OpenLLM-France/wikimedia huggingface dataset:
# Calculus/Centre of mass

This page or section of Calculus is a stub. You can help Wikibooks by expanding it.
${\vec {r}}_{G}={\frac {\displaystyle \sum \limits _{k=1}^{n}m_{k}{\vec {r_{k}}}}{\displaystyle \sum \limits _{k=1}^{n}m_{k}}}$
# Curl/Interviews

Interviews
Please feel free to add your own questions and answers!

# Interview with "The Fridge"
## Are you known as 'the Fridge' because you are a kewl programmer?

When last time I had a temperature I wasn't so kewl. I think Fridge is the transcription of the German word "Fritte" (like potato chips) which is my nickname in Germany.

## Is Curl evolutionary or revolutionary?

This binary question is not so easily answered. Curl is of course evolutionary because there have been other programming languages before. It wouldn't be the MIT if they hadn't learnt from previous mistakes. On the other hand Curl comes with a revolutionary license policy. Don't ask for details the answer might take months.

## What is your favourite piece of Curl programming? Hint: try and include curlchat

I would say the "Hello World" program, as it nicely shows how markup language is integrated in the object-oriented programming language. There are also some really good applications around, most of them are not available on the net but have a look a www.curlchat.info for example and you will know what I mean.

## Can Curl be used for programming mobile phones or PDA's?

No, not yet. If the Asian market produces enough revenue there might be a possibility that Curl is ported to these devices.

## Why is your baby son a worshipped deity?

I don't understand the question.

## How does Curl fit in with the Semantic Web?

Oh, a technical question. Curl is great in collection information and preparing them in a sensible way. Yes, Curl programs can give meaning to a arbitrary sets of data retrieved from different sources.

## What is your connection to alchemy and time travel?

Yesterday, I was working with Curl version 4.2 that was released in 1992. But unfortunately, I was already so rich (look at all these gold nuggets on my desk) that I couldn't to see the ingenuity of the release.

## Why are you so keen on Curl?

Because. Do you really want a personal answer?
# Curl/Example 1

Explanation
Curl commands appear between curly braces - hence the name "Curl".
In this example the first line of the code starts with a comment, the two vertical lines. This is similar to the REMark or // of other languages and is used for documentation.
{curl 3.0, 4.0, 5.0, 6.0 applet}
The second line is the 'herald ' - it declares the language and compatible Curl API version numbers and is similar to the <HTML> header in web pages. It is required. When multiple API version numbers are listed, that means that the applet is intended to be compatible with running in any of those versions of the Runtime Environment (RTE). A user can have more than one version of the RTE installed at the same time, but the highest version installed is the plug-in which will control the interactions with the browser, invoking lower numbered versions of the RTE if needed.
The remaining lines are the applet itself.
Hello World!
|| ======end of program ========
which displays the familiar Hello World!
# Curl/External links
## External links

* Download English version
* Download Japanese version
* Curl Links
* CurlChat - Chat program written in Curl
* Curl blog
* Curl Corp
# Curl/Example 4

This Example shows some OO capability along with Declarative layout.
Lines 1-3 are as described above.
Line four starts the definition of a new OO class called Circle that inherits from Ellipse (isa relationship).
Line 5 defines a field for the circle to hold the value of the diameter. Didn't really need it could just reference the width and height that is already stored for the ellipse. Likewise we should keep other programmers from changing the value of Width and Height independent of diameter. That's what I mean by simple OO examples are never enough.
Line 6 declares the constructor for the new class. A Little description on the parameters. the first parameter to Circle is a keyword argument that has a default value. Curl supports positional and keyword parameters. The second parameter is the ellipsis "...", also called 'rest arguments'. This is a construct for passing in an arbitrary number of arguments and you get to parse them. It is very helpful and usually isn't too much work.
Line 7 Saves in the diameter value in the objects field called diameter.
Line 8 calls the constructor for Ellipse but overwrites any mention of width and height with the diameter given.
The rest of the program closes out constructor and class definition then creates a simple display to hold a triple of circles. Note that other information is passed to the ellipse (fill-color) by way of the rest arguments. This is a screen capture of the output:
The dynamic nature of Curl can be used to create composite applications. Here comes a simple composite program that includes a chat capability and a web browser. Just save the script below as a file
say "c:\webbrowser.curl" and type the following line into your "Run..." field
Requirement is that you have Internet Explorer and Curl 3 installed.
You can also show the address bar, automagically fill in forms etc.
# Curl/Example 6

Curl is a gentle slope language. Here I will put some code to draw a UPC bar code that shows how you can program it using two techniques. Note that in the code below I have used markup and some text procs too. This is to demonstrate how these things can all be done so seamlessly in Curl.
I have implemented the UPC bar code using two techniques. The first technique uses Rule objects to draw the bars of the bar code. The second technique is more efficient. It uses the rendering APIs to render the bars of the bar code.
# Curl/Example 2

This displays a table just like the declarative HTML inside the Comment.
Lines 1 - 4 are standard.
Line 5 declares a new table.
Lines 6 - 9 put the values into four rows
Line 10 ends the table.
# Curl/Example 3

The above example shows some simple procedural code to create a table with the numbers 1 - 25 with Square and Cube Values. Lines 1-3 are as described above.
The 4th line starts a Value Block - this is a mechanism to hide some level of code within a Scope and to Return a Value - in this case to display in the web page. (Curl also has a do block that does not return anything)
Line 5 loads the row that holds the header information into the table.
Line 7 defines a new variable - my-table, of type Table and assigns it an initial value, the {Table} part of the line creates a new instance of Table. Curl does support an any type but its use is slower as the system has to make runtime checks on the type.
Line 9 creates a for iterator with a locally scoped variable i of type integer. Line 10 defines a local variable square and line 11 does the same for cube.
line 12 adds a new row to the table with the values of i, square and cube.
Line 13 ends the for construct.
Line 15 has the name of my-table so the value of my-table will be used as the result of the Value block.
Line 16 ends the value block.
# Easy Guide to the Internet/Getting Connected

The first thing that you need to do is get an ISP (a company that connects you to the Internet). There are a number of companies to choose from, if you want one that just does the job then there are plenty of choices, many with cheap prices. If you want a premium service then you should go for a well known service, the problem with these kind of services is they tend to be expensive. You can either go for a dial-up service (it uses your phone line unaided and tends to be cheaper) or broadband (a more expensive service which is faster) whatever service you choose, make sure they have good support numbers, you may need to ring them when you get set up!
When you are connected you should have a web-browser icon on your desktop, (some common ones are; Internet Explorer, Mozilla Firefox, Opera, Netscape and Safari) double click on it and you will enter the web-browser, you use these to view websites which is what the Internet is all about).
Wait! I'm not connected yet!
Oh, sorry. Don't worry though, you've got plenty of options.
# Easy Guide to the Internet/What's All the Fuss?

In this information age, you must have heard of Internet or its synonyms like Net, Web or Information Highway. However, you may or may not be familiar with the full potential of this tool. Even though the Internet has been around since the 1960s, it is only in the last two decades that it has become a household word. As with many other inventions, the origin can be traced to army use. The US military created it as a means of sharing information between a number of interconnected computers over a distance. The design then was rather primitive. The Internet in its modern form with various protocols like Transmission Control Protocol (TCP) and Internet Protocol (IP) came into being only in the early eighties. The creation of the World Wide Web by Tim Berners-Lee for the European Organisation for Nuclear Research (CERN) in 1989, has allowed the internet to be used in applications other than for sharing information. These include emails, phone, video messaging, instant messaging etc. The list is an ever expanding one, the only limit being human ingenuity.

## Internet Usage

The evolution of web communities has been drastic over the decades, ranging from scientists to heavy electronic game players. The Internet once was the ARPANET, created by the Advanced Research Projects Agency (ARPA) as a result of the USSR's launch of the space satellite of Sputnik. ARPA gave the ARPANET contract to BBN Technologies, and the physical network was built in 1969, linking four nodes: the University of California at Los Angeles, SRI (in Stanford), the University of California at Santa Barbara, and the University of Utah. In 1972, ARPA renamed "DARPA", or The Defense Advanced Research Projects Agency. The first e-mail program was also developed in the same year. Through the decades, the ARPANET became the DARPANET,
As of December, 2009, the total global internet audience has exceeded one billion visitors (excluding people age 14 and younger). Worldwide, there were 1,007,730 unique visitors .
Asia seems to be biggest user of the Internet, accounting for 42.2% of Internet users worldwide. China almost accounts for half of the Internet users in Asia . Europe comes in at the second biggest body of Internet users, accounting for 24.1% of all Internet users, North America at 15.1% of all Internet users, Latin America and the Caribbean at 10.5% of all Internet users, and finally, the rest 8% Internet users is from Africa, the Middle East, Oceania and Australia .

## References

* ↑ Prestipino, Peter A. (January 26, 2009). "Size of the Internet Audience". Website Magazine. Retrieved October 23, 2009. {{cite web}}: Cite has empty unknown parameter: |coauthors= (help)
* ↑ "Asia Internet Usage Stats and Population Statistics". Internet World Stats - Usage and Population Statistics. June 30, 2009. Retrieved October 23, 2009. {{cite web}}: Cite has empty unknown parameter: |coauthors= (help)
* ↑ "World Internet Usage Statistics News and World Population Stats". Internet World Stats - Usage and Population Statistics. June 30, 2009. Retrieved October 30, 2009. {{cite web}}: Cite has empty unknown parameter: |coauthors= (help)
# Easy Guide to the Internet/Sending an E-mail

When you first get on the Internet you will probably want to tell someone about it, huh? Well why not send an e-mail, you need to find an icon of an envelope, or find a link to the e-mail. You need to know someone who is also connected to the Internet and their e-mail address (it's just like the address you would use to send a letter), you can type a subject (general title) and you can then type the letter. Emails are almost always more informal than regular email so you will rarely address emails with 'Dear Sir' and regularly use more informal language.
# Easy Ido/Lesson five

Lesson four | Lesson six

## Compound words

* You can create compound words by combining two (or more) words. Like so: maro-salo for sea salt. The preceding word changes the meaning of the following. Just like in English, the first word describes the second one, so salo-maro would be a salt sea instead of sea salt. The hyphen between the words is not necessary: marosalo would also be correct, but it can be easier to read with the hyphens. The way you would do it in English, maro salo is, however, not correct. If you have two nouns and it is easier to pronounce, you can take the -o off the first one, so mar-salo would be correct as well. You don't want to make a word that's impossible to say though, so you would say letro-buxo instead of letr-buxo for postbox.

## Smaller particles

* Use di to show who owns or belongs to something. libro di John is "John's book".
* Use de to show where something is from. libro de John means "John's book" (the book you got from John).
* Use da to show what something is by. libro da John means "a book by John", (John wrote the book).
* Use pri to show what something is about. libro pri John means "a book about John", (John is the subject of the book).
* Use a or ad for the English word "to" when talking about direction. De Francia a Rusia - "From France to Russia", il parolis ad el - "he spoke to her".
* Use per to show what you are using to do something. Li voyajas per aviono - "They travel by aeroplane".
* Use kun to show that one thing is in company with something else. El iris kun sua spozo - "She went with her husband (spouse)".
* Use ek for the word "out", as in made out of something. shuo facita ek ledro - "a shoe made out of leather".
* Use en for the word "in". en mea chambro - "in my room".
* Use aden (to + in) to mean "into". aden mea chambro - "into my room".
* Use sur to mean "on". Pozez ol sur la lito - "Place it on the bed".
* Use adsur to mean "up onto". la kato saltis adsur la tablo - "the cat jumped up onto the table".
* Use alonge in the same way you use English "along". Irez alonge la rivero - "Go along the river".

## Word order

* You will have no problems following English word order when you write in Ido, but you can change things around a bit.
* As said before, adjectives can go before or after a noun, like in French.
* Adverbs go anywhere as long as the meaning is clear.
* The subject goes before the object, but you can put the subject after if you want by putting an -n on the object. Me manjas pano - "I eat bread", but: Men manjas pano - "(A) bread eats me". Of course you could just change the order and say Pano manjas me.

## Questions

* Ask yes or no questions by using ka or kad before a sentence. Vu iris a la urbo - "You went to the city". Ka vu iris a la urbo? - "Did you go to the city?" (NOTE: The choice between ka and kad is only about euphony. Just choose the one you think sounds better in each particular case).
* You don't change the word order when asking a question like in English.
* Other words: kande (when), quale (how), ube (where), quo (what), qua (who).
Lesson four | Top | Lesson six
# Easy Guide to the Internet/Other Computer Jargon

* Modem - Device that connects you to the Internet.
* Web Browser - A program that allows you to browse websites.
* Chat - A way of talking to people live.
* Web page - Like pages of a book, individual sections of a website.
* HTML - The language that most web pages are encoded in.
* Internet Explorer - A well known web browser created by Microsoft.
* Netscape Navigator - Another well known web browser created by Netscape.
# Easy Ido/Lesson eight
## Suffixes part two

* Use -e- to describe tint or colour. rozea (rose-coloured), oranjea (orange-coloured)
* Use -ebl- to indicate that something is possible. videbla (visible), kredebla (believable)
* Use -ed- to show quantity held by something. manuedo (handful)
* Use -eg- to indicate largeness. domego (mansion), pluvego (downpour)
* Use -et- to indicate smallness. ‎sigareto (cigarette)
* Use -em- to say that someone or something is inclined to something. laborema (industrious), ociema (lazy)
* Use -end- to express something to be done. solvenda (which must be solved)
* Use -er- to indicate customary but not professional activity or occupation for a person, or a characteristic action by an animal or even a thing. fotografero (amateur photographer), reptero (reptile), dansero (dancer)
# Easy Ido/Lesson seven

Lesson six | Lesson eight

## Verb + Infinitive

The English sentence 'I need to go home' is in the form Verb ('I need') + Infinitive ('to go'). Ido uses the same construction. Here are some verbs which can be found in sentences like this:
* povar - to be able (to do something)
* mustar - to have to (by necessity)
* bezonar - to need (to)
* volar - to want (to)
* devar - to have a duty (to), 'should'

## Times

One can talk about time using words such as the following:
* hiere - yesterday
* hodie - today
* morge - tomorrow
* horo - hour
* kloko - o'clock
* dio - day
* semano - week
* monato - month
* yaro - year

## Short words

Like in many languages, the hardest to learn can be the short words. To make matters worse, some words in Ido are very similar while their translations in English are quite different. The converse can also be true. Here are a few sets of words which need special attention.

### That

* ta - used when 'that' is an adjective, e.g. it precedes a noun. Ta libro esas granda, 'That book is big'.
* to - used when 'that' is a pronoun, e.g. it precedes a verb. To esas libro, 'That is a book'.
* ke - used when 'that' is a conjunction, e.g. it joins two clauses. Me pensas ke hundi esas animali, 'I think that dogs are animals'.

### N words

* nek - neither and nor. Me manjas nek frukti nek legumi, 'I eat neither fruits nor vegetables'.
* nur - only. Me havas nur un frato, 'I have only one sibling'.
* nun - now. Me mustas irar nun, 'I must go now'.
* nam - for, since. Me skribis la vorto, nam me ne savis olu, 'I wrote the word, for I did not know it'.

### Ul words

* ulo - something. Forsan ulo plu bona venos., 'Perhaps something better will come.'
* ulu - anyone, someone. Kad ulu savas ube ol esas?, 'Does anyone know where it is?'
* ula - any, some. Kad vu havas ula libri pri cienco?, 'Do you have any books about science?'

### Tr words

* tra - through. Me marchis tra la parko., 'I walked through the park.'
* tro - too. Mea libro esas tro olda., 'My book is too old.'
* tre - very. Ta libro esas tre interesanta., 'This book is very interesting.'

### Others

Once you have mastered the words above, try learning these last few. Also, try using them in sentences.
* dum - during
* yen - here is/are, there is/are (as in 'There is the train!')
* do - so, consequently
* ma - but
* ja - already
* se - if
* ya - indeed, truly
* tante - so (as in 'so big', 'so quickly')
Lesson six | Top | Lesson eight
# Commutative Algebra/Sequences of modules
## Modules in category theory

Definition 10.1 ($R$-mod):
For each ring $R$, there exists one category of modules, namely the modules over $R$ with module homomorphisms as the morphisms. This category is called $R$-mod.
We aim now to prove that if $R$ is a ring, $R$-mod is an Abelian category. We do so by verifying that modules have all the properties required for being an Abelian category.
Theorem 10.1:
The category of modules has kernels.
Proof:
For $R$-modules $M,N$ and a morphism $f:M\to N$ we define
    $\ker f:=\{m\in M|f(m)=0\}$.

## Sequences of augmented modules

Theorem 10.?:
Let $R$ be a ring and let $S\subseteq M$ be multiplicatively closed. Let $M,N,K$ be $R$-modules. Then
    $0\rightarrow M\rightarrow N\rightarrow K\rightarrow 0$ exact implies $0\rightarrow S^{-1}M\rightarrow S^{-1}N\rightarrow S^{-1}K\rightarrow 0$ exact.
-category-theoretic comment
# Commutative Algebra/The lattice of submodules, Noether isomorphism theorems
## Quotients
### Exercises

* Let $m,n\in \mathbb {N}$. Prove that $(m\mathbb {Z} )/(n\mathbb {Z} )\cong \mathbb {Z} {\big /}{\frac {n}{\gcd(m,n)}}\mathbb {Z}$.
# Commutative Algebra/Spectrum with Zariski topology

Definition 16.1:
Let $R$ be a commutative ring. The spectrum of $R$ is the set
    $\operatorname {Spec} (R):=\left\{p\leq R|p{\text{ prime}}\right\}$;
i.e. the set of all prime ideals of $R$.
On $\operatorname {Spec} R$, we will define a topology, turning $\operatorname {Spec} R$ into a topological space. This topology will be called Zariski topology, although only Alexander Grothendieck gave the definition in the above generality.

## Closed sets

Definition 16.2:
Let $R$ be a ring and $S\subseteq R$ a subset of $R$. Then define
    $V(S):=\left\{p\in \operatorname {Spec} R|S\subseteq p\right\}$.
The sets $V(S)$, where $S$ ranges over subsets of $R$, satisfy the following equations:
Proposition 16.3:
Let $R$ be a ring, and let $(S_{\alpha })_{\alpha \in A}$ be a family of subsets of $R$.
* $V(\emptyset )=\operatorname {Spec} R$ and $V(R)=\emptyset$
* $\bigcap _{\alpha \in A}V(S_{\alpha })=V\left(\bigcup _{\alpha \in A}S_{\alpha }\right)$
* If $A=\{\alpha _{1},\ldots ,\alpha _{n}\}$ is finite, then $V(S_{\alpha _{1}})\cup \cdots \cup V(S_{\alpha _{n}})=V(S_{\alpha _{1}}\cap \cdots \cap S_{\alpha _{n}})$.
Proof:
The first two items are straightforward. For the third, we use induction on $n$. $n=1$ is clear; otherwise, the direction $\subseteq$ is clear, and the other direction follows from lemma 14.20.$\Box$
Definition 16.4:
# Development Cooperation Handbook/Interviews/Vincenzo Pira

Testimonials - Development Cooperation Handbook Steps and Tools
Vincenzo Pira, employee of Armadilla, has a relevant Expertise in Designing and Managing International Cooperation Projects and Actions, related to Human Rights, Human Development, Human Aid , in Latin America, Syria, Mozambique and Angola. He has been one of the directors of the project Eugad which has collected many knowledge resources that have been collected in this handbook.
Vincenzo Pira, lavora con Armadilla, ed ha una lunga esperienza nei progetti di cooperazione internazionale. E' stato uno dei direttori del progetto Eugad che ha raccolto molte delle risorse di conoscenza utilizzate nel Development Cooperation Handbook.
* Interview on the MDGs (text)
* Intervista sulle sfide della Cooperazione Internazionale (video) -- Playlist on YouTube
* Other contributions by Vincenzo Pira for the Eugad project
* Spegando a Stefano gli obettivi di Eugad
# Development Cooperation Handbook/Interviews/Vincenzo Pira/Video Interview

Testimonials - Development Cooperation Handbook Steps and Tools
Vincenzo Pira, employee of Armadilla, has a relevant Expertise in Designing and Managing International Cooperation Projects and Actions, related to Human Rights, Human Development, Human Aid , in Latin America, Syria, Mozambique and Angola. He has been one of the directors of the project Eugad which has collected many knowledge resources that have been collected in this handbook.
Vincenzo Pira, lavora con Armadilla, ed ha una lunga esperienza nei progetti di cooperazione internazionale. E' stato uno dei direttori del progetto Eugad che ha raccolto molte delle risorse di conoscenza utilizzate nel Development Cooperation Handbook.
See also:
* Interview on the MDGs (text)
* Other contributions by Vincenzo Pira for the Eugad project
Per video a maggiore definizione vedere la ⇒ Playlist on YouTube
Per video a maggiore definizione vedere la ⇒ Playlist on YouTube
# Development Cooperation Handbook/Interviews/ Eusebio Leal

Testimonials - Development Cooperation Handbook Steps and Tools
Youtube ⇒ playlist
Eusebio Leal
Interview in Havana, Cuba on the 2 May 2015 by Carlo di Cicco for The Vrinda Project
Eusebio Leal Spengler, (born 11 September 1942 in Havana, Cuba), is the Havana City Historian, director of the restoration program of Old Havana and its historical center, Deputy to the National Assembly of the Popular Power in the IV, V and VI Legislature, Ambassador of Good Will of the United Nations, the University of Havana and has his masters in Latin American, Caribbean, and Cuban Studies. He is President of the Commission of Monuments in the City of Havana and a specialist in Archeological Sciences.

#### See also

⇒ Eusebio Leal Spengler

#### External links

* Eusebio Leal on Cuba Arte
* Eusebio Leal on Havana Cultural Patrimony