Can undead creatures (raised by a necromancy spell) climb a rope, climb a ladder, or swim?

I’m thinking about making a Necromancy wizard, but had a few questions about RAW.

Would undead from the animate undead spell (or any necromancer spells), e.g. skeletons or zombies, be able to climb a rope, climb a ladder, or swim?

I feel like they would be able to climb a ladder, the rope is a little iffy, and swimming would be a no.

That said, I haven’t found any restrictions or parameters in the PHB or DMG that mention those rules.

Any help would be appreciated, thanks!

How do you typeset raised indices in Mathematica?

I’m trying to follow a book that uses the variable $ x$ for dimension in cartesian coordinates and $ x’$ for the polar coordinates. I’d like to use this typesetting in my Mathematica notebook so I don’t have to mentally convert.

Instead of using $ r$ and $ \theta$ , how would you typeset something like:$ $ mat=\begin{bmatrix}cos x’^2 & -x’^1 sin x’^2 \sin x’^2 & x’^1 cos x’^2\end{bmatrix}$ $ Where $ x’^1$ is used in the place of $ r$ and $ x’^2$ is used in the place of $ \theta$ ? Is it practical to work with this kind of typesetting in Mathematica?

Can a creature be True Polymorphed into a corpse and then raised?

Inspired by If a corpse is polymorphed into a creature, does it retain personality?

True Polymorph can turn a creature into an object

Creature into Object. If you turn a creature into an object, it transforms along with whatever it is wearing and carrying into that form. The creature’s statistics become those of the object, and the creature has no memory of time spent in this form, after the spell ends and it returns to its normal form.

Since a corpse is an object, a creature can be True Polymorphed into a corpse.

Can it then be raised, by a spell such as revivify or true resurrection?

How would uncontrolled zombies react to a zombie raised by a necromancer?

If a necromancer raises a zombie, then orders the zombie to cross into area containing non-controlled zombies, how would the non-controlled zombies react? I’ve always assumed ‘wild’ undead don’t destroy one another, but is there a reason for that?

I’m asking about D&D 5e, but I’d be interested if any edition of D&D commented on this.

Can a Black Dragon Hatchling be raised to be good? Or is it inherently evil?

The following came up during my campaign:

The characters got their hands on some Black Dragon eggs. The PCs put out the thought that if they got the eggs to hatch, they could raise the dragons to be “good”.

In canon D&D, can a Black Dragon Hatchling be raised to be good?

Of course you can say DM discretion but I’m not asking about DM discretion. I’m asking about what would happen in the canon D&D universe in the “normal” case.

Decompose any number to its prime factors raised to their respective powers

Yo…a simple code which takes the given number as input and gives all of its prime factors raised to their respective powers…works well upto 106 after that it slows down greatly for some numbers..but works smoothly if the numbers don’t have many prime factors

Here’s the code:

x=int(input("Enter number:")) c=[]    #load the exponential powers here b=[]    #load the primes here i,k,f=0,0,2 l=100 def primes(i,n):            #returns all primes between i and n     primes = []     for possiblePrime in range(i,n+1):          isPrime = True         for num in range(2, int(possiblePrime ** 0.5) + 1):             if possiblePrime % num == 0:                 isPrime = False                 break         if isPrime:             primes.append(possiblePrime)     return(primes)  while x!=1:     try:         while x%b[k]==0:            #extract every prime from the number and store their resp exp powers             i+=1                    #counts the power of the prime stored in b[k]             x=x//b[k]               #Removes the prime number from the given number         k+=1         c.append(i)         i=0     except IndexError:              #if list of primes are not enough...add more of them             b=b+primes(f,l)                      l+=10000  print("Prime Numbers:    ",[b[i] for i in range(len(c)) if c[i]!=0])   #prints the primes     c=[c[i] for i in range(len(c)) if c[i]!=0]         print("Respective Powers:",c)                                          #prints their respective powers  

Sample Output:(i just took a random number)

Enter number:23412
Prime Numbers:###[2, 3, 1951]
Respective Powers: [2, 1, 1]

(how to add spaces in bloquotes..i just added the # character for spaces)

This means 23412=22×31×19511

Hope the code is readable…i’m not good at formatting so can someone help with that…or is the readablity of code fine?

Also all optimisations and improvements or suggestions are welcome