Can a simulacrum be healed by any means other the ‘complex process’ outlined in the spell?

Inspired by another discussion of Simulacra – can a simulacrum actually heal via any method other than the ‘complex process’ outlined in the spell? Or is that process simply another option? What if the copied creature type has Fast Healing, or Regeneration? Do Cure Wounds spells function on the simulacra? Is the simulacrum actually even a creature?

How complex of an object can be created via the Creation spell?

Inspired by this question about creating gunpowder with the Creation spell.

My reading of the spell (and components) would indicate that the spell can only create an item (or multiple items1) but of a single "type". This comes from most of the description using singular form when referring to type.

From the spell description:

You pull wisps of shadow material from the Shadowfell to create a nonliving object of vegetable matter within range: soft goods, rope, wood, or something similar. You can also use this spell to create mineral objects such as stone, crystal, or metal. The object created must be no larger than a 5-foot cube, and the object must be of a form and material that you have seen before.

And the required components:

Components: V, S, M (a tiny piece of matter of the same type of the item you plan to create)

But the linked question tries to create gunpowder; a combination of "a fuel (charcoal), an oxidizer (saltpeter or niter), and a stabilizer (sulfur) to allow for a constant reaction". This is not only multiple types of matter, but different types; some vegetable, some mineral 2.

There is also no mention of the time being different; as in, using the shortest duration of all types used in the creation.

I would think that if the spell was to able to create mixed types it would have very different phrasing.

So is the Creation spell limited to only one type of matter at a time, or can it be a combination of matter/types?

And if it possible to create something with multiple/mixed types, how complex can the item be?

  • Can they mix different elements of the same type like an apple and an orange to create a fruit salad?
  • Can they create a leather coat with a fur lining and metal buttons? Or would they have to create each thing separately and sew them together by hand?
  • How about a metal crown, with cloth padding on the interior and encrusted with gems?
  • They can create iron, but can they also create it fused with carbon to create steel?
  • People could be considered a combination of vegetable matter and minerals. Could a character create a corpse (nonliving object)?

1 I would also think that this creates only a single item (a rope), except for minerals it states "You can also use this spell to create mineral objects…". Otherwise the description sticks to singular object.

2 Admittedly, something like this could be done with multiple castings, each creating a specific type of matter. But the point of the question was do create a complete pile of gunpowder.

LIMIT and OFFSET a complex query

I have a query generated by a ORM (Sequelize), i ran into an issue where sequelize fails, look at those issues. https://github.com/sequelize/sequelize/issues/7344

https://github.com/sequelize/sequelize/issues/12200

Postgres Query:

 SELECT "feeds"."id",     "feeds"."title",     "feeds"."likes",     "feeds"."description",     "feeds"."files",     "feeds"."allowComments",     "feeds"."readConfirmation",     "feeds"."isDraft",     "feeds"."createdAt",     "feeds"."updatedAt",     "feeds"."companyId",     "feeds"."createdById",     "reads"."id" AS "reads.id",     "reads->feeds_reads"."createdAt" AS "reads.feeds_reads.createdAt",     "reads->feeds_reads"."updatedAt" AS "reads.feeds_reads.updatedAt",     "reads->feeds_reads"."feedId" AS "reads.feeds_reads.feedId",     "reads->feeds_reads"."userId" AS "reads.feeds_reads.userId",     "createdBy"."id" AS "createdBy.id",     "createdBy"."firstName" AS "createdBy.firstName",     "createdBy"."jobTitle" AS "createdBy.jobTitle",     "createdBy"."lastName" AS "createdBy.lastName",     "createdBy"."profilePicture" AS "createdBy.profilePicture",     "bookmarks"."id" AS "bookmarks.id",     "bookmarks->feeds_bookmarks"."createdAt" AS "bookmarks.feeds_bookmarks.createdAt",     "bookmarks->feeds_bookmarks"."updatedAt" AS "bookmarks.feeds_bookmarks.updatedAt",     "bookmarks->feeds_bookmarks"."feedId" AS "bookmarks.feeds_bookmarks.feedId",     "bookmarks->feeds_bookmarks"."userId" AS "bookmarks.feeds_bookmarks.userId",     "units"."id" AS "units.id",     "units"."parentId" AS "units.parentId",     "units->feeds_units"."createdAt" AS "units.feeds_units.createdAt",     "units->feeds_units"."updatedAt" AS "units.feeds_units.updatedAt",     "units->feeds_units"."feedId" AS "units.feeds_units.feedId",     "units->feeds_units"."unitId" AS "units.feeds_units.unitId",     "units->users"."id" AS "units.users.id",     "units->users->users_units"."createdAt" AS "units.users.users_units.createdAt",     "units->users->users_units"."updatedAt" AS "units.users.users_units.updatedAt",     "units->users->users_units"."userId" AS "units.users.users_units.userId",     "units->users->users_units"."unitId" AS "units.users.users_units.unitId",     "units->descendents"."id" AS "units.descendents.id",     "units->descendents"."parentId" AS "units.descendents.parentId",     "units->descendents->unitsancestor"."unitsId" AS "units.descendents.unitsancestor.unitsId",     "units->descendents->unitsancestor"."ancestorId" AS "units.descendents.unitsancestor.ancestorId",     "units->descendents->users"."id" AS "units.descendents.users.id",     "units->descendents->users->users_units"."createdAt" AS "units.descendents.users.users_units.createdAt",     "units->descendents->users->users_units"."updatedAt" AS "units.descendents.users.users_units.updatedAt",     "units->descendents->users->users_units"."userId" AS "units.descendents.users.users_units.userId",     "units->descendents->users->users_units"."unitId" AS "units.descendents.users.users_units.unitId",     "teams"."id" AS "teams.id",     "teams->feeds_teams"."createdAt" AS "teams.feeds_teams.createdAt",     "teams->feeds_teams"."updatedAt" AS "teams.feeds_teams.updatedAt",     "teams->feeds_teams"."feedId" AS "teams.feeds_teams.feedId",     "teams->feeds_teams"."teamId" AS "teams.feeds_teams.teamId",     "teams->peoples->teams_users"."createdAt" AS "teams.peoples.teams_users.createdAt",     "teams->peoples->teams_users"."updatedAt" AS "teams.peoples.teams_users.updatedAt",     "teams->peoples->teams_users"."userId" AS "teams.peoples.teams_users.userId",     "teams->peoples->teams_users"."teamId" AS "teams.peoples.teams_users.teamId",     "comments"."text" AS "comments.text",     "comments"."id" AS "comments.id",     "comments"."likes" AS "comments.likes",     "comments"."parentId" AS "comments.parentId",     "comments"."createdById" AS "comments.createdById",     "comments"."createdAt" AS "comments.createdAt",     "comments"."updatedAt" AS "comments.updatedAt",     "comments->createdBy"."id" AS "comments.createdBy.id",     "comments->createdBy"."firstName" AS "comments.createdBy.firstName",     "comments->createdBy"."lastName" AS "comments.createdBy.lastName",     "comments->createdBy"."jobTitle" AS "comments.createdBy.jobTitle",     "comments->createdBy"."profilePicture" AS "comments.createdBy.profilePicture",     "peoples->feeds_peoples"."createdAt" AS "peoples.feeds_peoples.createdAt",     "peoples->feeds_peoples"."updatedAt" AS "peoples.feeds_peoples.updatedAt",     "peoples->feeds_peoples"."feedId" AS "peoples.feeds_peoples.feedId",     "peoples->feeds_peoples"."userId" AS "peoples.feeds_peoples.userId" FROM "feeds" AS "feeds"     LEFT OUTER JOIN (         "feeds_reads" AS "reads->feeds_reads"         INNER JOIN "users" AS "reads" ON "reads"."id" = "reads->feeds_reads"."userId"     ) ON "feeds"."id" = "reads->feeds_reads"."feedId"     LEFT OUTER JOIN "users" AS "createdBy" ON "feeds"."createdById" = "createdBy"."id"     LEFT OUTER JOIN (         "feeds_bookmarks" AS "bookmarks->feeds_bookmarks"         INNER JOIN "users" AS "bookmarks" ON "bookmarks"."id" = "bookmarks->feeds_bookmarks"."userId"     ) ON "feeds"."id" = "bookmarks->feeds_bookmarks"."feedId"     LEFT OUTER JOIN (         "feeds_units" AS "units->feeds_units"         INNER JOIN "units" AS "units" ON "units"."id" = "units->feeds_units"."unitId"     ) ON "feeds"."id" = "units->feeds_units"."feedId"     LEFT OUTER JOIN (         "users_units" AS "units->users->users_units"        LEFT OUTER JOIN "users" AS "units->users" ON "units->users"."id" = "units->users->users_units"."userId"     ) ON "units"."id" = "units->users->users_units"."unitId"     LEFT OUTER JOIN (         "unitsancestor" AS "units->descendents->unitsancestor"         LEFT OUTER JOIN "units" AS "units->descendents" ON "units->descendents"."id" = "units->descendents->unitsancestor"."unitsId"     ) ON "units"."id" = "units->descendents->unitsancestor"."ancestorId"     LEFT OUTER JOIN (         "users_units" AS "units->descendents->users->users_units"         LEFT OUTER JOIN "users" AS "units->descendents->users" ON "units->descendents->users"."id" = "units->descendents->users->users_units"."userId"     ) ON "units->descendents"."id" = "units->descendents->users->users_units"."unitId"     LEFT OUTER JOIN (         "feeds_teams" AS "teams->feeds_teams"         INNER JOIN "teams" AS "teams" ON "teams"."id" = "teams->feeds_teams"."teamId"     ) ON "feeds"."id" = "teams->feeds_teams"."feedId"     LEFT OUTER JOIN (         "teams_users" AS "teams->peoples->teams_users"         INNER JOIN "users" AS "teams->peoples" ON "teams->peoples"."id" = "teams->peoples->teams_users"."userId"     ) ON "teams"."id" = "teams->peoples->teams_users"."teamId"     LEFT OUTER JOIN "comments" AS "comments" ON "feeds"."id" = "comments"."feedId"     LEFT OUTER JOIN "users" AS "comments->createdBy" ON "comments"."createdById" = "comments->createdBy"."id"     LEFT OUTER JOIN (         "feeds_peoples" AS "peoples->feeds_peoples"         INNER JOIN "users" AS "peoples" ON "peoples"."id" = "peoples->feeds_peoples"."userId"     ) ON "feeds"."id" = "peoples->feeds_peoples"."feedId" WHERE (         "peoples"."id" = 11         OR "feeds"."createdById" = 11         OR "teams->peoples"."id" = 11         OR "units->users"."id" = 11         OR "units->descendents->users"."id" = 11     )     AND "feeds"."companyId" = 4     AND "feeds"."isDraft" = false     AND "feeds"."createdAt" < '2020-12-09 12:59:34.017 +00:00' LIMIT 20; 

Here the limit is not applying to the feeds, i want 20 feeds but it’s giving me same feed 20 times.

How to plot a set of complex numbers with given argument and absoulute value bounds

I want to plot the following complex numbers $ $ z \in \text{(complex numbers)}:\pi/4 < \arg (z) \leq 5 \pi/4,\ 1 \leq |z| < 2 $ $

I don’t know how to graph it so that it would look like 2D without any unecessary details. The closest I found how I want it to look is, when I looked at how graphing of parametric function looks. I tried to use contour plot to graph it, but I just can’t seem to do it…

ContourPlot[ Im[F[z[x, y]]], {3 pi/4 < arg (z) <= 5 pi/4, 1 <= abs (z) < 2}, {x, -.2, .2}, {y, -.2, .2}, PlotRange -> All, Contours -> Range[-5, 5, .5], ContourLabels -> True]

Does anybody know how to graph my set?

How to Convert the complex notation into x, y-coordinates?

Convert the complex notation into x, y-coordinates; see also Accumulate and ListLinePlot.
enter image description here

I try to use the table to list all the summation value.( I suppose upper bounds N is 5)

plot1 = Table[{N,Sum[e^(2*Pi*I*n*Sqrt[2]),{n,1,N}]},{N,1,5}]; ListLinePlot[plot1]; 

But I just got an empty axis.
I think I need to convert the complex notation, I don’t know how to convert it.
Could you give me some suggestions?
Thank you!

How can we find the powers of a complex number?

this is the complex number im dealing with zb=(1/7)* (Cos[pi/3]+iSin[pi/3])

I need to represent for the first 10 powers in the plane. I also need to label the points with "z to the power n(n is the power for which i elevate zb)

I need to label the axes, i need to do all this in mathematica

My questions 1.How can I represent a complex number in mathematica 2.How can I represent for the first 10 powers the plane. 3.How can I label each point on the graph to the corresponding power?

my professor gave me a hint to use the callout[] command in mathematica. thank you!

Error in nonlinearmodel fit for a function with Definite Integral and complex number

I am trying to fit a function fun and Here is the code which I am trying, Please find the data here dataset

Data = Import[    "E:\Shelender\codes\Mathematica\Aelastic \ relaxation\datat.asc"]; real = Data[[All, {1, 2}]]; imag = Data[[All, {1, 3}]]; w = 1.26*10^8; k = 1.38*10^-23;  f[H_, s_, d_] := ((1/(Sqrt[2*Pi]*s*H))*Exp[(-(Log[(H/d)])^2/(2*s^2))]) dynamic[x_?NumericQ, s_?NumericQ, d_?NumericQ, A_?NumericQ,    t_?NumericQ] :=   A*(1 - NIntegrate[      f[H, s, d]/((1 + (I*w*t*Exp[((H)/(k*x))]))), {H,        0, \[Infinity]}])  fit = ResourceFunction["MultiNonlinearModelFit"][    Rationalize[{real, imag}, 0],     ComplexExpand[ReIm@dynamic[x, s, d, A, t]],     Rationalize[{{A, 1.0*10^-4}, {t, 1.0*10^-12}, {d, 10}, {s, 0.25}},      0], {x}, PrecisionGoal -> 3, AccuracyGoal -> 3];  fit["ParameterTable"] Show[ListPlot[{real, imag}],   Plot[{fit[1, x], fit[2, x]}, {x, 0,     Max[real[[All, 1]], imag[[All, 1]]]}, PlotRange -> All],   PlotRange -> All] 

Although I am not getting any error but fit values are completely off

How to determine if given “complex” time complexity is $O(n^2)$?

If a given time complexity, such as these:

  1. $ (n + \log n) * \sqrt{n+\log n}$
  2. $ n * (200 + \log^2 n)$
  3. $ (7+n^3)\log(n^5)$

is not determinable by just looking at it whether is it in class $ O(n^2)$ or not, how do I decide? If a time complexity is given, and in it there are more types of expressions (exponential, logarithmic, polinomial, … ) how do I decide which one determines the $ O(n^2)$ or $ O(n\log n)$ or … complexity?

Get modulus and plot complex function

I have the following function:

freq[a_, b_, t0_, tr_, s_] := -((b E^(-s (b + t0)) (b E^(s (b + t0)) (-1 +             b s) UnitStep[-b] - b E^(s t0) UnitStep[b] +          E^(s (b - tr)) (E^(s (t0 + tr)) (-1 + b s) UnitStep[-t0] +             E^(s tr) (-1 + b s - s t0) UnitStep[t0] -             E^(s (t0 + tr)) (-1 + b s) UnitStep[-t0 - tr] + (1 +                s (-b + t0 + tr)) UnitStep[t0 + tr])))/(s^2 tr)) 

Now I want to plot the function as follows:

Plot[ComplexExpand@Abs@ExpToTrig@freq[0, 1, 0, 10^-6, Iw], {w,0,10^9}] 

However that doesn’t work. I couldn’t exact the absolute value of the complex function to plot it.
(w is a real positive number)

Does anyone know how to plot that?

Making complex boolean circuits that give true as output only for a specific combination of boolean inputs

This is my first question on a stack exchange website so please bear with me. I am making challenges for a jeopardy style capture the flag event in my college and I had come across the minetest challenge in the hardware section of google CTF qualifier conducted last year. A clean and organized solution to this problem has been provided by liveoverflow.

I would like to design a simpler version of this problem for my college’s CTF event but I am unable to design a complex circuit that gives true output only for a specific combination of inputs. I know that a circuit with this functionality is not very difficult to implement and just needs to represent the following logic:

trueinput1 AND trueinput2 AND ... NOT falseinput1 AND NOT falseinput2 ...  

However I want it to be vast and complicated so that participants cannot decode its functionality just by doing a visual analysis. Is there any technique to complicate the boolean logic above and to design a corresponding circuit that looks ugly even for a small number of inputs(32/64).