In mathematics, the Rabinowitsch trick, introduced by George Yuri Rainich and published under his original name ,is a short way of proving the general case of the Hilbert Nullstellensatz from an easier special case (the so-called weak Nullstellensatz), by introducing an extra variable. The Rabinowitsch trick goes as follows. Let K be an algebraically closed field. Suppose the polynomial f in K[x1,...xn] vanishes whenever all polynomials f1,....,fm vanish. Then the polynomials f1,....,fm, 1 − x0f have no common zeros (where we have introduced a new variable x0), so by the weak Nullstellensatz for K[x0, ..., xn] they generate the unit ideal of K[x0 ,..., xn]. Spelt out, this means there are polynomials such that as an equality of elements of the polynomial ring . Since are free variables, this equality continues to hold if expressions are substituted for some of the variables; in particular, it follows from substituting that as elements of the field of rational functions , the field of fractions of the polynomial ring . Moreover, the only expressions that occur in the denominators of the right hand side are f and powers of f, so rewriting that right hand side to have a common denominator results in an equality on the form for some natural number r and polynomials . Hence which literally states that lies in the ideal generated by f1,....,fm. This is the full version of the Nullstellensatz for K[x1,...,xn]. (Wikipedia).
stereolab - puncture in the radax permutation
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From playlist the absolute best of stereolab
Rope Trick for my neighborhood
During my show, a rope is spotted in my sleeve. I pull it...
From playlist My Magic
algebraic geometry 8 strong nullstellensatz
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the proof of the strong nullstellensatz using the Rabinowitsch trick, and gives some examples.
From playlist Algebraic geometry I: Varieties
Commutative algebra 31 (Nullstellensatz)
This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. We describe the weak and strong Nullstellensatz, and give short proofs of them over the complex numbers using Rabinowitsch's
From playlist Commutative algebra
From playlist Trigonometry TikToks
In this video we will explore the difference between a radian and a degree and not only when to use each but how to convert between each other. ⭐️ Stop Memorizing the Unit Circle - https://www.youtube.com/watch?v=qW6Ua50fTw8 ✅ New Trigonometry Videos - https://youtube.com/playlist?list=P
From playlist Trigonometry in Pre-Calculus
This is my entry to Ericsurf6's contest. http://www.youtube.com/watch?v=yYlHLoGqNT0 Find me on FaceBook: http://www.facebook.com/pages/YouTube-TyYanns-page/130204640380067
From playlist Other...
Radian Measure (Mini Lesson) - Algebra 2
http://www.youtube.com/vinteachesmath This video provides a mini lesson on the concept of radian measure. In particular, this video shows how the unit circle, circumference, and degree measure of an angle can be used to explain the concept of radian measure. This video is appropriate fo
From playlist Trigonometry (old videos)
Sleight of Hand Magic Card Trick, Revealed!
A super simple, yet effective trick. Learn in seconds!
From playlist Magic Tricks
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1 quick super finger board trick. Slow motion!
From playlist Funny Videos, Parodies, Odds and ends!
You're about to learn 25 tricks that will help you to work faster, write better pandas code, and impress your friends. These are the BEST tricks I've learned from 5 years of teaching Python's pandas library. Don't miss the BONUS at the end of this video! TRICKS: 0:00 Introduction 0:43 1.
From playlist Data analysis in Python with pandas
Make Up YOUR OWN Math Trick Part 2 // Math Minute [#11] [NUMBER SENSE] [ALGEBRA]
Let’s make up a math trick! Following up on Math Minute #10 (https://youtu.be/y50vMg4Qgs0), today we’re going to use the area model for multiplication to make up OUR OWN math trick. We actually end up building two different tricks: a multiply numbers above and below 100 (by the same amount
From playlist Math Minutes
You're about to learn 21 tricks that will help you to work faster, write better pandas code, and impress your friends. These are the BEST tricks that I couldn't fit into my FIRST tricks video! 📔 JUPYTER NOTEBOOK: https://nbviewer.org/github/justmarkham/pandas-videos/blob/master/21_more_pa
From playlist Data analysis in Python with pandas
7 Derivative Tricks (Often not taught)
Here are 7 derivative tricks not often taught! This is my full derivative shortcuts course that will save you a ton of time and make your life easier. In my experience, most calculus teachers will not teach you these calc tricks. (at least they won't always be emphasized) I hope you enjoy
From playlist Math Tricks
Is THIS The Greatest Trick Ever Filmed?!
MY SHOP: https://www.1st.shop/ Cool Stuff Available here: https://bit.ly/3f8RDm0 Gaming Channel: https://www.youtube.com/chrisramsaytv My Twitch Channel: https://www.twitch.tv/chrisramsay52 ____________________________________________________________ 1000's of PUZZLES Available here: http:
From playlist REACTING TO MAGIC
Deep Learning 8: Unsupervised learning and generative models
Shakir Mohamed, Research Scientist, discusses unsupervised learning and generative models as part of the Advanced Deep Learning & Reinforcement Learning Lectures.
From playlist Learning resources
Anyone can do these quick magic tricks...
MY SHOP: https://www.1st.shop/ Special Thanks to @LeclericShow for Helping me with this list! 5 Tricks: https://www.penguinmagic.com/p/S3042 https://www.penguinmagic.com/p/S3019 https://www.penguinmagic.com/p/S8379 https://www.penguinmagic.com/p/8432 https://www.penguinmagic.com/p/12153
From playlist Tutorials
Same Tens Digit, Ones Digits Add to 10 [Math Trick Monday] #mathtrickmonday #mentalmath #numbersense
This is probably my all time favorite mental multiplication shortcut. Given two two-digit numbers that share a tens digit and which have ones digits that add up to 10, we can compute the product simply by multiplying the ones digits (this is the final two digits of the product), and then m
From playlist Number Sense (UIL / PSIA)
Learn how to convert an angle in decimal form of degrees to radians
👉 Learn all about angles of trigonometry. In this playlist, we will explore what makes up an angle and how to graph an angle in degrees or radians to determine the quadrant. We will then take a look at angle relationships such as determining the complementary angle, supplementary angles,
From playlist Convert Degrees to Radians