966.

#OpenAccess #OA #Article #DOI #Maths #Mathematics #Math #Algebra #Polynomials #Academia #Academics

One day, one decomposition
A235034: Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235034.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #divisors #polynomials #graph #threejs #webGL

One day, one decomposition
A235033: Numbers which are factored to a different set of primes in Z as to the irreducible polynomials in GF(2)[X]

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235033.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235033.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #primes #PrimeNumbers #irreducible #polynomials #graph #threejs #webGL

I ran across the Wikipedia article on Littlewood polynomials. It has a plot of all the roots of the degree 15 polynomials, that looks very nice. I thought I would create an animation showing the roots for degree 1, degree 2, etc. I also thought maybe I'd add a plot of the roots for something with degree higher than 15. Here is the degree 16 plot (this is reduced to 25% of the original image). It took 2 hours in Sage on my laptop, so I might try 17, even 18 - who knows? I have the thought that I ought to be able to reduce the precision, and this ought to speed things up a lot (since for plotting much lower precision than the default is needed). I don't particularly like blue, though: I'll have to try other colors.
https://en.wikipedia.org/wiki/Littlewood_polynomial

#mathematics #littlewood #littlewoodPolynomials #polynomials #plotting #sagemath #graphics #illustration

#Maths #Mathematics Truncated tetrahedron. An Archimedean solid, this polyhedron is mapped from the continuous polynomial ((x+y)/(z+1))^60+((y+z)/(x+1))^60+((z+x)/(y+1))^60 +(.6x+.6y+.6z)^60+(.6x+.6y-.6z)^60+(.6x-.6y+.6z)^60+(-.6x+.6y+.6z)^60-1=0 and comprises four regular hexagon and four equilateral triangle faces, twelve vertices and eighteen edges. #Polynomials

@rwxrwxrwx
I wrote this function #'LAMBDAISE that turns a cl-buchberger:polynomial into an unevaluated lambda form at run time. I feel like this is going to have a more elegant expression, but I figure if
the lambdaiseing is happening offline it's okay. What do you think? What do other #CommonLisp #lisp users think? #polynomials will use for synth later

#100daystooffload on codes for turning symbolic polynomials into lambda forms
https://gopher.tildeverse.org/tilde.club/0/~screwtape/synthember-100days-tooffload/008.lisp.txt

@82mhz @thankfulmachine @AlgoCompSynth

So....#Lagrange #polynomials. They are pretty dang clever and pretty dang amazing. You can get an analytic (if that's the word I want) polynomial fit! That you can take a continuous derivative!

For arbitrary data, I can see why it might not work.

But for a physical object that actually is moving according to a 2nd-order kinematics (piecewise--really 3rd-order overall) but all you have data for the the first two orders, it might be a good way to recover the higher order(s).

#math #numerical

Since I was teaching orthogonal #polynomials (OPs), I asked my class whether they’d read Great Expectations by #Dickens, which you may remember had APs :)

#Avocado themed #complex #polynomials

One day, one decomposition
A235034: Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235034.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #divisors #polynomials #graph #threejs #webGL

One day, one decomposition
A235034: Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235034.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #divisors #polynomials #graph #threejs #webGL

One day, one decomposition
A235034: Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235034.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #divisors #polynomials #graph #threejs #webGL

One day, one decomposition
A235034: Numbers whose prime divisors, when multiplied together without carry-bits (as encodings of GF(2)[X]-polynomials, with A048720), produce the original number; numbers for which A234741(n) = n

3D graph, threejs - webGL ➡️ https://decompwlj.com/3Dgraph/A235034.html
2D graph, first 500 terms ➡️ https://decompwlj.com/2Dgraph500terms/A235034.html

#decompwlj #math #mathematics #sequence #OEIS #javascript #php #3D #numbers #prime #divisors #polynomials #graph #threejs #webGL

@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true

@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true

@catselbow
Astonishing! I hadn't come across this before - absolutely fascinating!
#maths #mathematics #polynomial #polynomials #CatalanNumbers #combinatorics #Galois #GaloisTheory
https://www.tandfonline.com/doi/epdf/10.1080/00029890.2025.2460966?needAccess=true

Alright, future engineers!
**Factoring** breaks down a polynomial into a product of simpler expressions.
Ex: `x^2 + 5x + 6 = (x+2)(x+3)`
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!
**Factoring** breaks down a polynomial into a product of simpler expressions.
Ex: `x^2 + 5x + 6 = (x+2)(x+3)`
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!
**Factoring** breaks down a polynomial into a product of simpler expressions.
Ex: `x^2 + 5x + 6 = (x+2)(x+3)`
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!
**Factoring** breaks down a polynomial into a product of simpler expressions.
Ex: `x^2 + 5x + 6 = (x+2)(x+3)`
Pro-Tip: Always look for a Greatest Common Factor (GCF) first! It simplifies everything.
#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Factoring** breaks a polynomial into simpler expressions (factors) that multiply to it. Ex: `x^2+5x+6 = (x+2)(x+3)`. Pro-Tip: Always look for a Greatest Common Factor (GCF) first!

#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Factoring** breaks a polynomial into simpler expressions (factors) that multiply to it. Ex: `x^2+5x+6 = (x+2)(x+3)`. Pro-Tip: Always look for a Greatest Common Factor (GCF) first!

#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Factoring** breaks a polynomial into simpler expressions (factors) that multiply to it. Ex: `x^2+5x+6 = (x+2)(x+3)`. Pro-Tip: Always look for a Greatest Common Factor (GCF) first!

#Algebra #Polynomials #STEM #StudyNotes

Alright, future engineers!

**Factoring** breaks a polynomial into simpler expressions (factors) that multiply to it. Ex: `x^2+5x+6 = (x+2)(x+3)`. Pro-Tip: Always look for a Greatest Common Factor (GCF) first!

#Algebra #Polynomials #STEM #StudyNotes

Thank you for your comment! #Calculus of #polynomials could also be really simple. I hope you'll enjoy lazybones's darling;) Polynomials: n-dimensional cuboids. Epsilon, fuck off!

I've been making plots of the sets of roots of some polynomials. They look more interesting than I'd expected! And I've been making sounds from them, too. I have a bunch on this page of my website (I'll probably be adding more). Click on the images to embiggen them, and if you're in a hurry, the last sound on the page is the most catchy. https://www.madandmoonly.com/doctormatt/sound/littlewoodPolynomials/

#mathematics #math #maths #polynomials #sonification #illustration #sound

I've been making plots of the sets of roots of some polynomials. They look more interesting than I'd expected! And I've been making sounds from them, too. I have a bunch on this page of my website (I'll probably be adding more). Click on the images to embiggen them, and if you're in a hurry, the last sound on the page is the most catchy. https://www.madandmoonly.com/doctormatt/sound/littlewoodPolynomials/

#mathematics #math #maths #polynomials #sonification #illustration #sound

I've been making plots of the sets of roots of some polynomials. They look more interesting than I'd expected! And I've been making sounds from them, too. I have a bunch on this page of my website (I'll probably be adding more). Click on the images to embiggen them, and if you're in a hurry, the last sound on the page is the most catchy. https://www.madandmoonly.com/doctormatt/sound/littlewoodPolynomials/

#mathematics #math #maths #polynomials #sonification #illustration #sound

I've been making plots of the sets of roots of some polynomials. They look more interesting than I'd expected! And I've been making sounds from them, too. I have a bunch on this page of my website (I'll probably be adding more). Click on the images to embiggen them, and if you're in a hurry, the last sound on the page is the most catchy. https://www.madandmoonly.com/doctormatt/sound/littlewoodPolynomials/

#mathematics #math #maths #polynomials #sonification #illustration #sound

A now a message from the Society for the Protection of Polynomials.

Hi! We at the Society for the Protection of Polynomials remind you that factoring a polynomial is not a harmless operation. Whenever you factor a polynomial, you are causing untold damage to it.

Don't factor polynomials.

Keep them whole.

This was a message from the Society for the Protection of Polynomials.

#polynomials #SocietyForTheProtectionOfPolynomials

A now a message from the Society for the Protection of Polynomials.

Hi! We at the Society for the Protection of Polynomials remind you that factoring a polynomial is not a harmless operation. Whenever you factor a polynomial, you are causing untold damage to it.

Don't factor polynomials.

Keep them whole.

This was a message from the Society for the Protection of Polynomials.

#polynomials #SocietyForTheProtectionOfPolynomials

A now a message from the Society for the Protection of Polynomials.

Hi! We at the Society for the Protection of Polynomials remind you that factoring a polynomial is not a harmless operation. Whenever you factor a polynomial, you are causing untold damage to it.

Don't factor polynomials.

Keep them whole.

This was a message from the Society for the Protection of Polynomials.

#polynomials #SocietyForTheProtectionOfPolynomials

A now a message from the Society for the Protection of Polynomials.

Hi! We at the Society for the Protection of Polynomials remind you that factoring a polynomial is not a harmless operation. Whenever you factor a polynomial, you are causing untold damage to it.

Don't factor polynomials.

Keep them whole.

This was a message from the Society for the Protection of Polynomials.

#polynomials #SocietyForTheProtectionOfPolynomials

Notes on Lagrange Interpolating Polynomials

https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/

#HackerNews #LagrangeInterpolate #Polynomials #Math #Education #DataScience #Algorithms

Notes on Lagrange Interpolating Polynomials

https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/

#HackerNews #LagrangeInterpolate #Polynomials #Math #Education #DataScience #Algorithms

Notes on Lagrange Interpolating Polynomials

https://eli.thegreenplace.net/2026/notes-on-lagrange-interpolating-polynomials/

#HackerNews #LagrangeInterpolate #Polynomials #Math #Education #DataScience #Algorithms