## dnd 5e – 14th level Artificer (Magic Item Savant) + Metamagic Adept items to regain sorcery points

### You have found the only way for an Artificer to restore the Metamagic Adept SP apart from a long rest.

A 14th level Artificer has the Magic Item Savant feature:

You ignore all class, race, spell, and level requirements on attuning to or using a magic item.

So a 14th level Artificer may attune to the Bloodwell Vial, which says:

In addition, when you roll any Hit Dice to recover hit points while you are carrying the vial, you can regain 5 sorcery points.

Since you maximum SP is 2, you would only regain 2.

There is no other way to regain these 2 sorcery points, except through taking a long rest. As noted in my answer here, Metamagic Adept does not allow you to convert spell slots into SP.

This search on DNDBeyond shows all of the relevant results in their database that mention the phrase “sorcery points”. The only results are the Metamagic Adept feat, the Bloodwell Vial, and the Sorcerer class.

You can restore them a little bit quicker if you are a race that can long rest in 4 hours.

(Notably, a 13th level thief rogue could probably do something similar with their Use Magic Device feature.)

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## lie groups – The Hausdorff dimension of \$F^+_{m,n}\$ singular points

Let $$G:=SL(m+n,mathbb R)$$ and $$Gamma :=SL(m+n,mathbb Z)$$ and $$X:=G/Gamma$$.

(1) Let $$M$$ denote the set of all $$m times n$$ matrices with real entries. A matrix $$A in M$$ is called $$textit{singular}$$ if for all $$epsilon > 0$$, there exists $$Q_epsilon$$ such that for all $$Q ge Q_{epsilon}$$, there exist integer vectors $$p in mathbb Z^m$$ and $$q in mathbb Z^n$$ such that

$$begin{equation} |Aq+p|le epsilon Q^{-n/m} ~text{and}~ 0<| q | le Q. end{equation}$$

We denote the set of singular $$mtimes n$$ matrices by $$textbf{Sing}_{m,n}$$

By Dani’s correspondence principle (1985), this is equivalent to saying that $$(g_t u_A mathbb Z^n)$$ is divergent in the space of unimodular lattices where $$g_t:=begin{bmatrix} e^{t/m}I_m & 0 \ 0 & e^{-t/n}I_n end{bmatrix}$$
and
$$u_A:=begin{bmatrix} I_m & A \ 0 & I_n end{bmatrix}$$.

(2) Let $$F^+:={g_t:tge 0}$$ and let $$D(F^+, X)$$ be the set of points $$X$$ such that the trajectory $$F^+ x$$ is divergent (“leaving any compact set”).

I wonder how to show the following equation of Hausdorff dimensions:

$$dim(X)-dim(D(F^+, X))=mn- dim(textbf{Sing}_{m,n})$$

Intuitively this is very true through Dani’s correspondence (“codimension”=”codimension”!). But to prove it rigorously, are there any key theorems about the Hausdorff dimensions involved?

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## spells – How much Hit Points does casting a two action heightened 2-nd level Heal restore?

Heal

You channel positive energy to heal the living or damage the undead. If the target is a willing living creature, you restore 1d8 Hit Points.

Two Actions (somatic, verbal) The spell has a range of 30 feet. If you’re healing a living creature, increase the Hit Points restored by 8.

Heightened (+1) The amount of healing or damage increases by 1d8, and the extra healing for the 2-action version increases by 8.

I’m reading this as a two action heightened 2-nd level Heal restoring 2d8+16 Hit Points. Am I interpreting this correctly?

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## calculus and analysis – How does mathematica integrate around points where the integrand evaluates to ”indeterminate?”

I am interested in studying a numerical integral where the integrand, when evaluated naively at some points in the domain of integration, is indeterminate. However, when one carefully takes limits to these points, the integrand turns out to be finite. Since my actual integrand is multi-dimensional and complicated, let me pose my question in the context of a simple example instead. If I ask mathematica to evaluate $$frac{sin x}{x}$$ at $$x=0$$, it says it’s indeterminate (although we know that the actual value as $$x to 0$$ is finite). However, if I evaluate the numerical integral of this function from $$-1 leq x leq 1$$, it gives me the right result, i.e, a value that matches the result of analytic integration.

So my question is: in numerical integration, how does mathematica deal with points where if you ask mathematica to evaluate the integrand, it gives ”indeterminate.” Are these points omitted? If not, how are they accounted for? In the example above, mathematica was somehow able to deal with $$x=0$$ correctly when integrating numerically even though it said that the function evaluated at $$x=0$$ was indeterminate.

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## co.combinatorics – Zero-area-free embedding of points on the grid

Given $$n$$, I am looking for the smallest $$m$$ such that there is an $$n$$ element subset $$S$$ of the $$mtimes m$$ grid (i.e., $$n$$ points with integer coordinates in $$(0,m)^2$$) such that no matter how one picks a self-crossing polygon $$P$$ whose vertices are from $$S$$, the signed area of $$P$$ is never zero. Here signed area is defined as shading the regions of $$P$$ white and black so that touching regions receive different colors, and then taking the difference of the areas of the white and black regions. $$P$$ is required to be connected. A solution with small $$m$$ would have consequences in complexity theory, see here.

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## wi fi – Is there an application or a method to test the positioning on Android only by wi fi access points?

I need to test positioning only by wi fi access points.But when I turn on geolocation on my Android device the position is calculated by GPS+ GSM + Wi fi. My device doesn’t give the option to save it and only determine by the wi fi networks.

So is there some way or application that will give such an opportunity to use only Wi Fi access points for positioning?

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## windows 10 – how can I recover my pc without any restore points

I caught a hacker red handed on my computer but I panicked and switched it off and turned off my entire network.

Now with my internet disconnected I turned my computer back up just to find that every file in every drive of my computer had been affacted and now everything is a `.fair` file, with the exception of a `readme-warning.txt` file, existing in every directory which I didn’t open and will not open.

I’ve ran an Windows Defender complete check up and it found nothing malicious.

I can just format my computer with my bootable usb drive, but if I could salvage my files would just be amazing.

It’s important to note that I can use everything in my computer, I think the hacker didn’t have time to complete his hacking, but I don’t know for sure how long he was working with my computer.

## schema – Making similar points close in distance O(n) query by distance

I’m trying to create a database in DynamoDB that has many points with high dimensions. For the most part, I have designed the database to the regular access patterns. However, for a search endpoint, I quickly realized that my points need to be close by similarity.

Initially I thought it would be ok for me to use an index that represented a vector. For instance if there is a cat and no dog and a frog in picture 1 the vector would be 101

But in order to get a list of pictures with cats I would have to query for 1XX, where X is a wildcard. In this case it seems fine as there are only 3 dimensions so it would be O(1)

but with a high dimension it quickly becomes a limiting factor as we would have to query m number of dimensions O(m). I get that each of these points are on a different partition so each m dimensions can be queried at the same time. However, this solution is still not acceptable given the future usage.

Is there a way to define the distance function when using the sort index in DynamoDB or a more clever way of defining the feature vector in such a way that the points would be sorted by distance?

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## How do I find the roll, pitch, and yaw angles of a plane (/or a plane that coincides with 3 points in space ) in 3D?

Imagine that we have 3 points (P1,P2,P3). P1,P2,P3 creates a plane in 3D space. Let’s say the plane equation is Ax+By+Cz+D=0. How can I find the roll, pitch, yaw angles of this plane?
R(r,p,y)=Rz(y)Ry(p)Rx(r) order or any other order .

## How to combine two data points into one on a Google Sheets line chart?

I am trying to make a Google Sheets line chart. Why does this not work as a data range?

`A31:A69,A71:A94,D31:D68,=SUM(D69:D70),D71:D94`

X-axis = column A (date)

Y-axis = column D (dollars, numeric)

Only the first range ever shows, and it deletes the SUM, so the chart just looks like a `A31:A69,D31:D68` chart. Essentially, I just want to have the dollar amount for two dates combine into one (and discard the second date). I don’t want to change the original cells. It makes me wonder what’s the point of being able to add three or more data ranges.