coding style – Showing values hold for a a relation given on Mathematica

Find the values of A and B for 10 different positions of Fun1. I need to show thee relation B=16A holds for each of the ten values.

ClearAll(f, t, P, PO)
f(x_) := x^3
df(x_) = f'(x);
tan(x_, x0_) := f(x0) + df(x0) (x - x0)
NSolve(tan(x, 1.2) == f(x), x)
NSolve(tan(x, -2.4) == f(x), x)


Module({x, pts, names, offsets, ptlbls, arealbls}, x(0) = 1.2; 
 x(1) = -2.4; x(2) = 4.8;
 pts = {{x(0), f(x(0))}, {x(1), f(x(1))}, {x(2), f(x(2))}};
 names = {"Fun1", "Fun2", "Fun3"};
 offsets = {{10, -10}, {10, -10}, {-15, 3}};
 ptlbls = MapThread(Text(#1, Offset(#2, #3)) &, {names, offsets, pts});
 arealbls = {Text("A", Offset({-20, 2}, (pts((1)) + pts((2)))/2)), 
   Text("B", Offset({0, -35}, (pts((2)) + pts((3)))/2))};
 Plot(Evaluate@{f(x), tan(x, x(0)), tan(x, x(1))}, {x, -3, 5}, 
  Epilog -> {ptlbls, {Red, AbsolutePointSize(5), Point(pts)}, 
    arealbls}))


```

❓ASK – If Bitcoin must fully accepted then this must hold. | Proxies-free

Ya i believe in what u said, especially KYC, as i know many of the wallet provide for a peak of a particular amount of money, like Payeer, but talking about legacy or not, my country have not accepted this currency as a valid one, but lots of exchanges out in the cities are in it, selling or buying and almost its legal here, i believe any digital currency got it particlur features, like Ripple, Ether, Tether, they all come from validate support system like blockchain, so they are traceable, as we go further, my guess these giant cryptos will seat in shoes of common currencies smoothly but not like this “hey give me a satoshi” i believe Bitcoin is a diamond but we can consider Ripple as common cash, paper money will wipe out soon

abstract algebra – Does hold the isomorphism (A otimes_R B)/J(A otimes_R B) cong (A/J(A)) otimes_R (B/J(B)) for every commutative ring?

while reading an article, I saw the isomorphism $(A otimes_K B)/J(A otimes_K B) cong (A/J(A)) otimes_K (B/J(B))$ where $A$ and $B$ are two algebras over field $K$. Why is this isomorphism true? Also, if $A$ and $B$ are two algebras over the commutative ring $R$ then can we say this isomorphism true?

python game hold down keybind?

(help)
I am very new to python I started to make a pong game, but can’t get it to let me hold down the buttons for the paddel to move, im using the turtle not pygame

 def paddle_a_up():
   y = paddle_a.ycor()
   y += 15
   paddle_a.sety(y)


def paddle_a_down():
    y = paddle_a.ycor()
    y -= 15
    paddle_a.sety(y)


def paddle_b_up():
    y = paddle_b.ycor()
    y += 15
    paddle_b.sety(y)

def paddle_b_down():
    y = paddle_b.ycor()
    y -= 15
    paddle_b.sety(y)

# binds
wn.listen()
wn.onkey(paddle_a_up, "w")
wn.onkey(paddle_a_down, "s")
wn.onkey(paddle_b_up, "o")
wn.onkey(paddle_b_down, "i")

also I cant seem to get my arrow up and down to work with the binds so thats why im using “o” and “i” if you have a solution for that too, I’m very grateful, take care!

❓ASK – Is It a good idea to hold ethereum coin | Proxies-free

I have been thinking of holding some coins for ethereum but before I do that I would like to hear from you guys if it can be a profitable idea, in as much as I know money is found where there’s an idea. I have been reading articles and web pages of people who trust in the ethereum coin results of holding the ethereum coin have been a good step since they still have a long way to go. early this year before the break out of covid-19 the ethereum coin was somewhere at $167 at that time a friend of mine a cryptonist told me that it was the best time to buy the coin because whose value became low but i was inconsiderate in that matter but now I regret not holding because it’s true that the coin raised from about $167 to about $400 and currently is about $250 profit for just holding one ethereum coin yet this is not the end it’s just the beginning.

I therefore think it’s a good idea holding ethereum token, do you have objections and important things to consider that can be an advantage or a disadvantage, please share your ideas we are here to help each other make money online?

real analysis – Does $Vert fVert_{L^infty}^2leq Vert fVert_{L^2}Vert f’Vert_{L^2}$ hold?

I know that Sobolev’s embedding implies that $H^1(mathbb{R})hookrightarrow C(mathbb{R})cap L^infty(mathbb{R})$, which in particular implies that $$
Vert fVert_{L^infty}leq Vert fVert_{H^1}.
$$

Now, I was wondering about the following slightly more specific (?) inequality. More precisely, I was wondering if $fin H^1(mathbb{R})$, then the following inequality holds:
$$
Vert fVert_{L^infty}^2leq Vert fVert_{L^2}Vert f’Vert_{L^2}.
$$

The problem here is to be able to put a factor only with the $L^2$ norm of $f$. Does this inequality hold?

design – What information should a Game Piece hold?

In an OOP design, suppose I have some board type game that has pieces, such as chess, checkers.

In you opinion, what properties should pieces of that game board have?

imo, I feel like the pieces should only contain its respective rules, e.g. it can move like this, and it can do this. The issue I see with this is that, it would require a lot of data passing via arguments, A piece can only know how it is supposed to move if it knows its current location, and maybe location of other pieces etc. This list can become extensive the more dependent a piece is to the state of a game, this is what makes me nervous.

Assuming, I have proper singleton access of the board, the alternative is to let all pieces have access to the entire board instance, and also store data about its state with respect to the game (like its location). This way No arguments need to be passed. is this bad to do?

real analysis – Frequency projectors: Does $Vert (1-P_N)(f^m)Vert_{L^2}leq CVert fVert_{L^infty}^{m-1}Vert (1-P_N)f’Vert_{L^2}$ hold?

Let $minmathbb{N}$ fixed and consider $Ngg1$. Denote by $mathcal{F}$ the Fourier transform, and define the frequency proyector $P_N$ given by $$
mathcal{F}(P_Nf)(xi)=phi_N(xi)mathcal{F}(f)(xi),
$$

where $phi_Nin C_0^infty(mathbb{R})$ is a function supported in the ball $B(0,2N)$, such that $phi_Nequiv 1$ in $B(0,N)$ and $0leq phi_Nleq 1$. Finally, define $overline{P_N}:=1-P_N$. Now, I am wondering the following: Consider any function $fin L^infty(mathbb{R})setminus L^2(mathbb{R})$ such that its derivative $f’in H^2(mathbb{R})$. Hence, if I’m not wrong, $mathcal{F}(f)$ should have very good integrability properties at $xi=pminfty$, but bad behaviour around $xi=0$. So, I am wondering that, if I take out a ball around the frequency-origin, can I bound the $L^2$ norm of $f^m$ for any $m$? More specifically, does the following bound hold $$
Vert overline{P_N}(f^m)Vert_{L^2}leq C Vert fVert_{L^infty}^{m-1}Vert overline{P_N}fVert_{L^2}? quad hbox{or maybe} quad
Vert overline{P_N}(f^m)Vert_{L^2}leq C Vert fVert_{L^infty}^{m-1}Vert overline{P_N}f’Vert_{L^2}?
$$

For me it looks that it should be so obviously true, but I haven’t been able to prove it, particularly because I don’t see how to put $overline{P_N}$ in only one of the $f$‘s. In my opinion it doesn’t look trivial that it is possible to keep $overline{P_N}$ in only one $f$ on the right-hand side. A (maybe important) observation is that, if $f$ satisfies the previous hypothesis, then so does $f^m$ for any $m$, that is $f^min L^infty$ and $(f^m)’in L^2$, etc.

dnd 5e – Can Minotaur Players be targeted by Hold Person and other similar spells?

Minotaur player characters are barrel-chested humanoids.

It says it in the introduction to the playable race, and on page 18 of Guildmaster’s Guide to Ravnica and page 22 of Mythic Odysseys of Theros:

Minotaurs are barrel-chested humanoids.

So a minotaur is affected by hold person.

As you have observed, the two playable races that are not humanoids are given racial traits that explicit designate them as non-humanoids.

NPCs use statblocks

Interstingly enough, the description of the minotaur in the Monster Manual describes minotaurs like so:

Their fur stained with the blood of fallen foes, minotaurs are massive, bull-headed humanoids

Yet, their creature type is monstrosity. Why? NPCs use statblocks. The introduction to the Monster Manual says:

A monster’s statistics, sometimes referred to as its stat block, provide the essential information that you need to run the monster.

One of these statistics is creature type, and a monster’s statblock includes all of its creature types.

PCs use playable races

In contrast with NPCs, player characters use the character creation material found in the various sourcebooks of Dungeons and Dragons. In our particular case, we can find the minotaur playable race in Guildmaster’s Guide to Ravnica and Mythic Odysseys of Theros. The Races section of Theros says:

This chapter provides information about the following common playable races of Theros, as well as racial traits for all of them except humans.

The traits described in this chapter are the traits used for player characters playing as minotaurs. Consequently, nowhere in this chapter (or the parallel chapter in Ravnica) are Minotaurs described as monstrosities, rather they are explicitly described as humanoids.

Finally, since they lack a racial trait like the Satyr and Centaur that explicitly names their creautre type as anything other than humanoid, we conclude that when the book says “Minotaurs are barrel-chested humanoids”, it means they are humanoids.

Humanoid is explicitly the default creature type.

In Chapter 1 of the PHB we see:

Every character belongs to a race, one of the many intelligent humanoid species in the D&D world.

This is found in the Step-by-Step Character Creation chapter of the PHB. Further, we have an important rule to follow, from the Introduction of the PHB:

hat said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.

The races which break this general rule about humanoid PCs (Satyr, Centaur) have specific rules which create the exception:

Your creature type is fey, rather than humanoid.

Since we see nothing similar for the Minotaur playable race, we conclude Minotaur PCs are humanoids.

I can discern my PC’s creature type without the Monster Manual.

After all of this, we can finally offer this compelling heuristic argument.

Heuristic 1: I don’t need the Monster Manual to create my character.

Everything I need to create my player character is found in the Player’s Handbook, or if I am using non-PHB player options, whatever the attendant sourcebook is. In our case, if I am playing a Minotaur, I should be able to know everything I need to know about my Minotaur player character by consulting the PHB and either Ravnica or Theros.

Heuristic 2: Ravnica and Theros do not contain NPC statblocks for the Minotaur.

The reason we know that an NPC Minotaur has creature type monstrosity is because it says so in the Monster Manual on its statblock. But Ravnica and Theros do not contain a statblock for the Minotaur.

If I am a new player creating a Minotaur player character using Theros or Ravnica, I will first encounter in the PHB the statement:

Every character belongs to a race, one of the many intelligent humanoid species in the D&D world.

Then, as I go on to read the playable races section of Ravnica or Theros, I will never encounter the word “monstrosity” in relation to Minotaurs, only the statement:

Minotaurs are barrel-chested humanoids.

Minotaurs may be big, hairy, and terrifying. But even Minotaurs are people who want to be held sometimes.

Thomas casts hold person.