text:
User talk:216.229.90.232

Speedy deletion nomination of Sam Phillips (musician)
A tag has been placed on Sam Phillips (musician) requesting that it be speedily deleted from Wikipedia. This has been done under section G12 of the criteria for speedy deletion, because the article appears to be a clear copyright infringement. For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or printed material, and as a consequence, your addition will most likely be deleted. You may use external websites as a source of information, but not as a source of sentences. This part is crucial: say it in your own words.

If the external website belongs to you, and you want to allow Wikipedia to use the text — which means allowing other people to modify it — then you must verify that externally by one of the processes explained at Donating copyrighted materials. If you are not the owner of the external website but have permission from that owner, see Requesting copyright permission. You might want to look at Wikipedia's policies and guidelines for more details, or ask a question here.

If you think that this notice was placed here in error, you may contest the deletion by adding  to the top of the page that has been nominated for deletion (just below the existing speedy deletion or "db" tag), coupled with adding a note on the talk page explaining your position, but be aware that once tagged for speedy deletion, if the page meets the criterion, it may be deleted without delay. Please do not remove the speedy deletion tag yourself, but don't hesitate to add information to the page that would render it more in conformance with Wikipedia's policies and guidelines.  ttonyb (talk) 02:47, 19 February 2010 (UTC)

Proposed deletion of Dan Michaels

The article Dan Michaels has been proposed for deletion  because of the following concern:
 * Non-notable producer and artist. See WP:MUSIC

While all contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the  notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing  will stop the proposed deletion process, but other deletion processes exist. The speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Claritas (talk) 18:52, 9 May 2010 (UTC)

Proposed deletion of Anchorman (disambiguation)

The article Anchorman (disambiguation) has been proposed for deletion  because of the following concern:
 * Per WP:2DABS, hatnote best in these circumstances

While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the notice, but please explain why in your edit summary or on the article's talk page.

Please consider improving the article to address the issues raised. Removing will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Boleyn (talk) 16:38, 12 November 2014 (UTC)

Proposed deletion of Canticle of the Plains

The article Canticle of the Plains has been proposed for deletion  because of the following concern:
 * Fails notability. I have the album, but it is not notable.

While all constructive contributions to Wikipedia are appreciated, content or articles may be deleted for any of several reasons.

You may prevent the proposed deletion by removing the notice, but please explain why in your edit summary or on |the article's talk page.

Please consider improving the article to address the issues raised. Removing will stop the proposed deletion process, but other deletion processes exist. In particular, the speedy deletion process can result in deletion without discussion, and articles for deletion allows discussion to reach consensus for deletion. Walter Görlitz (talk) 07:05, 31 January 2016 (UTC)

Nomination of Gospel Music Association for deletion
A discussion is taking place as to whether the article Gospel Music Association is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The article will be discussed at Articles for deletion/Gospel Music Association& until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article. – Muboshgu (talk) 00:57, 11 April 2020 (UTC)

title: User talk:216.229.90.232


text: User:Bryan (usurped)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: User:Bryan (usurped)


text:
Apple Records discography

This is the discography of Apple Records, a record label formed by the Beatles in 1968. During its early years, the label enjoyed a fair degree of commercial success, most notably with Mary Hopkin and Badfinger, as well as discovering acts such as James Taylor and Billy Preston who would go on to greater success with other labels. However, by the mid-1970s, Apple had become little more than an outlet for the Beatles' solo recordings (although, as the solo Beatles were actually still under contract to EMI, the Apple label was, in truth, only a cosmetic addition to their releases). After EMI's contract with the Beatles ended in 1976, the Apple label was finally wound up. The label was reactivated in the 1990s with many of the original Apple albums being reissued on compact disc, and the company now oversees new Beatles releases such as the Anthology and 1 albums as well as the 2009 Beatles remastering programme. In 2010, Apple set about remastering and reissuing its back catalogue for a second time.

For convenience, releases are divided into UK and US releases. However, some releases which were designated a UK-sequence catalogue number were only issued in certain mainland European countries. Additionally, with the Beatles still being under contract to EMI, all of the group's records (and the majority of their UK solo releases) retained the numbering systems of Parlophone (for the UK, New Zealand and South Africa), Capitol (for the US) and EMI (for Australia). The Republic of Ireland released eight Apple singles in 1970–71, six of which had unique catalogue numbers. Since the 2013 takeover of EMI by Universal Music, the titles have yet to be reissued with Universal catalogue numbers and UPCs.

Singles
Not planned for release. A special recorded "message" medley from Frank Sinatra to Maureen Starkey. One single-sided single pressed and the master tape has been destroyed. Early UK editions credited to 'White Trash'. Only released in Italy – 17.01.69. Not given a full release, as EMI would not distribute. Only 2000 copies were pressed in the UK. An unnumbered US Apple acetate also exists. Only released in France – 07.03.69. Only released in Europe and Japan – 18.07.69. Mail order only EP featuring: The Iveys "Storm in a Teacup" / James Taylor "Something's Wrong" / Jackie Lomax "Little Yellow Pill" / Mary Hopkin "Pebble and the Man". Not issued. Planned release date – 19.09.69. APPLE 16 was also allocated to Mortimer's unreleased recording of "On Our Way Home". Not issued. Planned release date - .12.69. Not issued in UK. Issued as APPLE 28 in some European countries. Issued as APPLE 27 in some European countries. Not issued. Not issued in UK. Planned release date for Lennon – 5.12.72. Cancelled release. Made it only to the acetate stage. Planned release date – 24.9.73. Re-issued with "Let Me Roll It" as the B side on 18.02.74. Re-issued on 07.02.75 (UK) and 20.02.75 (US) with the same catalogue numbers but with the A and B sides reversed. Released as part of a series of EMI "Golden 45's". Four track EP featuring: Mary Hopkin "Those Were The Days" / Billy Preston "That's the Way God Planned It" / Jackie Lomax "Sour Milk Sea" / Badfinger "Come and Get It". Re-issued from 1975 with the same catalogue number (and sometimes artwork) on Capitol after McCartney's contract moved from Parlophone. Re-issued with the same catalogue number on the Parlophone label. Originally issued on Parlophone. Double A Side. Released on Parlophone before the establishment of Apple Records (New Zealand). Originally released APon green vinyl and reissued on black vinyl. Some issues list "McCartney's Wings". Released as a 7" 45rpm and a 10" 78rpm. Demo copies have the tracks "Band On The Run" (Edited Version) / "Band On The Run" (Full Version). Also released as a double A side and with reversed A and B side. Released in "East Asia" (Hong Kong) by Parlophone, Catalogue number PEA-501. Released in "East Asia" (Hong Kong) by Parlophone, Catalogue number PEA-502. Due to extreme demands on production, EMI also contracted Decca and Philips to press this release. Due to extreme demands on production, EMI also contracted Philips to press this release. Due to industrial action, EMI also contracted Decca to press this release. Originally planned for release with flipped sides. Released in Japan as AR-2520 on 05.06.70. Released in several European countries in early February 1972. Released in Sweden in December 1968 and Norway in April 1969 as SD 6061. Released in the Philippines as AL 60838. Released in several European countries in March 1975. Released in France as APF 506.

Albums
Not released. Planned release date – 30.05.69. Later issued on Elektra Records as Accept No Substitute. SAPCOR 7 was also earmarked for a 20.06.69 album release by Trash. Not issued in the UK. Planned release date – 04.07.69. Only released in Germany, Italy and Japan (with alternate catalogue numbers). Regular album release to replace the Box Set package which accompanied the original UK issue. From Then to You and The Beatles Christmas Album are the same album, being a collection of the Beatles Fan Club-only Christmas flexi discs issued between 1963 and 1969. Similarly, these two albums were only available to members of "The Beatles Fan Club". Only issued in mono despite stereo 'SW' prefix on US release. This album had previously been issued in full on Philles Records in the US and has since been reissued many times on various labels. Released in Brazil in mono without the 'S' prefix. Planned for release in Brazil in mono without the 'S' prefix but only released in stereo. Reissued on vinyl 10.12.96 with "Do You Mind" bonus track. Released in New Zealand as SAPCOR 101. This album has since been reissued on various labels. This album was reissued in 1977 on Ring O'Records, Catalogue number 2320 104, with different artwork. Tetragrammaton catalogue number as EMI refused to distribute. Later re-issued on EMI's Music for Pleasure label in the UK with a different catalogue number: Mind Games (MFP 5058) in 1980, Ringo (MFP 50508) in 1980, Dark Horse (MFP 50510) in 1980, Rock 'n' Roll (MFP 50522) in 1981, and Blast from Your Past (MFP 50524) in 1981. Later re-issued on EMI's Fame label in the UK with a different catalogue number: Wild Life (FA 3101) in 1984,  Red Rose Speedway (FA 3193) in 1987. Originally planned for release as STAP-01. Pressed in the UK for export only, not released in the UK. This is the cassette release of the Dutch LP with catalogue number 5C 052-93536.

Zapple Records
Zapple was a short-lived subsidiary of Apple designed to release spoken word and avant garde recordings.

Not released by Zapple. Released by Harvest Records in 1973 (ST-424) and on CD by Collectors' Choice Music in 2005 (CCM-540-2).

1990s remasters
Apple began the process of reissuing the back catalogue on compact disc in 1991, with many of the CDs containing bonus tracks. By this time, the releases in the UK and US were virtually identical. This list does not include Beatles or solo albums, which were re-released on compact disc by Parlophone or Capitol.

2009 remasters
2009 saw the remastered reissues of the Beatles back catalogue. A worldwide release date of 9 September 2009 (09.09.09) was set to tie in with the release of The Beatles: Rock Band music video game. Replacing the CD editions which had been issued in 1987, all of the original Beatles albums were reissued in new packaging with mini DVD documentaries and, unlike the 1987 issues, the first four albums (Please Please Me, With The Beatles, A Hard Day's Night and Beatles For Sale) were made available on CD in stereo for the first time. Also, the Past Masters collection of non-album material was now issued as a double CD set, as opposed to the two separate discs issued in 1988. In addition, two box sets were issued, one containing all 16 remastered stereo albums and a second limited edition box set containing the mono mixes of all the albums up to and including The Beatles (the later albums did not receive a separate mono mix). The stereo box also features a DVD "The Mini Documentaries" which contains all the short films that are on the CDs in CD-ROM format.

Although the Apple logo is shown on all the 2009 remasters, the labels on the actual discs are those that appeared on the original LPs. So all the albums from "Please Please Me" through "Sgt. Pepper's Lonely Hearts Club Band" feature a Parlophone label. "Magical Mystery Tour", which was first released in an album version in the US, has a Capitol label. The remaining albums, originally released on Apple, feature the green "A-side" label, excepting "The Beatles" which features the green "A-side" label on disc 1, and the 'white' (cut apple) "B-side" label on disc 2. For the "Past Masters" double-CD set, the first disc has a Parlophone label, and the second disc a green "A-side" Apple label. The DVD that accompanies "The Beatles in Stereo" box set has a red Apple label (similar to that on the original US "Let It Be" LP).

In late 2010, the compilation albums 1962–1966 and 1967–1970 were issued again, in addition a box set "1962–1970" containing both sets, released in the UK and Europe, and a similar box set released in the US with added photo cards and a stamp. Shortly afterwards, the entire remastered catalogue was finally made available to download on iTunes after years of legal wrangling between the Beatles and Apple Inc.

Also available as a USB flash drive. Issued 07.12.09.

2010 remasters
With the 1990s reissues out of print, many of the original Apple albums were re-released for a second time in new remastered versions in October 2010. These remasters were also made available on iTunes, just a few weeks before the Beatles back catalogue was finally released for download. Several of the iTunes versions included exclusive tracks not available on the standard CD issue, although these tracks were included on a bonus double CD as part of the Apple Box Set, which collected all of the remastered albums in one package. All of the 2010 remasters had been previously issued in the 1990s reissue programme apart from a 21-track compilation entitled  Come and Get It: The Best of Apple Records  which included a number of single-only tracks which now received their first official release on compact disc.

title: Apple Records discography


text:
Talk:Roh Moo-hyun

Policy
I replaced the previous penultimate paragraph which seemed to me to lack a degree of objectivity.

The removed text was:

'As president, Roh continues the engagement policy or Sunshine policy towards North Korea started by the president before him, Kim Dae-Jung. Yet, his cabinet's recent attitude towards this policy seemed compromised due to geo-political situation of which has been highly escalated due to North Korea's nuclear programme. However, it is widely perceived that this government is not capable of tackling issues around. His support for US military forces in Korea, even after possible reunification, needs enduring scrutiny due to lack of confidence in his policy.'

TJOB 23:57, Feb 24, 2004 (UTC)

Impeachment
Now that this article is featured in the "In the News" box on the Main Page, I've cleaned up the article vis-a-vis Roh's impeachment. One side note: he was impeached on March 12, not March 11. Although it was March 11 in the western hemisphere, it was Friday, March 12 in Korea. --Sewing 18:54, 12 Mar 2004 (UTC)

Just minor comments...
"His victory was a dramatic surprise, made possible by a last-minute betrayal by a political ally that backfired." -- In my opinion, this is an exaggeration and contains some--perhaps unconscious--bias of the writer. It was indeed one of factors that led to Roh's victory, but there were other more important reasons. I would like to change "made possible by" especially.

Notes on "Impeachment"-- It appearss to me that some people on this discussion board do not fully understand what the word 'impeachment' means. Roh, just like Bill Clinton of US, was 'impeached,' which means his power as the president was temporarily suspended and he was brought before the Supreme Court. However, he was not 'convicted,' which means the Court did not find him guilty. Thus, in strict definition, Roh's impeachment was not "illegal" or "failed," as this article says. It should say he was impeached but not convicted. --Hychu — Preceding comment added by 140.247.71.110 (talk) 25 June 2007 (UTC). Signature added by SUM1 (talk) 7 February 2020

Impeachment split
Saw that @Holidayruin proposed that the section for Roh's impeachment be split off in 11 Dec 2021. Wanted to create a discussion thread for it.

I oppose it because it meets neither criteria in WP:WHENSPLIT. It's also an old request, so I'll probably just remove it unless someone wants to rediscuss it. toobigtokale (talk) 21:16, 21 July 2023 (UTC)

 * My main intention was to say that a new article should be made for the impeachment. This is an important moment in South Korean political history, and it is very common for impeachments to have their own Wikipedia article (see Impeachment of Park Geun-hye, Second impeachment of Donald Trump, Impeachment of Dilma Rousseff, etc). I know it's not a large section. It just needs more work and editing.
 * Furthermore, the Impeachment of Roh Moo-hyun already has an article on the Korean Wikipedia (노무현 대통령 탄핵소추).
 * Holidayruin (talk) 17:25, 22 July 2023 (UTC)
 * I agree that it’s an important topic and deserves more discussion. But it doesn’t meet the criteria for splitting. Topics that deserve their own article (again, I agree that this totally does) isn’t sufficient to merit a split toobigtokale (talk) 19:31, 22 July 2023 (UTC)
 * @Holidayruin any updates? Maybe we can/should open an official split discussion using the template to invite other opinions toobigtokale (talk) 19:27, 27 July 2023 (UTC)
 * If no updates, I'll go ahead and remove the template for now. It's been over a week with no response, and I think the policy falls pretty clear in this case. toobigtokale (talk) 03:56, 31 July 2023 (UTC)

title: Talk:Roh Moo-hyun


text:
Miller–Rabin primality test

The Miller–Rabin primality test or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar to the Fermat primality test and the Solovay–Strassen primality test.

It is of historical significance in the search for a polynomial-time deterministic primality test. Its probabilistic variant remains widely used in practice, as one of the simplest and fastest tests known.

Gary L. Miller discovered the test in 1976. Miller's version of the test is deterministic, but its correctness relies on the unproven extended Riemann hypothesis. Michael O. Rabin modified it to obtain an unconditional probabilistic algorithm in 1980.

Mathematical concepts
Similarly to the Fermat and Solovay–Strassen tests, the Miller–Rabin primality test checks whether a specific property, which is known to hold for prime values, holds for the number under testing.

Strong probable primes
The property is the following. For a given odd integer n > 2, let’s write n − 1 as 2sd where s is a positive integer and d is an odd positive integer. Let’s consider an integer a, called a base, which is coprime to n. Then, n is said to be a strong probable prime to base a if one of these congruence relations holds: This simplifies to first checking for $$a^d \bmod n = 1$$ and then $$a^{2^r d} = n-1 $$ for successive values of r. For each value of r, the value of the expression may be calculated using the value obtained for the previous value of r by squaring under the modulus of n.
 * $$a^{d} \equiv 1 \pmod{n}$$;
 * $$a^{2^r d} \equiv -1 \pmod{n}$$ for some 0 ≤ r < s.

The idea beneath this test is that when n is an odd prime, it passes the test because of two facts:
 * by Fermat's little theorem, $$a^{n-1} \equiv 1 \pmod{n}$$ (this property alone defines the weaker notion of probable prime to base a, on which the Fermat test is based);
 * the only square roots of 1 modulo n are 1 and −1.

Hence, by contraposition, if n is not a strong probable prime to base a, then n is definitely composite, and a is called a witness for the compositeness of n.

However, this property is not an exact characterization of prime numbers. If n is composite, it may nonetheless be a strong probable prime to base a, in which case it is called a strong pseudoprime, and a is a strong liar.

Choices of bases
Thankfully, no composite number is a strong pseudoprime to all bases at the same time (contrary to the Fermat primality test for which Fermat pseudoprimes to all bases exist: the Carmichael numbers). However no simple way of finding a witness is known. A naïve solution is to try all possible bases, which yields an inefficient deterministic algorithm. The Miller test is a more efficient variant of this (see section Miller test below).

Another solution is to pick a base at random. This yields a fast probabilistic test. When n is composite, most bases are witnesses, so the test will detect n as composite with a reasonably high probability (see section Accuracy below). We can quickly reduce the probability of a false positive to an arbitrarily small rate, by combining the outcome of as many independently chosen bases as necessary to achieve the said rate. This is the Miller–Rabin test. There seems to be diminishing returns in trying many bases, because if n is a pseudoprime to some base, then it seems more likely to be a pseudoprime to another base.

Note that $a^{d} ≡ 1 (mod n)$ holds trivially for $a ≡ 1 (mod n)$, because the congruence relation is compatible with exponentiation. And $a^{d} = a^{2^{0}d} ≡ −1 (mod n)$ holds trivially for $a ≡ −1 (mod n)$ since $d$ is odd, for the same reason. That is why random $a$ are usually chosen in the interval $1 < a < n − 1$.

For testing arbitrarily large $n$, choosing bases at random is essential, as we don't know the distribution of witnesses and strong liars among the numbers 2, 3, ..., $n − 2$.

However, a pre-selected set of a few small bases guarantees the identification of all composites up to a pre-computed maximum. This maximum is generally quite large compared to the bases. This gives very fast deterministic tests for small enough n (see section Testing against small sets of bases below).

Proofs
Here is a proof that, if n is a prime, then the only square roots of 1 modulo n are 1 and −1. $$

Here is a proof that, if n is an odd prime, then it is a strong probable prime to base a. $$

Example
Suppose we wish to determine if $$n = 221$$ is prime. We write $$n - 1 \text{ as } 2^2 \times 55$$, so that we have $$s = 2 \text{ and } d = 55$$. We randomly select a number $$a$$ such that $$2 \leq a \leq n-2$$.

Say $$a = 174$$:

$$ \begin{align} a^{{s^0}d} \text{ mod } n \rightarrow & 174^{{2^0} 55} \text{ mod } 221 \equiv 174^{55} \equiv 47 \text{. Since } 47 \neq 1 \text{ and } 47 \neq n - 1 \text{, we continue.} \\ & 174^{{2^1} 55} \text{ mod } 221 \equiv 174^{110} \equiv 220 = n - 1 \end{align} $$

Since $$220 \equiv -1 \text{ mod } n$$, either 221 is prime, or 174 is a strong liar for 221. We try another random $$a$$, this time choosing $$a = 137$$:

$$ \begin{align} a^{{s^0}d} \text{ mod } n \rightarrow & 137^{{2^0} 55} \text{ mod } 221 \equiv 137^{55} \equiv 188 \text{. Since } 188 \neq 1 \text{ and } 188 \neq n - 1 \text{, we continue.} \\ & 137^{{2^1} 55} \text{ mod } 221 \equiv 137^{110} \equiv 205 \neq n - 1 \end{align} $$

Hence 137 is a witness for the compositeness of 221, and 174 was in fact a strong liar. Note that this tells us nothing about the factors of 221 (which are 13 and 17). However, the example with 341 in a later section shows how these calculations can sometimes produce a factor of n.

For a practical guide to choosing the value of a see Testing against small sets of bases.

Miller–Rabin test
The algorithm can be written in pseudocode as follows. The parameter k determines the accuracy of the test. The greater the number of rounds, the more accurate the result.

Input #1: n > 2, an odd integer to be tested for primality Input #2: k, the number of rounds of testing to perform Output: “composite” if n is found to be composite, “probably prime” otherwise

let s > 0 and d odd > 0 such that n − 1 = 2sd # by factoring out powers of 2 from n − 1 repeat k times: a ← random(2, n − 2) # n is always a probable prime to base 1 and n − 1 x ← ad mod n repeat s times: y ← x2 mod n if y = 1 and x ≠ 1 and x ≠ n − 1 then # nontrivial square root of 1 modulo n return “composite” x ← y if y ≠ 1 then return “composite” return “probably prime”

Complexity
Using repeated squaring, the running time of this algorithm is $O(k log^{3} n)$, where n is the number tested for primality, and k is the number of rounds performed; thus this is an efficient, polynomial-time algorithm. FFT-based multiplication (Harvey-Hoeven algorithm) can decrease the running time to $O(k log^{2} n log log n) = Õ(k log^{2} n)$.

Accuracy
The error made by the primality test is measured by the probability that a composite number is declared probably prime. The more bases a are tried, the better the accuracy of the test. It can be shown that if n is composite, then at most $1⁄4$ of the bases a are strong liars for n. As a consequence, if n is composite then running k iterations of the Miller–Rabin test will declare n probably prime with a probability at most 4−k.

This is an improvement over the Solovay–Strassen test, whose worst‐case error bound is 2−k. Moreover, the Miller–Rabin test is strictly stronger than the Solovay–Strassen test in the sense that for every composite n, the set of strong liars for n is a subset of the set of Euler liars for n, and for many n, the subset is proper.

In addition, for large values of n, the probability for a composite number to be declared probably prime is often significantly smaller than 4−k. For instance, for most numbers n, this probability is bounded by 8−k; the proportion of numbers n which invalidate this upper bound vanishes as we consider larger values of n. Hence the average case has a much better accuracy than 4−k, a fact which can be exploited for generating probable primes (see below). However, such improved error bounds should not be relied upon to verify primes whose probability distribution is not controlled, since a cryptographic adversary might send a carefully chosen pseudoprime in order to defeat the primality test. In such contexts, only the worst‐case error bound of 4−k can be relied upon.

The above error measure is the probability for a composite number to be declared as a strong probable prime after k rounds of testing; in mathematical words, it is the conditional probability $$\Pr(M\!R_k \mid \lnot P)$$ where P is the event that the number being tested is prime, and MRk is the event that it passes the Miller–Rabin test with k rounds. We are often interested instead in the inverse conditional probability $$\Pr(\lnot P \mid M\!R_k)$$: the probability that a number which has been declared as a strong probable prime is in fact composite. These two probabilities are related by Bayes' law:

 * $$\begin{align}

\Pr(\lnot P \mid M\!R_k) & = \frac{\Pr(\lnot P \land M\!R_k)}{\Pr(\lnot P \land M\!R_k) + \Pr(P \land M\!R_k)} \\ & = \frac{1}{1 + \frac{\Pr(M\!R_k \mid P)}{\Pr(M\!R_k \mid \lnot P)} \frac{\Pr(P)}{\Pr(\lnot P)}} \\ & = \frac{1}{1 + \frac{1}{\Pr(M\!R_k \mid \lnot P)} \frac{\Pr(P)}{1 - \Pr(P)}} \end{align}$$

In the last equation, we simplified the expression using the fact that all prime numbers are correctly reported as strong probable primes (the test has no false negative). By dropping the left part of the denominator, we derive a simple upper bound:

 * $$\Pr(\lnot P \mid M\!R_k) < \Pr(M\!R_k \mid \lnot P) \left(\tfrac{1}{\Pr(P)} - 1\right)$$

Hence this conditional probability is related not only to the error measure discussed above — which is bounded by 4−k — but also to the probability distribution of the input number. In the general case, as said earlier, this distribution is controlled by a cryptographic adversary, thus unknown, so we cannot deduce much about $$\Pr(\lnot P \mid M\!R_k)$$. However, in the case when we use the Miller–Rabin test to generate primes (see below), the distribution is chosen by the generator itself, so we can exploit this result.

Miller test
The Miller–Rabin algorithm can be made deterministic by trying all possible values of a below a certain limit. Taking n as the limit would imply $O(n)$ trials, hence the running time would be exponential with respect to the size $log n$ of the input. To improve the running time, the challenge is then to lower the limit as much as possible while keeping the test reliable.

If the tested number n is composite, the strong liars a coprime to n are contained in a proper subgroup of the group (Z/nZ)*, which means that if we test all a from a set which generates (Z/nZ)*, one of them must lie outside the said subgroup, hence must be a witness for the compositeness of n. Assuming the truth of the extended Riemann hypothesis (ERH), it is known that the group is generated by its elements smaller than $O((ln n)^{2})$, which was already noted by Miller. The constant involved in the Big O notation was reduced to 2 by Eric Bach. This leads to the following primality testing algorithm, known as the Miller test, which is deterministic assuming the GRH:

Input: n > 2, an odd integer to be tested for primality Output: “composite” if n is composite, “prime” otherwise

let s > 0 and d odd > 0 such that n − 1 = 2sd # by factoring out powers of 2 from n − 1 for all a in the range [2, min(n − 2, ⌊2(ln n)2⌋)]: x ← ad mod n repeat s times: y ← x2 mod n if y = 1 and x ≠ 1 and x ≠ n − 1 then # nontrivial square root of 1 modulo n return “composite” x ← y if y ≠ 1 then return “composite” return “prime”

The full power of the generalized Riemann hypothesis is not needed to ensure the correctness of the test: as we deal with subgroups of even index, it suffices to assume the validity of GRH for quadratic Dirichlet characters.

The running time of the algorithm is, in the soft-O notation, $Õ((log n)^{4})$ (using FFT‐based multiplication).

The Miller test is not used in practice. For most purposes, proper use of the probabilistic Miller–Rabin test or the Baillie–PSW primality test gives sufficient confidence while running much faster. It is also slower in practice than commonly used proof methods such as APR-CL and ECPP which give results that do not rely on unproven assumptions. For theoretical purposes requiring a deterministic polynomial time algorithm, it was superseded by the AKS primality test, which also does not rely on unproven assumptions.

Testing against small sets of bases
When the number n to be tested is small, trying all $a < 2(ln n)^{2}$ is not necessary, as much smaller sets of potential witnesses are known to suffice. For example, Pomerance, Selfridge, Wagstaff and Jaeschke have verified that
 * if n < 2,047, it is enough to test a = 2;
 * if n < 1,373,653, it is enough to test a = 2 and 3;
 * if n < 9,080,191, it is enough to test a = 31 and 73;
 * if n < 25,326,001, it is enough to test a = 2, 3, and 5;
 * if n < 3,215,031,751, it is enough to test a = 2, 3, 5, and 7;
 * if n < 4,759,123,141, it is enough to test a = 2, 7, and 61;
 * if n < 1,122,004,669,633, it is enough to test a = 2, 13, 23, and 1662803;
 * if n < 2,152,302,898,747, it is enough to test a = 2, 3, 5, 7, and 11;
 * if n < 3,474,749,660,383, it is enough to test a = 2, 3, 5, 7, 11, and 13;
 * if n < 341,550,071,728,321, it is enough to test a = 2, 3, 5, 7, 11, 13, and 17.

Using the work of Feitsma and Galway enumerating all base 2 pseudoprimes in 2010, this was extended (see ), with the first result later shown using different methods in Jiang and Deng:
 * if n < 3,825,123,056,546,413,051, it is enough to test a = 2, 3, 5, 7, 11, 13, 17, 19, and 23.
 * if n < 18,446,744,073,709,551,616 = 264, it is enough to test a = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37.

Sorenson and Webster verify the above and calculate precise results for these larger than 64‐bit results:
 * if n < 318,665,857,834,031,151,167,461, it is enough to test a = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37.
 * if n < 3,317,044,064,679,887,385,961,981, it is enough to test a = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, and 41.

Other criteria of this sort, often more efficient (fewer bases required) than those shown above, exist. They give very fast deterministic primality tests for numbers in the appropriate range, without any assumptions.

There is a small list of potential witnesses for every possible input size (at most b values for b‐bit numbers). However, no finite set of bases is sufficient for all composite numbers. Alford, Granville, and Pomerance have shown that there exist infinitely many composite numbers n whose smallest compositeness witness is at least $(ln n)^{1/(3ln ln ln n)}$. They also argue heuristically that the smallest number w such that every composite number below n has a compositeness witness less than w should be of order $Θ(log n log log n).$

Variants for finding factors
By inserting greatest common divisor calculations into the above algorithm, we can sometimes obtain a factor of n instead of merely determining that n is composite. This occurs for example when n is a probable prime to base a but not a strong probable prime to base a.

If x is a nontrivial square root of 1 modulo n,
 * since $x^{2} ≡ 1 (mod n)$, we know that n divides $x^{2} − 1 = (x − 1)(x + 1)$;
 * since $x ≢ ±1 (mod n)$, we know that n does not divide $x − 1$ nor $x + 1$.

From this we deduce that $A = gcd(x − 1, n)$ and $B = gcd(x + 1, n)$ are nontrivial (not necessarily prime) factors of n (in fact, since n is odd, these factors are coprime and n = AB). Hence, if factoring is a goal, these gcd calculations can be inserted into the algorithm at little additional computational cost. This leads to the following pseudocode, where the added or changed code is highlighted:

Input #1: n > 2, an odd integer to be tested for primality Input #2: k, the number of rounds of testing to perform Output: (“multiple of”, m) if a nontrivial factor m of n is found, “composite” if n is otherwise found to be composite, “probably prime” otherwise

let s > 0 and d odd > 0 such that n − 1 = 2sd # by factoring out powers of 2 from n − 1 repeat k times: a ← random(2, n − 2) # n is always a probable prime to base 1 and n − 1 x ← ad mod n repeat s times: y ← x2 mod n if y = 1 and x ≠ 1 and x ≠ n − 1 then # nontrivial square root of 1 modulo n return (“multiple of”, gcd(x − 1, n)) x ← y if y ≠ 1 then return “composite” return “probably prime”

This is not a probabilistic factorization algorithm because it is only able to find factors for numbers n which are pseudoprime to base a (in other words, for numbers n such that $a^{n−1} ≡ 1 mod n$). For other numbers, the algorithm only returns “composite” with no further information.

For example, consider n = 341 and a = 2. We have $n − 1 = 85 × 4$. Then $2^{85} mod 341 = 32$ and $32^{2} mod 341 = 1$. This tells us that n is a pseudoprime base 2, but not a strong pseudoprime base 2. By computing a gcd at this stage, we find a factor of 341: $gcd(32 − 1, 341) = 31$. Indeed, $341 = 11 × 31$.

In order to find factors more often, the same ideas can also be applied to the square roots of −1 (or any other number). This strategy can be implemented by exploiting knowledge from previous rounds of the Miller–Rabin test. In those rounds we may have identified a square root modulo n of −1, say R. Then, when $x^{2} mod n = n − 1$, we can compare the value of x against R: if x is neither R nor n−R, then $gcd(x − R, n)$ and $gcd(x + R, n)$ are nontrivial factors of n.

Generation of probable primes
The Miller–Rabin test can be used to generate strong probable primes, simply by drawing integers at random until one passes the test. This algorithm terminates almost surely (since at each iteration there is a chance to draw a prime number). The pseudocode for generating b‐bit strong probable primes (with the most significant bit set) is as follows:

Input #1: b, the number of bits of the result Input #2: k, the number of rounds of testing to perform Output: a strong probable prime n

while True: pick a random odd integer n in the range [2b−1, 2b−1] if the Miller–Rabin test with inputs n and k returns “probably prime” then return n

Complexity
Of course the worst-case running time is infinite, since the outer loop may never terminate, but that happens with probability zero. As per the geometric distribution, the expected number of draws is $$\tfrac{1}{\Pr(M\!R_k)}$$ (reusing notations from earlier).

As any prime number passes the test, the probability of being prime gives a coarse lower bound to the probability of passing the test. If we draw odd integers uniformly in the range [2b−1, 2b−1], then we get:

 * $$\Pr(M\!R_k) > \Pr(P) = \frac{\pi\left(2^b\right) - \pi\left(2^{b-1}\right)}{2^{b-2}}$$

where π is the prime-counting function. Using an asymptotic expansion of π (an extension of the prime number theorem), we can approximate this probability when b grows towards infinity. We find:

 * $$\Pr(P) = \tfrac{2}{\ln2} b^{-1} + \mathcal{O}\left(b^{-3}\right)$$
 * $$\tfrac{1}{\Pr(P)} = \tfrac{\ln2}{2} b + \mathcal{O}\left(b^{-1}\right)$$

Hence we can expect the generator to run no more Miller–Rabin tests than a number proportional to b. Taking into account the worst-case complexity of each Miller–Rabin test (see earlier), the expected running time of the generator with inputs b and k is then bounded by $O(k b^{4})$ (or $Õ(k b^{3})$ using FFT-based multiplication).

Accuracy
The error measure of this generator is the probability that it outputs a composite number.

Using the relation between conditional probabilities (shown in an earlier section) and the asymptotic behavior of $$\Pr(P)$$ (shown just before), this error measure can be given a coarse upper bound:

 * $$\Pr(\lnot P \mid M\!R_k)

< \Pr(M\!R_k \mid \lnot P) \left( \tfrac{1}{\Pr(P)} - 1 \right) \leq 4^{-k} \left( \tfrac{\ln2}{2} b - 1 + \mathcal{O}\left(b^{-1}\right) \right). $$

Hence, for large enough b, this error measure is less than $$\tfrac{\ln2}{2} 4^{-k} b$$. However, much better bounds exist.

Using the fact that the Miller–Rabin test itself often has an error bound much smaller than 4−k (see earlier), Damgård, Landrock and Pomerance derived several error bounds for the generator, with various classes of parameters b and k. These error bounds allow an implementor to choose a reasonable k for a desired accuracy.

One of these error bounds is 4−k, which holds for all b ≥ 2 (the authors only showed it for b ≥ 51, while Ronald Burthe Jr. completed the proof with the remaining values 2 ≤ b ≤ 50 ). Again this simple bound can be improved for large values of b. For instance, another bound derived by the same authors is:
 * $$\left(\frac{1}{7} b^\frac{15}{4} 2^{-\frac b 2}\right) 4^{-k}$$

which holds for all b ≥ 21 and k ≥ b/4. This bound is smaller than 4−k as soon as b ≥ 32.

title: Miller–Rabin primality test


text:
Fire department

A fire department (North American English) or fire brigade (Commonwealth English), also known as a fire company, fire authority, fire district, fire and rescue, or fire service in some areas, is an organization that provides fire prevention and fire suppression services as well as other rescue services.

Fire departments are most commonly a public sector organization that operate within a municipality, county, state, nation, or special district. Private and specialist firefighting organizations also exist, such as those for aircraft rescue and firefighting.

A fire department contains one or more fire stations within its boundaries, and may be staffed by firefighters, who may be professional, volunteers, conscripts, or on-call. Combination fire departments employ a mix of professional and volunteer firefighters. In some countries, fire departments may also run an ambulance service, staffed by volunteer or professional EMS personnel.

Organization
Fire departments are organized in a system of administration, services, training, and operations; for example:

A fire service is normally set up where it can have fire stations, fire engines and other relevant equipment strategically deployed throughout the area it serves, so that dispatchers can send fire engines, fire trucks, or ambulances from the fire stations closest to the incident. Larger departments have branches within themselves to increase efficiency, composed of volunteers, support, and research.
 * Administration is responsible for supervision, budgets, policy, and human resources.
 * Service offers protection, safety, and education to the public.
 * Training prepares people with the knowledge and skills to perform their duties.
 * Operations performs tasks to mitigate harm to persons, property, and the environment.

 * Volunteers give additional support to the department in a state of emergency.
 * Support organizing the resources within and outside of the department.
 * Research is to give advantages in new technologies for the department.

Jurisdiction
Most places are covered by a public sector fire department, which is established by a local or national government and funded by taxation. Even volunteer fire departments may still receive some government funding.

The typical size of a fire department varies greatly by country. In the United States, firefighting is usually organized on a municipal level. Some municipalities belong to "fire protection districts" that are served by the same fire department, such as the San Ramon Valley Fire Protection District. Austria, Germany and Canada also organize fire services at a municipal level. In France, fire services mostly cover one department. In the United Kingdom, most fire services cover one or more counties, while Scotland and Northern Ireland each have a single fire service. In Australia, state governments run the fire services, although three states have separate agencies for metropolitan and rural areas. Poland, the Czech Republic, Israel, Italy, New Zealand, and the Philippines have national fire and rescue services.

Responsibilities
Fire departments may also provide other emergency services, such as aircraft rescue and firefighting, hazardous materials mitigation, technical rescue, and wildland firefighting.

In some countries or regions (e.g., the United States, Germany, Japan, Hong Kong, Macau), fire departments can be responsible for providing emergency medical services. The EMS personnel may either be cross-trained as firefighters or a separate division of emergency medical technicians and paramedics. While some services act only as "first responders" to medical emergencies, stabilizing victims until an ambulance can arrive, other fire services also operate ambulance services.

Ancient Rome
The earliest known firefighting service was formed in Ancient Rome by Marcus Egnatius Rufus who used his slaves to provide a free fire service. These men fought fires using bucket chains and also patrolled the streets with the authority to impose corporal punishment upon those who violated fire-prevention codes. The Emperor Augustus established a public fire department in 24 BCE, composed of 600 slaves distributed amongst seven fire stations in Rome.

1600s and 1700s
Fire departments were again formed by property insurance companies beginning in the 17th century after the Great Fire of London in 1666. The first insurance brigades were established the following year. Others began to realize that a lot of money could be made from this practice, and ten more insurance companies set up in London before 1832: The Alliance, Atlas, Globe, Imperial, London, Protector, Royal Exchange, Sun Union and Westminster. Each company had its own fire mark, a durable plaque that would be affixed to the building exterior. Although a popular legend says a company's fire brigade would not extinguish a burning building if it did not have the correct fire mark, there is little evidence to support this; evidence shows insurance companies required their firefighters to fight every fire they encountered.

Amsterdam also had a sophisticated firefighting system in the late 17th century, under the direction of artist Jan van der Heyden, who had improved the designs of both fire hoses and fire pumps.

The city of Boston, Massachusetts established America's first publicly funded, paid fire department in 1678.

Fire insurance made its debut in the American colonies in South Carolina in 1736, but it was Benjamin Franklin who imported the London model of insurance. He established the colonies' first fire insurance company in Philadelphia named the Philadelphia Contributionship, as well as its associated Union Volunteer Fire Company, which was an unpaid (volunteer) company.

A document dated in 1686 informs about the payment system of four so called "fire servants" (German: Feuerknecht) in Vienna, which is the official founding year of the Vienna Fire Department.

In 1754, Halifax, Nova Scotia established the Halifax Regional Fire and Emergency, which is today Canada's oldest fire department. In 1764, Haddonfield, New Jersey established the second oldest fire company in the United States.

Another early American fire department, staffed by unpaid volunteers, was established in the city of Petersburg, Virginia in 1773.

1800s
In the 19th century, cities began to form their own fire departments as a civil service to the public, obliging private fire companies to shut down, many merging their fire stations into the city's fire department. In 1833, London's ten independent brigades all merged to form the London Fire Engine Establishment (LFEE), with James Braidwood as the Chief Officer. Braidwood had previously been the fire chief in Edinburgh, where the world's first municipal fire service was founded in 1824, and he is now regarded, along with Van der Heyden, as one of founders of modern firefighting. The LFEE then was incorporated into the city's Metropolitan Fire Brigade in 1865 under Eyre Massey Shaw.

In 1879, the University of Notre Dame established the first University-based fire department in the United States.

1900s
The first motorized fire department was organized in 1906 in Springfield, Massachusetts, where Knox Automobile had developed the first modern fire engine one year earlier.

title: Fire department


text:
Hotel California (album)

Hotel California is the fifth studio album by American rock band the Eagles, released on December 8, 1976, by Asylum Records. Recorded by the band and produced by Bill Szymczyk at the Criteria and Record Plant studios between March and October 1976, it was the band's first album with guitarist Joe Walsh, who had replaced founding member Bernie Leadon, and the last to feature founding bassist Randy Meisner. The album cover features a photograph of the Beverly Hills Hotel, taken by David Alexander.

Hotel California was an immediate critical and commercial success, topping the US Billboard Top LPs & Tapes chart. At the 20th Grammy Awards, the title track won Record of the Year, and "New Kid in Town" won Best Arrangement for Voices. The album was also nominated for Album of the Year but lost to Fleetwood Mac's Rumours (1977). Three singles were released from the album, with the title track and "New Kid in Town" topping the Billboard Hot 100 and "Life in the Fast Lane" reaching No. 11.

Hotel California is one of the best-selling albums of all time. It has been certified 26× Platinum by the Recording Industry Association of America (RIAA) in the US, and has sold over 32 million units worldwide, making it the band's second best-selling album after Their Greatest Hits (1971–1975) (1976). Ranked by various publications as one of the greatest albums of all time, it was placed at number 37 on Rolling Stone list of the "500 Greatest Albums of All Time" in 2003 and 2012, re-positioned to number 118 in the 2020 edition. A 40th anniversary special edition of Hotel California was released in November 2017. The band played the album in its entirety during the Hotel California 2020 Tour.

Theme
The first song written for the album was "Hotel California", which became the theme for the album. Don Henley said of the themes of the songs in the album: They're the same themes that run through all of our work: loss of innocence, the cost of naiveté, the perils of fame, of excess; exploration of the dark underbelly of the American dream, idealism realized and idealism thwarted, illusion versus reality, the difficulties of balancing loving relationships and work, trying to square the conflicting relationship between business and art; the corruption in politics, the fading away of the Sixties dream of "peace, love and understanding." On the title "Hotel California", Henley said that "the word, 'California,' carries with it all kinds of connotations, powerful imagery, mystique, etc., that fires the imaginations of people in all corners of the globe. There's a built-in mythology that comes with that word, an American cultural mythology that has been created by both the film and the music industry." In an interview with the Dutch magazine ZigZag shortly before the album's release, Henley said: This is a concept album, there's no way to hide it, but it's not set in the old West, the cowboy thing, you know. It's more urban this time (…) It's our bicentennial year, you know, the country is 200 years old, so we figured since we are the Eagles and the Eagle is our national symbol, that we were obliged to make some kind of a little bicentennial statement using California as a microcosm of the whole United States, or the whole world, if you will, and to try to wake people up and say 'We've been okay so far, for 200 years, but we're gonna have to change if we're gonna continue to be around.'"

Composition
Bernie Leadon, who was the principal country influence in the band, left the band after the release of the previous album One of These Nights. For Hotel California, the band made a conscious decision to move away from country rock, and wrote some songs that are more rock & roll, such as "Victim of Love" and "Life in the Fast Lane". Leadon was replaced by Joe Walsh who provided the opening guitar riff of "Life in the Fast Lane" that was then developed into the song. The title for "Life in the Fast Lane" was inspired by a conversation between Frey and his drug dealer during a high speed car ride.

The chord progression and basic melody of the title track, "Hotel California", was written by Don Felder. Don Henley wrote most of the lyrics, with contributions from Glenn Frey. Henley noted that the hotel had become a "literal and symbolic focal point of their lives at that time", and it became the theme of the song. Frey wanted the song to be "more cinematic", and to write it "just like it was a movie". Henley sought inspiration for the lyrics by driving out into the desert, as well as from films and theatre. Parts of the lyrics of "Hotel California" as well as the song "Wasted Time" were based on Henley's break up with his then girlfriend Loree Rodkin.

Frey, in the "Hotel California" episode of In the Studio with Redbeard, spoke about the writing of "The Last Resort". Frey said: "It was the first time that Don took it upon himself to write an epic story and we were already starting to worry about the environment… we're constantly screwing up paradise and that was the point of the song and that at some point there is going to be no more new frontiers. I mean we're putting junk, er, garbage into space now."

Recording
The album was recorded between March and October 1976 at Criteria Studios in Miami and Record Plant Studios in Los Angeles, and produced by Bill Szymczyk. Although the band favored Los Angeles, the producer Szymczyk wanted to record in Miami as he had developed a fear of living on a fault line in Los Angeles after experiencing an earthquake, and a compromise was then struck to split the recording between both places. While the band were recording the album, Black Sabbath were recording Technical Ecstasy in an adjacent studio at Criteria Studios. The band was forced to stop recording on numerous occasions because Black Sabbath were too loud and the sound was coming through the wall. The last track of the album, "The Last Resort", had to be re-recorded a number of times due to noise from the next studio.

For the title track "Hotel California", after the arrangement and instrumentation had been refined, several complete takes were recorded. The best parts were then spliced together, in all 33 edits on the two‑inch master, to create the final version. In contrast, "Victim of Love" was recorded in a live session in studio apart from the lead vocal and the harmony on the choruses which were added later. Don Felder initially sang the lead vocals in the many early takes for the song, but the band felt that his efforts were not up to the required standard, and Henley then took over as the lead. Producer Szymczyk claims that the basic tracks for the entire album were recorded in complete takes, but he does not describe how individual songs were recorded (other than the aforementioned "Hotel California" and "Victim of Love").

According to Henley in a 1982 interview, the Eagles "probably peaked on Hotel California." Henley said: "After that, we started growing apart as collaborators and as friends."

Artwork
The front cover artwork is a photograph of The Beverly Hills Hotel shot just before sunset by David Alexander with design and art direction by Kosh. According to Kosh, Henley wanted him to find a place that can portray the Hotel California of the album title, and "portray it with a slightly sinister edge". Three hotels were photographed, and the one with The Beverly Hills Hotel was selected as the cover. Both The photographer and Kosh shot the image 60 feet above Sunset Boulevard on top of a cherry picker. As the image was taken from an unfamiliar vantage point in fading light, most people did not initially recognize the hotel. However, when the identity of Beverly Hills Hotel was revealed, the hotel threatened legal action over the use of the image.

The rear album cover was shot in the lobby of the Lido Hotel in Hollywood. The gatefold image shows the same lobby but filled with members of the band and their friends. Henley said: "I wanted a collection of people from all walks of life, It’s people on the edge, on the fringes of society." A shadowy figure appears on the balcony above the lobby, which led to speculations over the person's identity.

Kosh designed a Hotel California logo as a neon sign which was used on the album cover and in its promotional materials. As it proved difficult to bend real neon tubings into the desired shape of the script, the neon effect of the logo was achieved with airbrush by Bob Hickson. Additional portraits of the band used in the album package and promotional materials were shot by Norman Seeff.

Release
The album was released by Asylum Records on December 8, 1976, in vinyl, cassette and 8-track cartridge formats. It was considered for quadraphonic release in early 1977, but this idea was dropped following the demise of the quadraphonic format. On the album's 25th anniversary in 2001, it was released in a Multichannel 5.1 DVD-Audio disc. On August 17, 2011, the album was released on a hybrid SACD in Japan in The Warner Premium Sound series, containing both a stereo and a 5.1 mix.

Original vinyl pressings of Hotel California (Elektra/Asylum catalog no. 7E-1084) had custom picture labels of a blue Hotel California logo with a yellow background. These also had text engraved in the run-out groove of each side, continuing an in-joke trend the band had started with their third album On the Border. The text reads: Side one: "Is It 6 O'Clock Yet?"; Side two: "V.O.L. Is Five-Piece Live", indicating that the song "Victim of Love" was recorded in a live session in studio, with no overdubbing. Joe Walsh and Glenn Frey confirm this on the inner booklet of The Very Best Of. This only referred to the instrumental track, however; the lead vocal and harmony for the chorus were added later. This was in response to those who criticized the Eagles' practice of copious overdubbing of instruments and that they were too clinical and soulless in the studio. They wanted to demonstrate that they could play together without overdubs if they wanted to.

A 40th anniversary deluxe edition was released on November 24, 2017. The set includes the original remastered album, and a second CD that features 10 live tracks from the concert at The Forum, recorded in October 1976 two months before the original release of the album. This bonus CD was also issued as a stand-alone vinyl LP in 2021.

Critical reception
Hotel California was met with generally positive reviews. Village Voice critic Robert Christgau felt it was their "most substantial if not their most enjoyable LP", while Charley Walters of Rolling Stone felt it showcased "both the best and worst tendencies of Los Angeles-situated rock". Both critics picked up on the album's California themes – Christgau remarking that while it may in places be "pretentious and condescending" and that "Don Henley is incapable of conveying a mental state as complex as self-criticism", the band couldn't have written the songs on side one "without caring about their California theme down deep"; Walters in contrast felt the "lyrics present a convincing and unflattering portrait of the milieu itself", and that Don Henley's vocals express well "the weary disgust of a victim (or observer) of the region's luxurious excess". Billboard gave the album high praise: "The casually beautiful, quietly-intense multileveled vocal harmonies and brilliant original songs that meld solid emotional words with lovely melody lines are all back in force, keeping the Eagles at the acme of acoustic electric soft rock." It noted that, even though the album did not try out any new departure other than the "Procol Harum-type" title track, "the album proves that there's a lot more left to explore profitably and artistically in the L.A. countryish-rock style."

Retrospective reviews have also been positive. Robert Hilburn of the Los Angeles Times, writing after the band broke up, called the album "a legitimate rock masterpiece", in which the band "examined their recurring theme about the American Dream with more precision, power and daring than ever in such stark, uncompromising songs as "Hotel California" and "The Last Resort"." William Ruhlmann from AllMusic later said "Hotel California unveiled what seemed almost like a whole new band. It was a band that could be bombastic, but also one that made music worthy of the later tag of 'classic rock', music appropriate for the arenas and stadiums the band was playing." Steve Holtje, writing for CultureCatch in 2012, felt that even though "an awful lot of the album is snarky whining from co-leaders Don Henley and Glenn Frey, two guys who didn't really seem like they had that much they could legitimately complain about", in the final analysis "Hotel California and the underrated concept album Desperado stand as the group's greatest statements".

Ultimate Classic Rock critic Sterling Whitaker rated both "Wasted Time" and "The Last Resort" as being among the Eagles' 10 most underrated songs.

Accolades
Hotel California was the Eagles' sixth album (including Their Greatest Hits (1971–1975)), and fifth of original material. It became a critical and commercial success. In a poll of rock critics and DJs in 1987, it was ranked 48 out of 100. In a public poll for the 1994 edition of All Time Top 1000 Albums, it was voted number 107, and then number 67 in the 2000 edition. In 2001, the TV network VH1 placed Hotel California at number 38 on their 100 Greatest Albums of All Time list. Hotel California was ranked 13th in a 2005 survey held by British television's Channel 4 to determine the 100 greatest albums of all time. In 2003, the album was ranked number 37 on Rolling Stone magazine's list of the 500 greatest albums of all time, maintaining the rating in a 2012 revised list, dropping to number 118 in the 2020 reboot of the list. The album also was placed at the 99th spot on Apple Music's 100 Best Albums list in 2024.

The song "Hotel California" was ranked number 49 on Rolling Stone list of "The 500 Greatest Songs of All Time" in 2004. It maintained the ranking in 2010, and was re-ranked at number 311 in 2021.

Awards and nominations
The album and its tracks were nominated for five Grammy awards in 1978, winning two; Record of the Year for the title track and Best Arrangement for Voices for "New Kid in Town". However, the band's manager Irving Azoff refused requests by the ceremony's producer for the band to attend or perform at the ceremony unless a win was guaranteed. The band therefore did not appear at the ceremony to collect their awards. Henley later said: "The whole idea of a contest to see who is 'best' just doesn't appeal to us."

Commercial performance
The album first entered the US Billboard 200 at number four, reaching number one in its fourth week in January 1977. It topped the chart for eight weeks (non-consecutively), and it was certified platinum by the Recording Industry Association of America (RIAA) in a week of release. In its first year of release it sold nearly 6 million copies in the United States, and by July 1978 it has sold 9.5 million copies worldwide (7 million in the US and 2.5 million elsewhere internationally). On March 20, 2001, the album was certified 16× platinum by the Recording Industry Association of America, denoting shipment of 16 million in the United States, and had sold over 17 million copies in the US by 2013. Worldwide the album has sold 32 million copies. On August 20, 2018, the album was certified 26× platinum by the RIAA for 26 million units consumed in the United States under the new system that tallies album and digital track sales as well as streams.

The album produced two number one hit singles on the US Billboard Hot 100: "New Kid in Town", on February 26, 1977, and "Hotel California" on May 7, 1977.

Personnel
Adapted from AllMusic and album liner notes.

Eagles
 * Glenn Frey – harmony and backing vocals, guitars, keyboards, piano, clavinet, synthesizer, lead vocals on “New Kid In Town”
 * Don Henley – lead vocals, harmony and backing vocals, drums, percussion, synthesizer on “The Last Resort”
 * Randy Meisner – harmony and backing vocals, bass, lead vocals on “Try and Love Again,” guitarrón on “New Kid in Town”
 * Don Felder – backing vocals, guitars, pedal steel guitar on “The Last Resort”
 * Joe Walsh – harmony and backing vocals, guitars, slide guitar, keyboards, piano, organ, synthesizer, lead vocals on “Pretty Maids All in a Row”

Production
 * Bill Szymczyk – producer, engineer, mixing
 * Allan Blazek, Bruce Hensal, Ed Mashal– engineers
 * Jim Ed Norman – string arrangements, conductor
 * Sid Sharp – concert master
 * Don Henley, John Kosh – art direction
 * John Kosh – design
 * David Alexander – photography
 * Kosh – artwork
 * Norman Seeff – poster design
 * Ted Jensen – mastering and remastering
 * Lee Hulko – original LP mastering

Allegedly stolen lyric sheets
In July 2022, three men, all involved in rare book and memorabilia dealing, were indicted by a Manhattan, New York City, grand jury on felony charges of conspiracy and possession of stolen property; one was further charged with hindering prosecution. Prosecutors alleged that they had forged provenance documents attempting to demonstrate that they were the lawful owners of some of Frey and Henley's original drafts of lyrics for songs on the album, including "Hotel California" and "Life in the Fast Lane" and "New Kid in Town", when they in fact knew those materials, around a hundred handwritten pages on yellow notebook paper estimated to be worth $1 million in total, to have been stolen. Their plot had come to light after, having sold Henley some of the documents for $8,500 in 2012, they returned to Henley offering to sell him some more after listing them at Sotheby's four years later; he then filed a complaint with the New York County district attorney's office. All three protested their innocence through their attorneys.

The three were alleged to have acquired the documents from Ed Sanders, a journalist who had been hired to write a biography of the band around the time of Hotel California. Sanders did not finish the work until after the band had broken up and the project was eventually canceled. He is not charged or named in the indictment, but in a news release announcing it, the D.A.'s office described the papers as "originally stolen in the late 1970s by an author who had been hired to write a biography of the band." The indictment also quotes an "Individual 1" as telling one of the indicted men in an email that he "was staying at Henley's place in Malibu and had total access to his boxes of stuff, and there was a lot, and I compiled a box of files I wanted and his assistant mailed them to me." The Los Angeles Times found also that an archived version of the 2016 Sotheby's listing online identified Sanders as the then-owner.

title: Hotel California (album)


text:
Liberalization

Liberalization or liberalisation (British English) is a broad term that refers to the practice of making laws, systems, or opinions less severe, usually in the sense of eliminating certain government regulations or restrictions. The term is used most often in relation to economics, where it refers to economic liberalization, the removal or reduction of restrictions placed upon (a particular sphere of) economic activity. However, liberalization can also be used as a synonym for decriminalization or legalization (the act of making something legal after it used to be illegal), for example when describing drug liberalization.

In economy and trade
Economic liberalization refers to the reduction or elimination of government regulations or restrictions on private business and trade. It is usually promoted by advocates of free markets and free trade, whose ideology is also called economic liberalism. Economic liberalization also often involves reductions of taxes, social security, and unemployment benefits.

Economic liberalization is often associated with privatization, which is the process of transferring ownership or outsourcing of a business, enterprise, agency, public service or public property from the public sector to the private sector. For example, the European Union has liberalized gas and electricity markets, instituting a competitive system. Some leading European energy companies such as France's EDF and Sweden's Vattenfall remain partially or completely in government ownership. Liberalized and privatized public services may be dominated by big companies, particularly in sectors with high capital, water, gas, or electricity costs. In some cases they may remain legal monopolies, at least for some segments of the market like consumers. Liberalization, privatization and stabilization are the Washington Consensus's trinity strategy for economies in transition.

The Bretton Woods Conference of 1944, which recommended the establishment of International Monetary Fund (IMF) and the World Bank, had also recommended the establishment of an International Trade Organization (ITO). Although, the IMF and the World Bank were established in 1946, the proposal for ITO did not materialize. Instead, the General Agreement on Tariff and Trade (GATT), a less ambitious institution, was formed in 1948. The primary objective of GATT is to expand international trade by liberalizing trade so as to bring about all round economic prosperity. GATT was signed in 1947, came into effect in 1948 and lasted until 1994. It was replaced by the World Trade Organization in 1995. The original GATT text (GATT 1947) is still in effect under the WTO framework. Thus liberalization was born.

There is also a concept of hybrid liberalization. For instance, in Ghana, cocoa crops can be sold to competing private companies, but there is a minimum price for which it can be sold and all exports are controlled by the state. The term liberalization has its origin in the political ideology liberalism, which took form by the early 19th century.

In social policy and government
In social policy, liberalization may refer to a relaxation of laws restricting certain practices or activities, such as divorce, abortion, or psychoactive drugs. Regarding civil rights, it may refer to the elimination of laws prohibiting homosexuality, private ownership of firearms or other items, same-sex marriage, inter-racial marriage, or inter-faith marriage.

There is a distinct difference between liberalization and democratization. Liberalization can take place without democratization, and deals with a combination of policy and social change specialized to a certain issue, such as the liberalization of government-held property for private purchase. Democratization is politically highly specialized; it can arise from a liberalization but works on a broader level of governmental liberalization.

title: Liberalization


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Puja (Hinduism)

Puja (पूजा), also spelt pooja, is a worship ritual performed by Hindus to offer devotional homage and prayer to one or more deities, to host and honour a guest, or to spiritually celebrate an event. It may honour or celebrate the presence of special guests, or their memories after they die. The word puja is roughly translated into English as 'reverence, honour, homage, adoration, or worship'. Puja, the loving offering of light, flowers, and water or food to the divine, is the essential ritual of Hinduism. For the worshipper, the divine is visible in the image, and the divinity sees the worshipper. The interaction between human and deity, between human and guru, is called a Darshanam.

In Hindu practice, puja is done on a variety of occasions, frequencies, and settings. It may include a daily puja done in the home, or occasional temple ceremonies and annual festivals. In other cases, puja is held to mark a few lifetime events such as the birth of a baby, house entering ceremony or grihapravesh, first rice-eating ceremony or annaprasana, wedding, sacred thread ceremony or upanayana ceremony for the Brahmins or to begin a new venture. The two main areas where puja is performed are in the home and at temples to mark certain stages of life, events or some festivals such as Durga Puja, Kali Puja, Janmashtami, and Lakshmi Puja. Puja is not mandatory in Hinduism. It may be a routine daily affair for some Hindus, a periodic ritual for some, and rare for other Hindus. In some temples, various pujas may be performed daily at various times of the day; in other temples, they may be occasional.

All significant Indian holidays, including Rakhi, Diwali, Holi, Karva Chauth, Ganesh Chaturthi, Janmashtami, and Navaratri, have rituals known as puja.

For example, a chirathu also known as a diya, clarified butter wicks, bells, flowers, incense sticks, cones, roli or kumkum (a red powder with turmeric mixed in applied to the forehead), rice, tilakam, chandanam (sandal sticks), idols, and samagri havanam are some common items utilized in puja. In Hinduism, puja is a sattvik work.

Puja varies according to the sect, region, occasion, deity honored, and steps followed. In formal Nigama ceremonies, a fire may be lit in honor of the god Agni, without an idol or image present. In contrast, in Agama ceremonies, an idol or icon or image of a deity is present. In both ceremonies, a lamp (Diya) or incense stick may be lit while a prayer is chanted or a hymn is sung. Puja is typically performed by a Hindu worshiper alone, though sometimes in the presence of a priest who is well-versed in complex rituals and hymns. In temples and priest-assisted events puja, food, fruits, and sweets may be included as sacrificial offerings to the ceremony or deity, which, after the prayers, becomes prasadam – food shared by all gathered.

Both Nigama and Agama puja are practised in Hinduism in India. In the Hinduism of Bali, Indonesia, Agama puja is most prevalent inside homes and in temples. Puja is sometimes called Sembahyang in Indonesia.

Etymology
Puja has unclear origins. J. A. B. van Buitenen states that "puja" emerged from yajna rituals, linking it to the Pravargya Vedic rite. The Rigveda in hymn 8.17 uses the word "Sachipujanayam" (शाचिपूजनायं) in the twelfth verse, where it is an epithet for god Indra in a context of vocative singular "praise". The ancient scholar and Vedic text commentator Sāyana explains the term as a form of "praise, worship, invocation". The Grhyasutras use puj in the context of rites, as does Sanskrit scholar Pāṇini. However, none of these texts imply puja as a form of devotional prayer worship.

According to Natalia Lidova, puja is unlikely to be of Indo-Aryan and Vedic origin because it lacks a Sanskrit root and it also lacks cognate parallels in other Indo-European languages. Its root are probably Dravidian in origin, but the evidence for this alternative hypothesis is also largely missing possibly because devotional worship is not as ancient as Hinduism. Collins states that the roots may be "pu" (flower) and "ge" (make), or a form of "making flower sacrifice". However, this proposal is problematic because "pu" comes from an Indo-European root, while "ge" from Dravidian. Charpentier suggests the origin of the word puja may lie in the Dravidian languages. Two possible Malayalam roots may be 'to smear with something' or  "to do with flowers" (from  'flower' and  'to do'). Tamil roots have also been suggested: 'to smear with something' or  "to do with flowers" (from  'flower' and  'to do'). or similar Telugu roots (from  'flower' and  'to do').

According to the Shiva Purana, puja is derived from cognate of two Sanskrit words puh and jayate, puh meaning 'achievement of fruits of enjoyment' while jayate refers to 'something to be born'. Hence puja refers to the rite by which one attains fruits of enjoyment of things like good ideas and knowledge.

Origins
According to scholars, one of the earliest mentions of pūjā is in the Grihya Sutras, which provide rules for domestic rites. These sutras, dated to be about 500 BC, use the term puja to describe the hospitality to honour priests who were invited to one's home to lead rituals for departed ancestors. As with vedic times, the general concept of puja remained the same, but expanded to welcoming the deity along with the deity's spiritual essence as one's honored guest. The Puranic corpus of literature, dating from about 6th century CE, contain extensive outline on how to perform deity puja (deva pūjā). Deity puja thus melds Vedic rites with devotion to deity in its ritual form. As with many others aspects of Hinduism, both Vedic puja and devotional deity puja continued, the choice left to the Hindu.

As a historical practice, pūjā in Hinduism, has been modelled on the idea of hosting a deity, or important person, as an honoured and dearest guest in the best way one can, given one's resources, and receiving their happiness and blessing in return. Paul Thieme suggests from passages in the Rāmāyaṇa that the word pūjā referred to the hospitable reception of guests and that the things offered to guests could be offered to the gods and their dwellings. The rituals in question were the "five great sacrifices" or pañcamahāyajña recorded in the Gṛhyasūtra texts (for this literature, see Kalpa). The development of pūjā thus emerged from Vedic domestic traditions and was carried into the temple environment by analogy: just as important guests had long been welcomed in well-to-do homes and offered things that pleased them, so too were the gods welcomed in temple-homes and offered things that pleased them. Copper-plate charters recording grants of lands to temples show that this religious practice was actively encouraged from the mid-4th century.

Significance
In the earliest texts describing Vedic puja, the significance of puja was to host the priest so that he could make direct requests to the gods. An example petition prayer made during a Vedic puja, according to Wade Wheelock, is:

Indra-Agni, slayers of Vrtra with the beautiful thunderbolt, prosper us with new gifts; O Indra, bring treasures with your right hand; O Agni grant the enjoyments of a good household; Give [us] vigour, wealth in cattle, and possession of good horses. – ÄsvSü

The purpose of the requests are to burn the past karmas to be able to experience oneness with the Brahman through the help of the deity. It is a form of bhakti Yoga whose final result aims to be the consciousness of god through homage to god. Nevertheless, even with this evolved theoretical spiritual significance, many people use puja as vehicle to petition desires and appeals, such as for good health of one's child, speedy recovery from illness, success in venture envisioned or such. In the structure and practice of puja, the mantras and rituals focus on spirituality, and any petitions and appeals are tacked only to the end of the puja.

Zimmer relates puja to yantras, with the rituals helping the devotee focus on the spiritual concepts. Puja in Hinduism, writes Zimmer, is a path and process of transformation of consciousness, where the devotee and the spiritual significance of the deity are brought together. This ritual puja process, in different parts of India, is considered to be liberating, releasing, purifying and a form of Yoga of spirit and emotions.

Puja in Hinduism sometimes involves themes beyond idols or images. Even persons, places, rivers, concrete objects or anything is seen as manifestations of divine reality by some Hindus. The access to the divine is not limited to renunciatory meditation as in yoga school of Hinduism or idols in bhakti school. For some the divine is everywhere, without limit to its form, and a puja to these manifestations signifies the same spiritual meaning to those who choose to offer a prayer to persons, places, rivers, concrete objects or anything else.

Durga Puja
Durga Puja, also known as Durgotsava or Sharodotsav, is an annual festival celebrated in the Indian subcontinent, particularly in Bengal, Assam, and other eastern Indian states as well as in Bangladesh. It honors the Hindu goddess Durga and celebrates her victory over the demon Mahishasura. The festival spans ten days, with the last five being the most significant. During this time, elaborate rituals are performed both in homes and public spaces, including the construction of temporary structures called pandals. Durga Puja features scripture recitations, performances, feasting, gift-giving, and public processions known as melā. It holds great significance in the Shaktism tradition of Hinduism and coincides with Navaratri and Dussehra celebrations observed by other Hindu traditions. The festival celebrates not only the triumph of good over evil but also serves as a harvest festival, honoring Durga as the motherly power behind life and creation. Durga Puja involves the worship of various deities, including Lakshmi, Saraswati, Ganesha, and Kartikeya, alongside Durga. It culminates with the immersion of clay sculptures of the goddess into rivers or water bodies, symbolizing her return to the divine cosmos.

Guru puja
In the case of great spiritual masters, there is also a custom to perform puja for a living person especially at Guru Purnima. Gurus are sometimes chosen as objects of puja and honoured as living gods or seen as the embodiment of specific deities. Gurus are sometimes adorned with symbolic clothes, garlands and other ornaments, and celebrated with incense, washing and anointing their feet, giving them fruits, food and drink and meditating at their feet, asking for their blessing.

Govardhan Puja
Govardhan Puja, also known as Annakut or Annakoot, is a Hindu festival celebrated on the first lunar day of the bright fortnight of the month of Kartika, typically falling on the fourth day of Diwali. During this festival, devotees honor Govardhan Hill and express gratitude to Lord Krishna by preparing and offering a diverse array of vegetarian foods.

For followers of Vaishnavism, Govardhan Puja commemorates the event described in the Bhagavata Purana where Lord Krishna lifted Govardhan Hill to shield the villagers of Vrindavan from heavy rainfall. This act symbolizes divine protection for devotees who wholly rely on God for refuge. To mark this occasion, devotees present a symbolic "mountain of food" representing Govardhan Hill as an offering to God, reaffirming their faith and devotion.

Govardhan Puja is widely observed by various Hindu denominations across India and beyond.

Temple pūjā
Temple (Mandir) pūjā is more elaborate than the domestic versions and typically done several times a day. They are also performed by a temple priest, or pujari. In addition, the temple deity (patron god or goddess) is considered a resident rather than a guest, so the puja is modified to reflect that; for example the deity is "awakened" rather than "invoked" in the morning. Temple pujas vary widely from region to region and for different sects, with devotional hymns sung at Vaishnava temples for example. At a temple puja, there is often less active participation, with the priest acting on behalf of others.

Puja Elements

A full home or temple puja can include several traditional upacaras or "attendances". The following is an example puja; these steps may vary according to region, tradition, setting, or time particularly in ways the deity is hosted. In this example, the deity is invited as a guest, the devotee hosts and takes care of the deity as an honored guest, hymns and food are offered to the deity, after an expression of love and respect the host takes leave and with affection expresses good bye to the deity. Indologist Jan Gonda has identified 16 steps (shodasha upachara) that are common in all varieties of puja:

 * 1) Avahana (“invocation”). The deity is invited to the ceremony from the heart.
 * 2) Asana. The deity is offered a seat.
 * 3) Padya. The deity's feet are symbolically washed.
 * 4) Water is offered for washing the head and body
 * 5) Arghya. Water is offered so the deity may wash its mouth.
 * 6) Snana or abhisekha. Water is offered for symbolic bathing.
 * 7) Vastra (“clothing”). Here a cloth may be wrapped around the image and ornaments affixed to it.
 * 8) Upaveeda or Mangalsutra. Putting on the sacred thread.
 * 9) Anulepana or gandha. Perfumes and ointments are applied to the image. Sandalwood paste or kumkum is applied.
 * 10) Pushpa. Flowers are offered before the image, or garlands draped around its neck.
 * 11) Dhupa. Incense is burned before the image.
 * 12) Aarathi. A burning lamp is waved in front of the image.
 * 13) Naivedya. Foods such as cooked rice, fruit, clarified butter, sugar, and betel leaf are offered.
 * 14) Namaskara or pranama. The worshipper and family bow or prostrate themselves before the image to offer homage.
 * 15) Parikrama or Pradakshina. Circumambulation around the deity.
 * 16) Taking leave.

Sometimes additional steps are included:
 * 1) Dhyana (“Meditation”). The deity is invoked in the heart of the devotee.
 * 2) Acamanıya. Water is offered for sipping.
 * 3) Aabaran. The deity is decorated with ornaments.
 * 4) Chatram. Offering of umbrella.
 * 5) Chamaram Offering of fan or fly-whisk (Chamara).
 * 6) Visarjana or Udvasana. The deity is moved from the place.

There are variations in this puja method such as:
 * 1) Pancha upachara puja (puja with five steps).
 * 2) Chatushasti upachara puja (puja with 64 steps).

The structure of elaborate puja also varies significantly between temples, regions, and occasions.

Archana puja is a brief intercessionary puja on behalf of an individual that can be undertaken after the main puja.

Quick pūjā
A quick puja has the same structure as acts people would ordinarily perform for a quick reception, hospitality and affectionate interaction with a beloved guest. First the deity is greeted, acknowledged by name and welcomed, sometimes with a diya or lighted incense stick. The devotee proceeds to connect with the spiritual manifestation by meditating (a form of darshan), or chanting hymns and mantras, then personal prayers follow. After the prayer is finished, the spiritual visitor as the guest is affectionately thanked and greeted goodbye. A quick meditative puja is sometimes offered by some Hindus without an idol or image. According to Chris Fuller, an anthropologist, Hindu texts allow flexibility and abbreviated puja according to the occasion, needs, and personal preferences.

In Balinese Hinduism
In Hinduism of Bali Indonesia, puja is sometimes called Sembahyang. The word originates from two words in old Javanese: sembah and hyang. Sembah means to respect and bow down; Hyang means divine, God or Sang Hyang Widhi Wasa, holy man, and ancestors. So to pray means to respect, bow down, surrender to the divine and ancestors.

Sembahyang (puja) is an obligation for Balinese Hindus, the prayers and hymns are derived from the Vedas. A family typically offers prayers every day, with Kewangen and other offerings. Kewangen means aromatic, and it is made from leaves and flowers in form of auspicious Vedic symbols. Balinese use kewangen to worship the divine, both in form of Purusha (soul) and Pradana (body). As with India, Balinese make offerings, including symbolic inclusion of fire, incense and mantras.

As a social and human rights event
Pūjā in Hinduism has served as a means for Hindu communities outside India to gather, socialize, discover new friends and sometimes discuss ways to address social discrimination of Hindus. For example, Marion O'Callaghan reports that the Hindu diaspora brought as indentured laborers to Trinidad by the British colonial government, suffered discriminatory laws that did not recognize traditional Hindu marriages or inheritance rights of children from a traditional Hindu marriage, nor did the non-Hindu majority government allow pyre cremation or construction of crematorium. These Hindu rituals were considered pagan and uncivilized. Pujas offered a way for Hindus to meet, socially organize and petition their human rights. Over time, pujas became as much a social and community recreational event as a religious event.

Critique of pūjā in the Pūrva Mīmāṃsaka school
Although pujā is accepted as a valid religious activity by Hindus at large, it has long been criticised by Mīmāṃsā thinkers. The foundational work of this school was the Karmamīmāṃsāsūtra or "Aphorisms for Enquiry into the Act," composed by Jaimini. The earliest surviving commentary was by Śabara who lived around the end of the fourth century. Śabara's commentary, known as Śabarabhāṣya held pride of place in Mīmāṃsā in that Sabara's understanding was taken as definitive by all later writers.

In his chapter entitled Devatādikaraṇa (9: 1: 5: 6–9), Śabara examined the popular understanding of the gods and attempted to refute the belief that they have material bodies, are able to eat the offerings made to them, and are capable of being pleased and so able to reward worshippers. Basing himself on the Vedas (he refused to accept the Mahābhārata, Purāṇa texts or even the Smṛti literatures as valid sources of authority), Śabara concluded that the gods are neither corporeal nor sentient and thus unable to enjoy offerings or own property. For this he appealed to empirical observation, noting that offerings do not decrease in size when given to the gods; any decrease is simply due to exposure to the air. Likewise he argued that substances are offered to gods not according to the wishes of the gods, but that "what is vouched for by direct perception is that the things are used according to the wishes of the temple servants (pratyakṣāt pramāṇāt devatāparicārakāṇām abhiprāyaḥ).

In the course of his discussion, Śabara's asserted that "there is no relation between the case of guests and the sacrificial act." This incidental remark provided sound historical proof that pūjā was built on analogy with atithi, the ancient Vedic tradition of welcoming guests. What Śabara was maintaining was that this analogy was not valid.

While the Mīmāṃsakas continued to maintain this interpretation for centuries, their defeat in debate at the hands of Śaṅkarācārya led to theirs being a minority view. Mīmāṃsakas flourished even into the 17th century, as evidenced by the commentaries of Nīlakaṇṭha.

Regional names
Puja is called பூசை in Tamil, bucha (บูชา) in Thai, and sometimes also পুজো  in Bengali.

title: Puja (Hinduism)


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Code generation (compiler)

In computing, code generation is part of the process chain of a compiler and converts intermediate representation of source code into a form (e.g., machine code) that can be readily executed by the target system.

Sophisticated compilers typically perform multiple passes over various intermediate forms. This multi-stage process is used because many algorithms for code optimization are easier to apply one at a time, or because the input to one optimization relies on the completed processing performed by another optimization. This organization also facilitates the creation of a single compiler that can target multiple architectures, as only the last of the code generation stages (the backend) needs to change from target to target. (For more information on compiler design, see Compiler.)

The input to the code generator typically consists of a parse tree or an abstract syntax tree. The tree is converted into a linear sequence of instructions, usually in an intermediate language such as three-address code. Further stages of compilation may or may not be referred to as "code generation", depending on whether they involve a significant change in the representation of the program. (For example, a peephole optimization pass would not likely be called "code generation", although a code generator might incorporate a peephole optimization pass.)

Major tasks
In addition to the basic conversion from an intermediate representation into a linear sequence of machine instructions, a typical code generator tries to optimize the generated code in some way.

Tasks which are typically part of a sophisticated compiler's "code generation" phase include:
 * Instruction selection: which instructions to use.
 * Instruction scheduling: in which order to put those instructions. Scheduling is a speed optimization that can have a critical effect on pipelined machines.
 * Register allocation: the allocation of variables to processor registers
 * Debug data generation if required so the code can be debugged.

Instruction selection is typically carried out by doing a recursive postorder traversal on the abstract syntax tree, matching particular tree configurations against templates; for example, the tree  might be transformed into a linear sequence of instructions by recursively generating the sequences for   and , and then emitting the instruction.

In a compiler that uses an intermediate language, there may be two instruction selection stages—one to convert the parse tree into intermediate code, and a second phase much later to convert the intermediate code into instructions from the instruction set of the target machine. This second phase does not require a tree traversal; it can be done linearly, and typically involves a simple replacement of intermediate-language operations with their corresponding opcodes. However, if the compiler is actually a language translator (for example, one that converts Java to C++), then the second code-generation phase may involve building a tree from the linear intermediate code.

Runtime code generation
When code generation occurs at runtime, as in just-in-time compilation (JIT), it is important that the entire process be efficient with respect to space and time. For example, when regular expressions are interpreted and used to generate code at runtime, a non-deterministic finite state machine is often generated instead of a deterministic one, because usually the former can be created more quickly and occupies less memory space than the latter. Despite its generally generating less efficient code, JIT code generation can take advantage of profiling information that is available only at runtime.

Related concepts
The fundamental task of taking input in one language and producing output in a non-trivially different language can be understood in terms of the core transformational operations of formal language theory. Consequently, some techniques that were originally developed for use in compilers have come to be employed in other ways as well. For example, YACC (Yet Another Compiler-Compiler) takes input in Backus–Naur form and converts it to a parser in C. Though it was originally created for automatic generation of a parser for a compiler, yacc is also often used to automate writing code that needs to be modified each time specifications are changed.

Many integrated development environments (IDEs) support some form of automatic source-code generation, often using algorithms in common with compiler code generators, although commonly less complicated. (See also: Program transformation, Data transformation.)

Reflection
In general, a syntax and semantic analyzer tries to retrieve the structure of the program from the source code, while a code generator uses this structural information (e.g., data types) to produce code. In other words, the former adds information while the latter loses some of the information. One consequence of this information loss is that reflection becomes difficult or even impossible. To counter this problem, code generators often embed syntactic and semantic information in addition to the code necessary for execution.

title: Code generation (compiler)