solving self consistent equations

I couldn’t attach pic of my self consistent equations in the comment section that I am trying to solve in an earlier message threading

(Elimination of the variables)enter image description here

I am trying to solve for z for given x = 0.057, y = 0.01 self consistently

Code from earlier threading is

y = 1/100;  x = 57/1000;  gE[(n_Integer)?NonNegative] := 1/g[n] - Sqrt[1 + z^2/(Pi*(2*n + 1)*y + (44*x*Pi*g[n])/10)^2];  sce[0] = (2*Pi*1*((Pi*1*(g[0] - 1))/(100*(((Pi*1)/100 + (44*Pi*x)/10)*((Pi*1)/100 + (44*Pi*x*g[0])/10)))))/100 + 6431/10000;  sce[(n_Integer)?Positive] := (2*Pi*1*(((2*n + 1)*Pi*1*(g[n] - 1))/(100*((((2*n + 1)*Pi*1)/100 + (44*Pi*x)/10)*(((2*n + 1)*Pi*1)/100 + (44*Pi*x*g[n])/10)))))/100;  nmax = 3;  nValues = Range[0, nmax];  ee = Flatten[{Total[sce /@ nValues], gE /@ nValues}];  xed0 = GroebnerBasis[ee, {z}, g /@ nValues, MonomialOrder -> EliminationOrder];   NSolve[xed0 == 0, z] 

For nmax = 3 it doesn’t converge and keeps on running and I am aware of @ Daniel Lichtblau comment that here complexity arises as nmax increases.

Question: Is there any other way of solving above self consistent equations?

self extending factory: return type and serialization

I’m trying to implement a better management for the objects in my game project. With input from another thread here on S.O., I decided to implement different collections for different types for better access. Seems to be a common way. So far I #included all the class files and added containers (just maps right now) for each type I needed/wanted, as well as functions to create/add/remove etc., that take care of what is needed. That way no free objects exist (object’s constructors are private) that could be missed somewhere. But ofc that means for every new type the container/manager/factory needs to be modified and that’s error prone. So I wanted to try and make it self extending with a registration like this:

template<typename ObjectType> class Registration {     public:         Registration(const std::string& typeID)                                                                                                         {             EntMan::getInstance()->registerTypeCreator(typeID, [] (Properties* props)->Entity* {return new ObjectType(props); } );         } }; 

saving it in a std::map<std::string, std::function<Entity*(Properties* props)> >. This works, ofc it’s a common pattern, but has especially one flaw: the return type. I could add as much additional containers, defined by tags for example, as I want (shurely helps with iteration/preselection), but the contained items would always be just base class pointers. So if I get an item I still would need to dynamic_cast (or static_cast with if(object->getType == "someThing") ) it to the derived type to get full derived access to the object. Seems wasteful and error prone. Integrating all functionality with virtual functions would solve this, but in the end turns the base in a kind of blob class. Doesn’t feel right either. Let alone the fact that it would also be also pretty horrible for data locality. Not my main concern right now, but maybe will be in the future.

I’m a bit uneasy with the Properties "parameter amalgamation"-workaround aswell, to fullfill the std::function criteria of having the same signature, as it’s a bit error prone doing it "by hand" for example, but should be less of a problem once it’s abstracted away with parsing those as prefabs from files and accessing those. Still, it also would mean a lot of wasted space to save those as prefabs… So I’m at my wits end here.

How could I go on from here, if I need…

  • different collections for different types (for preselection)
  • acessors delivering the proper derived types (for avoiding casts and blobs)
  • self extending, no modification needed just for adding types
  • serializable use (ie: create("stone") for use with parsing functions of xml data etc. )

Can this be done? Or is this a dead end? No good idea at all? Thanks in advance for any help.

Alter Self and Extraordinary Special Qualities

Suppose you are a dwarf and use Alter Self to become a different dwarf. Do you lose your darkvision?

The text of Alter Self states:

You keep all extraordinary special attacks and qualities derived from class levels, but you lose any from your normal form that are not derived from class levels.

Since darkvision is an extraordinary special quality not derived from class levels, it appears you would lose that ability, but this seems very counterintuitive. Would the same be true for Polymorph? Does it require a ninth level spell for you to keep your darkvision when trying to become a different dwarf?

can disguise self hide wings?

Can disguise self hide an aaracocras natural wings because they are hiding as a "different race"? Would this allow a creature to create wings to become an aaracocra? if a creature has wings and hides them, would they be revealed if used in flight? if a creature manifests wings while under disguise self’s effects, would they need to recast it to hide them?

disguise self and polymorph

premise: I am under the effects of disguise self to look like a human and I am in fact, an elf. I then cast polymorph on myself to turn into a T-rex and then take enough damage to make me lose concentration on polymorph, would I appear to be an elf or human after the spell drops? What if the spell was dropped due to the polymorphed T-rex running out of health?

Can a Spell with “Self” Range be Cast by Homunculus Servant?

I’m playing an artificer for the first time and trying to decide whether or not to use an infusion for the homunculus servant. But I’m wondering about the channel magic ability. It says “The homunculus delivers a spell you cast that has a range of touch.” I’d like to know if I can use a spell with a range of self in place of a spell with a range of touch.

As far as I understand it, broader ranges are inclusive of smaller ranges, so if you can cast a spell at sixty feet, you can also cast it at fifteen feet because fifteen feet is closer than sixty feet. And if you can cast it at a distance of touch you can cast it on yourself, because you are closer than the furthest thing you can touch. So I’m really wondering if the same reasoning that applies to the effect of the spell applies to the ability to cast the spell. If you can cast a spell at a range of touch does that imply that you can also cast a spell with a range of self?

in D&D3.5, how do Magic Jar and Alter Self interact?

In D&D3.5, how do Magic Jar and Alter Self interact?

Suppose I am a normal human wizard, and I cast Magic Jar, then possess a huge zombie. Now I want to cast Alter Self. What are my options for picking a type? Which body changes?

Alter Self says, in relevant part:

You assume the form of a creature of the same type as your normal form. The new form must be within one size category of your normal size. The maximum HD of an assumed form is equal to your caster level, to a maximum of 5 HD at 5th level. You can change into a member of your own kind or even into yourself.

I’m ideally looking for a Rules-As-Written answer here, but any well-argued answer is good too.

Can a Way of Astral Self Monk use wisdom related scores for jumping?

I have several questions on the interactions between the Arms of Astral Self and the Jumping mechanics. According to the 3rd level feature, Arms of the Astral Self:

While the spectral arms are present, you gain the following benefits:

  • You can use your Wisdom modifier in place of your Strength modifier when making Strength checks and Strength saving throws.
  • You can use the spectral arms to make unarmed strikes.
  • When you make an unarmed strike with the arms on your turn, your reach for it is 5 feet greater than normal.
  • The unarmed strikes you make with the arms can use your Wisdom modifier in place of your Strength or Dexterity modifier for the attack and damage rolls, and their damage type is force.

The Jumping session of the PHB states:

Long Jump

When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance. Either way, each foot you clear on the jump costs a foot of movement.

This rule assumes that the height of your jump doesn’t matter, such as a jump across a stream or chasm. At your DM’s option, you must succeed on a DC 10 Strength (Athletics) check to clear a low obstacle (no taller than a quarter of the jump’s distance), such as a hedge or low wall. Otherwise, you hit it.

High Jump

When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance. Either way, each foot you clear on the jump costs a foot of movement. In some circumstances, your DM might allow you to make a Strength (Athletics) check to jump higher than you normally can.

You can extend your arms half your height above yourself during the jump. Thus, you can reach above you a distance equal to the height of the jump plus 1½ times your height.

My questions would be, assuming that I have Arms of the Astral Self activated:

  1. Can I use my Wisdom Score instead of my strenght score to determine my long jump distance?
  2. Can I make a Wisdom (Athletics) check instead of a Strenght (Athletics) check?
  3. Can I use my Wisdom modifier instead of my Strenght modifier to determine my high jump’s height?
  4. Can the extra 5 feet range of the Arms of Astral Self be used when accounting for "extending your arms half your height above yourself" on the high jump, making it 1½ your height + 5 feet instead of only 1½ your height?

I am aware that some of the answers to these questions are up to DM discretion, so I would like to know, if possible, what would be the RAW interpretation and also how would you rule it in your games.

In advance, I’m extremely grateful to whoever takes time to answer these 🙂

Dispel a self targeting spell emanating from within an antimagic field

So, a character has an artifact granting the ability to cast Holy Aura. Another character casts Antimagic Field and the two effects overlap, so that the origins of both spells are within both spell effects.

Can someone cast Dispel Magic on the Holy Aura effect since its radius (30ft) exceeds that of the Antimagic Field (10ft)?

The argument raised against being able to dispel it, is that since the effect is active on a creature, then it is the creature that must be targeted, differentiating this case from a Grease spell for example.

Disguise Self / Silent Image when camouflaging an item into another item

A spellcaster uses Disguise Self to pass as a simple bodyguard. In particular, the quarterstaff that she uses as a spell focus, which normally looks like an obviously magical item (runes, faint lights, the works), is disguised to look like a simple martial weapon (the kind of quarterstaff that a monk would use).

She is asked to drop her weapons in a box before meeting a mob boss. She doesn’t want to reveal that she is a spellcaster.

  1. At the moment where you cast the spell, Disguise Self applies to belongings on your person. What about afterwards? Would the quarterstaff, once put in the box, immediately take back its previous appearance?

  2. If the answer is "yes", could Silent Image be used to maintain the illusion? I would want to create the exact image of the fake quarterstaff "around" the actual quarterstaff to keep it camouflaged. Is that a possible use of the spell? Would someone picking up the quarterstaff, without examining it too closely, immediately notice the illusion, assuming the weight/material of the illusion is similar to the real one?

  3. Is it still possible to control the illusion (in particular, to keep it around the quarterstaff if it moves) even after the spellcaster has dropped her spell focus?