## Determine third normal form in case of two functional dependencies

Assume I’m given an entity `E` which has attributes `A`, `B` and `C`, (each of them is a candidate key, but let’s say I can introduce some `EID` that serves as a PK) with functional dependencies: `A` determines `C` and `B` determines `C`. How would I get this into a third normal form?

I have tried the following:

``E(EID(PK), AID(FK), BID(FK)) A(AID(PK), C) B(BID(PK), C) ``

but in this representation, I’m have the attribute `C` twice in my database. Can anyone advise on a more appropriate way of getting into a third normal form?

## Real solutions of third and fourth degree equations

A few hours ago I "discovered" that if a third or fourth degree equation has distinct real solutions, it’s possible to calculate them avoiding complex numbers.

In particular, we have:

``poly = (x - 1)(x - 2)(x - 3); {c, b, a} = CoefficientList[poly, x][[1 ;; 3]]; d = a^2/3 - b; e = 2 a^3/27 - a b/3 + c; f = ArcCos[-3 Sqrt[3] e/(2 d Sqrt[d])]; N[{-a/3 + 2 Sqrt[3 d] Cos[(f - 4 Pi)/3]/3,    -a/3 + 2 Sqrt[3 d] Cos[(f - 2 Pi)/3]/3,    -a/3 + 2 Sqrt[3 d] Cos[(f - 0 Pi)/3]/3}] ``

{1., 2., 3.}

``poly = (x - 1)(x - 2)(x - 3)(x - 4); {d, c, b, a} = CoefficientList[poly, x][[1 ;; 4]]; e = 3 a^2/4 - 2 b; f = 2 c - a b + a^3/4; g = b^2 + 12 d - 3 a c; h = 27 a^2 d - 9 a b c + 2 b^3 - 72 b d + 27 c^2; i = ArcCos[h/(2 g Sqrt[g])]; j = (e + 2 Sqrt[g] Cos[i/3])/3; N[{-a/4 - (Sqrt[j] + Sqrt[e - j + f/Sqrt[j]])/2,    -a/4 - (Sqrt[j] - Sqrt[e - j + f/Sqrt[j]])/2,    -a/4 + (Sqrt[j] - Sqrt[e - j - f/Sqrt[j]])/2,    -a/4 + (Sqrt[j] + Sqrt[e - j - f/Sqrt[j]])/2}] ``

{1., 2., 3., 4.}

After a few moments of joy, however, I noticed that, for example, if I write `(x - 10^-15)` instead of `(x - 1)`, I get respectively `6.66134*10^-16` and `8.88178*10^-16` instead of `10^-15` as the solution.

I intuitively believe that it’s a numerical problem and that the main cause is `ArcCos`, but I’m not too sure and also I’m not able to establish if something can be done to solve the issue, or if I have to give up and I must necessarily rely on it to the good Newton method.

Thank you!

## If one character is grappling another, will they be pulled by a third character casting Thorn Whip?

My Fighter NPC and a Barbarian PC were prone, and the Fighter had the Barbarian grappled. A PC Druid then used thorn whip (PHB, p. 282) to pull the Fighter.

Do both the Fighter and Barbarian get pulled? Can the Druid even pull the Fighter?

## How can I transfer this code (originally for FPS template) for use in a Third Person Template?

I learned how to create a blueprint for making a character be able to pick up and drop objects: It did not work, and I believe the reason is because it was originally made to work for the FPS template that Unreal comes with. I decided to use the Third Person template, and I think that’s why it’s not working. Am I correct? What blueprint coding should I be looking at? What’s missing, or what’s preventing this from working? Thanks!

## Are the 3.5e Dragonlance books third party or official works?

When 3rd edition rolled around, Wizards of the Coast handed the maintenance of the Dragonlance setting to Sovereign Press, the printing company owned by Dragonlance co-founder Margaret Weis. They released several Dragonlance books all the way until the end of their licence, not too long before 4th Edition came rolling around.

But I’m curious if this means that those Dragonlance books are canon. I rarely see them being referenced by guides and people talking about character builds in general, and even then in only a select few cases. which lead me to suspect that the books are not “official” works like the regular, the Forgotten Realms and the Eberron books are.

Is this true? Are they third party works because they’re printed by Sovereign Press rather than Wizards of the Coast? Or are they still official because Sovereign Press was licensed to print them, and they are an established setting and bear the WotC seal of approval?

## In what ways can you trust a third party server with your data?

What can you do that will make it easier for you to trust a third-party server? For example, using Intel sgx enclaves.

## GroupBy and Rule to select the first and third elements based on the second

Let’s say I have a matrix like

``m={{1,a,2},{4,b,3},{6,a,8},{7,c,10},{2,c,5}} ``

How can I use GroupBy to pick the first and third elements using the second one? I tried

``GroupBy[m, #[[2]]&->#[[{1,3}]]&] ``

which is apparently wrong.

## Can the third benefit of the Mobile feat prevent multiple creatures you attack in a single turn from making opportunity attacks against you that turn?

I am playing a monk. I wanted to use the Mobile feat, specifically the third option that prevents opportunity attacks, to do the following:

1. hit creature 1 with my attack, then move away from creature 1
2. then use Flurry of Blows on creature 2, then move away
3. then make an unarmed strike on creature 3

…all without provoking opportunity attacks from any of them, thanks to the Mobile feat.

However, I was told that I can not do that because it only works for one creature and only my action is a "melee attack" or some such reason.

Is my interpretation right according to "rules as written", or am I misunderstanding how it works? It seems quite vague.

## How could I make the results of a yes/no vote inaccessible unless it’s unanimous in the affirmative, without a trusted third party?

A family of N people (where N >= 3) are members of a cult. A suggestion is floated anonymously among them to leave the cult. If, in fact, every single person secretly harbors the desire to leave, it would be best if the family knew about that so that they could be open with each other and plan their exit. However, if this isn’t the case, then the family would not want to know the actual results, in order to prevent infighting and witch hunting.

Therefore, is there some scheme by which, if everyone in the family votes yes, the family knows, but all other results (all no, any combination of yes and no) are indistinguishable from each other for all family members?

Some notes:

• N does have to be at least 3 – N=1 is trivial, and N=2 is impossible, since a yes voter can know the other person’s vote depending on the result.
• The anonymous suggestor is not important – it could well be someone outside the family, such as a someone distributing propoganda.
• It is important that all no is indistinguishable from mixed yes and no – we do not want the family to discover that there is some kind of schism. However, if that result is impossible, I’m OK with a result where any unanimous result is discoverable, but any mixed vote is indistinguishable.