How to name base classes so that it’s most convenient for those extending a framework?

I’m designing a game engine that is supposed to be overridden. I have, for example, a class called Character. Should I prefix this with BaseCharacter or should I expect that whoever uses the framework prefixes their classes with GameNameCharacter or CharacterGameName?

What would be most convenient to you?

Create custom endpoints by extending the Resource Base class

I created a custom endpoints by extending the core of Drupal. but I can not retrieve JSON data. I do not know what value to put in ‘note: serialization_class

/** * Provides a resource to get bundles by entity. * * @RestResource( *   id = "dna_custom_endpoint", *   label = @Translation("DNA custom endpoint"), *   serialization_class = ??????, *   uri_paths = { *     "canonical" = "/dnarest/{type}" *   } * ) */ 

You know comprehensive guides that explain?

public function patch($  type = 'type') {     ??????? } 

if you use what you said ( serialization_class = “Drupal\Core\Entity\Entity”,) to me this generates fatal error PHP :

Drupal\Core\Entity\Exception\NoCorrespondingEntityClassException: The Drupal\Core\Entity\Entity class does not correspond to an entity type. in Drupal\Core\Entity\EntityTypeRepository->getEntityTypeFromClass() (line 103 of /Applications/MAMP/htdocs/dnaphone/core/lib/Drupal/Core/Entity/EntityTypeRepository.php). 

Extending Green’s theorem from very special regions to more general regions

Green’s theorem

Let $ C$ be a positively oriented and consists of a finite union of disjoint,piecewise smooth simple closed curve in a plane, and let $ D$ be the region bounded by $ C$ . If $ P$ and $ Q$ are functions of $ (x, y)$ defined on an open region containing $ D$ and have continuous partial derivatives there, then $ $ \oint_C (Pdx+Qdy)=\iint_D (\frac{\partial Q }{\partial x}-\frac{\partial P}{\partial y})dxdy$ $ where the path of integration along $ C$ is anticlockwise.

In almost all textbooks, authors only proved it when $ D$ is a simple region or the region $ D$ can be cut up into finitely many simple regions without common interiors.My questions is how to generalize those special regions to more general regions as Green’s theorem gives? I need a rigorous complete proof.Likewise Green’s theorem,the divergence theorem and Stokes’s theorem have the same situation requiring some rigorous proofs from very special regions to more general regions.

Extending root partition

I have installed Ubuntu server 16.4 using entire disk with LVM and when I tried to install Ubuntu-Desktop from command line, it failed in middle saying there isn’t enough space. I am quite new to linux. I need to increase root partition from command-line so that i can install Desktop and other software. Please help me how to go about it in simplest way.

Design approach for extending class functionality – Embedded C++

For my company i am refactoring our embedded C/C++ code base to increase re-usability for commonly used functionality. Currently i am refactoring our command line interface but i ran into a design issue.

Our core command line interface is good and stable as is but in some project there is a need or wish to add additional functionality to it. For example to provide a command history or privilege levels for specific commands.

My design issue comes from the fact that some projects require only one of the extensions and others use multiple or even all.

My question: What would be appropriate approach to allow such extensibility as described above.

Currently i have looked into simple inheritance and the decorator pattern but haven’t been able to make a proper design out of it. With inheritance i ran into the diamond of death and with the decorator i failed because of lack of knowledge. Maybe i am looking to much for a one fits all design where multiple different approaches maybe better.

Surfaces extending modified geodesic paths

What happens if the usual geodesic equation on an n-manifold is directly modified from a source dimension 1 space (giving a path) to a dimension 2 space (giving a surface). I suspect that this gives a totally geodesic surface, but I was hoping for somewhere to discuss modifications (adding extra terms like a connection on the 2D source space) and the integrability conditions quite explicitly.

This must be well known in differential geometry, just not to me as a non-expert, so please give a reference rather than just down voting.

Extending section of étale morphism of adic spaces

This question is related to Lifting points via étale morphism of adic spaces.

Fix a complete non-archimedean field $ k$ . Let $ (A,A^+)$ be a complete strongly noetherian Huber pair over $ (k,k^\circ)$ . Let $ f\colon A\to B$ be a finite étale morphism of rings; endow $ B$ with the natural $ A$ -module topology and let $ B^+$ be the integral closure of $ A^+$ in $ B$ . Then $ f$ defines a morphism of complete Huber pairs $ f\colon (A,A^+)\to (B,B^+)$ over $ (k,k^\circ)$ .

Let now $ x\in \operatorname{Spa}(A,A^+)$ and suppose that $ \operatorname{Spa}(k(x),k(x)^+)\to X:=\operatorname{Spa}(A,A^+)$ lifts to $ Y:=\operatorname{Spa}(B,B^+)$ . Denote the corresponding point in $ Y$ by $ y$ . Then the inclusion $ k(x)\subset \widehat{k(x)}$ factors through $ k(y)$ : $ $ k(x)\subset k(y)\subset \widehat{k(x)}. $ $ Thus, if we assume that $ k(x)$ is already complete, we obtain $ k(x)=k(y)$ . Now the morphism $ f_y\colon \mathcal{O}_{X,x}\to \mathcal{O}_{Y,y}$ induced by $ f$ is étale at the closed point of $ \mathcal{O}_{Y,y}$ . Since $ \mathcal{O}_{X,x}$ is henselian, the equality $ k(x)=k(y)$ implies that $ f_y$ has a section $ s\colon \mathcal{O}_{Y,y}\to \mathcal{O}_{X,x}$ , so that we obtain a map $ s\colon B\to \mathcal{O}_{X,x}$ . The noetherian assumption implies that this lifts to a morphism $ s\colon B\to \mathcal{O}_X(U)$ , for $ U$ a rational subset of $ X$ containing $ x$ .
In other words, the morphism $ f\colon Y\to X$ admits a section $ s\colon U\to Y$ locally around $ x$ .

$ \textbf{Question}$ : How can I argue if the residue field $ k(x)$ is not necessarily complete?

Help is highly appreciated.