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NIST Releases Updated Handbook of Math Functions 128

Posted by kdawson
from the essential-reference dept.
An anonymous reader writes "NIST announced the publishing of the NIST Handbook of Mathematical Functions reference text (967 pp), also available in digital form at the Digital Library of Mathematical Functions. Access it with a MathML-enabled browser (Firefox or IE+plugin) to view equations as scalable text rather than bitmaps; the 3-D graphs can also be viewed with a VRML plugin for local rotating / zooming." The original Handbook of Mathematical Functions was published 46 years ago; the revision has been in the works for a decade.
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NIST Releases Updated Handbook of Math Functions

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  • Ob (Score:5, Funny)

    by Hognoxious (631665) on Friday May 14, 2010 @09:48AM (#32206572) Homepage Journal

    Let the number of the post be defined by a monotonically increasing function f, such that the initial value of f is zero.

    • by cosm (1072588)

      Let the number of the post be defined by a monotonically increasing function f, such that the initial value of f is zero.

      Corollary 1.1:

      Let the rate of posting trolls be defined by the the exponentially decaying 4th degree wave function of T(t), with a maximum frequency of /b/tards approximated inside t[10,60] seconds, with T(t) approaching 0 as t approaches infinity.

    • Re:Ob (Score:5, Funny)

      by SoVeryTired (967875) on Friday May 14, 2010 @11:21AM (#32207668)

      f(x) = x satisfies that condition.

      Perhaps you meant monotonically decreasing nonnegative function on the nonnegative reals with f(0) = 0, or something to that effect...

      As I'm sure you can tell, I'm a big hit at parties.

      • by jd (1658)

        It can't be real, unless you assume that there can be fractions of a post. Actually, no, you'd still be able to use the set of all quotients for that. Since it's starting at 0, you would presumably define it over the set of cardinal numbers. If you'd started at 1, you would use the N+ natural numbers. However, on the basis of this post alone, I would actually advocate defining posts over the set of complex numbers, so as to deal with imaginary components.

    • by blair1q (305137)

      That renders as "0th post" in my browser.

      How do I submit a bug report?

      Or shall I just flame-shame you into fixing it?

      • That renders as "0th post" in my browser.
        How do I submit a bug report?

        I'm a C programmer, you insensitive clo01@m.

        One day I'll fix that bloody pointer error.

    • by rcamans (252182)

      Let the number of the interesting post be defined by the zero function...

      • by jd (1658)

        Actually, you want something like:

        Let interesting posts be defined on the set of cardinal numbers such that the number of interesting posts is less than or equal to the total number of posts not allocated to the set of posts defined by trolls, funnies and miscellaneous posts, and where a post is moderated as interesting by that set of users who don't do this to give funny posts karma and who also have an excellent karma and who also have an above-average achievements score and who know something about the s

  • 42 (Score:3, Funny)

    by Yvan256 (722131) on Friday May 14, 2010 @09:51AM (#32206586) Homepage Journal

    That's all you need to know about maths.

  • may be offtopic (Score:4, Interesting)

    by mapkinase (958129) on Friday May 14, 2010 @10:05AM (#32206742) Homepage Journal

    If you are looking for a good math reference I would recommend Mathematical Handbook for Scientists and Engineers by Korns [amazon.com]

    Russian translation of it was a must-have for every member of Russian "technicheskaya intelligentsiya".

  • Opera MathML support (Score:4, Interesting)

    by molo (94384) on Friday May 14, 2010 @10:05AM (#32206748) Journal

    Opera has had MathML support since 9.5, but it looks like this page serves up PNGs for equations to Opera unless the user-agent is changed. When the user-agent is changed, MathML is served up, but the rendering is off, with little blank boxes dotted around (see this page for example: http://dlmf.nist.gov/2.7 [nist.gov] ). Anyone else getting similar results?

    -molo

    • Re: (Score:2, Informative)

      by hakey (1227664)
      You don't need to change user-agent. Take a look at the customization page http://dlmf.nist.gov/help/customize [nist.gov]. I wish all sites had something like that.
      • by bcrowell (177657)

        You don't need to change user-agent. Take a look at the customization page http://dlmf.nist.gov/help/customize [nist.gov]. I wish all sites had something like that.

        No, all sites should not have something like this. End users should not have to do something special like this to work around the fact that IE doesn't support MathML properly. (IE requires a plugin, and even with the plugin, it doesn't support standard mathml; web authors have to make special IE-only versions of their pages with nonstandard kludges writte

    • by bcrowell (177657)

      Opera has had MathML support since 9.5, but it looks like this page serves up PNGs for equations to Opera unless the user-agent is changed. When the user-agent is changed, MathML is served up, but the rendering is off, with little blank boxes dotted around (see this page for example: http://dlmf.nist.gov/2.7 [nist.gov] ). Anyone else getting similar results?

      This is just one of many examples of the pain and suffering caused by MS's failure to implement the MathML standard in IE. Webmasters shouldn't have to special-

  • by jambox (1015589)
    I did comp sci at university and they made me make a model of the campus in VRML. This is the first time I've heard of it since!
    • Would SVG be better?
      • by jambox (1015589)
        Only if you could do without the extra dimension..?!
        • I was thinking that multiple dimensions can be handled by JavaScript. Then projecting the result function to 2D. I'm trying to avoid server side throttling.
    • by mangu (126918)

      Lat time I saw a website with VRML was in 2002. It was a great idea that failed, I don't know why.

      • It was created in a time when bandwidth was too expensive and computers too slow. Today computers aren't still fast enough, but something like it may appear again in the near future, and be adopted this time. (Or, if we are luck, people won't be affected by NIH, and use the already existent VRML. But I wouldn't bet on it.)
        • Re: (Score:2, Funny)

          by Anonymous Coward

          I wouldn't bet on it either, for the same reason modern games aren't supplied in DOOM WAD files.

        • by blair1q (305137)

          When phones are capable of running it, it might start to catch on again.

          Actually, my Nexus One does pretty good with 3D graphics, but the apps are pretty simplified. Having them be fully interactive with most of the information transfer occurring over the data link would bog it down to a small fraction of an FPS.

          So the 2-D click-and-wait model still makes the most sense for the machinery that's gaining market share the fastest.

      • by burni2 (1643061)

        1.) sluggish plugins
        2.) slow rendering / in '97
        3.) not widely known

        4.) it was a good idea .. do you really expect good ideas to succeed ?

  • 967 pages? (Score:3, Funny)

    by ProdigyPuNk (614140) on Friday May 14, 2010 @10:09AM (#32206786) Journal
    That would take forever to actually read through... I guess if you understand most of these functions you don't have to worry about a wife or girlfriend anyway...
  • ...more than welcome if they could make an off-line digital DLMF in any of pdf, djvu, odt or any other format...
  • by mapkinase (958129) on Friday May 14, 2010 @10:12AM (#32206812) Homepage Journal

    It also has alternative coding for every equation in TeX, pMML [wikipedia.org] (XML wrapped default coding) and PNG

  • by richg74 (650636) on Friday May 14, 2010 @10:34AM (#32207092) Homepage
    And I have found it to be invaluable reference. It's not a textbook; it assumes you basically know the math, but just need to check the details. One other feature, quite handy for programmers of quantitative applications: it has approximations for many functions (e.g., the cumulative normal density function), with notes on their accuracy and range of applicability.
    • It's not a textbook; it assumes you basically know the math

      That applies to every math book out there.

    • Me too. Discovered it during a grad course in numerical analysis. With the CRC Handbook in one hand and the HBMF in the other, you had a great deal of summarized practical math at your disposal. Throw in Numerical Recipes in FORTRAN (later released in C) -- icing on the cake.
  • by bcrowell (177657) on Friday May 14, 2010 @10:44AM (#32207224) Homepage

    MathML has been around since 1998, which is a heck of a long time by web standards, and yet IE still doesn't support it out of the box. That's why IE users can't view this book properly without a plugin to provide mathml support. Yet another reason to encourage everyone you know to drop IE and get a decent browser. Supporting mathml in IE is also a ridiculous pain in the neck for people creating web pages. Even if you are willing to tell your readers that they can't view your site without the plugin, you still can't write standard xhtml with mathml embedded in it; if you want it to work with the MathPlayer plugin for IE, you have to write all kinds of ugly, nonstandard hacks, and serve up a different version of the page to IE users than to everyone else. The end result of all this is that MathML doesn't get used nearly as much as it should.

    For instance, Wikipedia renders bitmaps as equations, using software called texvc. A guy named D.M. Harvey at Harvard wrote software called blahtex that can be used as a drop-in replacement for texvc, rendering math as either MathML or bitmaps as required. There was a long discussion of this on WikiProject Mathematics, and there was a clear consensus that texvc was old, lame technology, and needed to be replaced with blahtex. However, the people who run the software setup for WP never implemented it -- never, apparently, even bothered to give an actual response, just blew it off. The attitude would presumably have been different if the situation with IE had been different. Since most people access WP with IE, those people would still have had to be served a version of the pages with bitmaps. That would have been a hassle in terms of software.

    I believe that the current plan is for html 5 to include support for embedded mathml and svg tags (even though html 5 isn't xhtml). It will be interesting to see whether MS supports this aspect of html 5, or just does a partial implementation that omits these features.

    • by gringer (252588)

      Wikipedia renders bitmaps as equations

      That sounds quite difficult. Are the bitmap-derived equations small enough to fit into the margins of the articles?

    • by BitZtream (692029)

      They've already committed themselves to SVG support in IE9, though I don't remember anything about MathML it doesn't interest me directly so I may have just ignored/overlooked that bit.

      As far as WP implementing it ... does the current software work and fill the needs that need to be filled? If so perhaps they simply did the intelligent thing and didn't try to fix what was working fine.

      You'll find a lot of people don't upgrade software just because someone rewrote it.

      • Re: (Score:3, Insightful)

        by bcrowell (177657)

        As far as WP implementing it ... does the current software work and fill the needs that need to be filled? If so perhaps they simply did the intelligent thing and didn't try to fix what was working fine.

        The current software renders equations as bitmaps. The bitmaps look lousy. They're less legible than mathml. They look awful when you print them. They're the wrong size compared to the text. People who are visually impaired can use the controls in their browser to enlarge the font in the web page, but that

    • Seriously?

      What proportion of the web-browsing public do you estimate will ever touch a page with a single div of MathML on it?

      When it reaches 1/50, Microsoft will probably consider adding support. Then probably forget about it.

  • I would love to see the same thing with statistical formulae, does anyone know if such a creature exists?

  • A great resource, easier to use than a heavy, giant book, and full of beautiful and useful graphs. However: web text with math mixed in as graphics can be done in a way that is pleasant enough to read, but NIST's pictorial mathematics is not optimal: the size of the symbols is not matched very well with the surrounding text and, because of extreme anti-aliasing, the contrast is very low. Since this is this way most users will see this material, it's a shame they didn't do a better job.
    • by bcrowell (177657)

      A great resource, easier to use than a heavy, giant book, and full of beautiful and useful graphs. However: web text with math mixed in as graphics can be done in a way that is pleasant enough to read, but NIST's pictorial mathematics is not optimal: the size of the symbols is not matched very well with the surrounding text and, because of extreme anti-aliasing, the contrast is very low. Since this is this way most users will see this material, it's a shame they didn't do a better job.

      They did do a better

      • by lee1 (219161)

        I don't use Internet Explorer. I said "Since this is this way most users will see this material [meaning, obviously, as PNG images, because most people can't see MathML) , it's a shame they didn't do a better job [at creating the PNG equations. Duh.]".

        I did browse the site using Firefox, and the MathML rendering, while generally easier to read than the PNG version, has the usual problems, namely, poor typography and the occasional unavailable or incorrect character. The latter occurs frequently enough tha

        • Re: (Score:2, Informative)

          by krull (48492)

          Install the STIX fonts as they suggest. I did and now the equations all render in MathML just fine and look pretty good...

          http://www.stixfonts.org/ [stixfonts.org]

          • by lee1 (219161)

            Install the STIX fonts as they suggest.

            As they suggest where? I looked around at the stix site, but it seems that I'll have to spend more time there to actually find out how to download the fonts. I saw a sugestion that I need to register as a beta tester to use them. Is this true?

        • by blair1q (305137)

          I browsed it using Firefox, and it bitched about having to load certain fonts, and then rendered several glyphs as black rectangles.

          Fuzzy PNGs would have been an improvement.

  • If you don’t know what they mean, you could as well be an automaton applying them.
    And if you do, you don’t need them anyway, as you grasp the concept behind it, and can build your formulas yourself.

    But hey, the automatons that leave school, having been though “math” as something where you are obsessed with “the right way”(TM) to write it, and learnin everything by heart without ever understanding it, is gonna love it...

    • Re:Useless. (Score:5, Insightful)

      by Daniel Dvorkin (106857) * on Friday May 14, 2010 @01:40PM (#32209668) Homepage Journal

      Yes, you can derive all of mathematics from a fairly small set of axioms every time you want to do something. The point of having a reference handy is that you don't have to. You see, in the modern world we have this thing called a "body of knowledge," the idea being that smart people can do new work which builds on the previous work of other smart people. It's been quite a successful approach so far; perhaps you should give it a try?

  • by NicknamesAreStupid (1040118) on Friday May 14, 2010 @12:19PM (#32208364)
    Roughly how long would it take to implement the entire NIST library as functions in C++ just using the standard C math library (abs, acos . . .tan, tanh)?
    • The NIST code is mostly in fortran, but what's so bad about fortran? It's well suited to numerical computation, pretty easy to learn, and there's always f2c, which will turn fortran into C.

    • by krull (48492)

      Keep in mind the reference is not just function definitions. The main content is actually approximations to functions (asymptotic, series, and polynomial) and various formulas involving relationships between functions.

    • by u38cg (607297)
      About two and a half days.
  • by Anonymous Coward

    I finally got around to reading the NIST Handbook of Mathematical Functions.

    Turns out the Zeta function did it.

  • The submitter could have benefitted everyone and noted that this is the long awaited version of the original that was known as the Abramowitz_and_Stegun [wikipedia.org] because it was so useful in certain areas. Because it was printed as a government publication it was automatically in the public domain. This new version [wikipedia.org] was wholly created and printed through NIST so it is under copyright. That's an unfortunate side stepping of our rights as citizens. It was created with public money, it should be public domain.
    • by lee1 (219161)

      That's an unfortunate side stepping of our rights as citizens.

      What rights are these, and where do they come from? They are not legal rights, of course, as the assignment of copyright was done according to the law.

      It was created with public money, it should be public domain.

      Does not follow. Should all the government's classified information be made public domain immediately because it was created with public money? Should members of the public be able to reproduce without attribution my scientific papers

      • by whitis (310873)

        Should all the government's classified information be made public domain immediately because it was created with public money?

        Protection of classified materials is done through a mechanism separate from copyright, with much higher penalties. Likewise, private information is protected by privacy laws. But what is published by the federal government for the consumption of he general public is supposed to be public domain.

        Should members of the public be able to reproduce without attribution my scientific papers because the research was supported by tax dollars? I hope not. (This is what "public domain" means: far more than free access.)

        You appear to work for a contractor. Your work was supported by tax dollars but not performed by employees of the federal government. The copyright status depends on the contract terms. There is also

        • by lee1 (219161)

          Protection of classified materials is done through a mechanism separate from copyright

          I was supplying a counterexample to the idea that something "publicly funded" implies that it should be in the "public domain". My counterexample stands; I don't see how your comments are relevant to this point.

          You appear to work for a contractor. Your work was supported by tax dollars but not performed by employees of the federal government.

          No, I am a federal employee. If all the authors on a paper are federal employe

  • You 'll have to pry Abramowitz and Stegun out of my cold, dead hands.
  • Epic Fail (Score:4, Interesting)

    by whitis (310873) on Friday May 14, 2010 @03:40PM (#32211898) Homepage

    I have been waiting for this to come out for a while but I see a number of reasons for disappointment.

    First, a big part of the reason for having a library of mathematical functions compiled by a government agency is to have a public domain source that can be reused for any purpose in any field of endeavor. They screwed that up royally: "© 2010 NIST". Commerfcial use is specifically prohibited. Ironic considering that NIST is part of the US Department of Commerce. And since comercial use is prohibited, it can't be used in software distributed under a permissive license which allows commercial use.

    Second, they call it a "digital library" but it isn't. It is more or less a book in html by chapters. They used MathML instead of OpenMATH. MathML is too presentational and not sufficiently semantic. You should be able to configure OpenMATH or MathML or PNG produced from the OpenMath and you should be able to download OpenMath content dictionaries.

    It is still useful as a free-for-viewing-only ebook, but that is only a tiny fraction of what it should have been. Tax payers got gyped. We paid perhaps 90% of the cost for 20% of the result, and the copyright even interferes with someone else finishing the job.

    • Re:Epic Fail (Score:4, Interesting)

      by belmolis (702863) <billposer AT alum DOT mit DOT edu> on Friday May 14, 2010 @04:48PM (#32212900) Homepage

      I am wondering what the legal basis for the restriction on commercial use might be. US government publications are in the public domain - there is no crown copyright at the federal level in the US. So the only situation in which they can legitimately impose restrictions is when they are reproducing material whose copyright is owned by others.

      • Re: (Score:2, Informative)

        by BBTaeKwonDo (1540945)
        http://dlmf.nist.gov/about/notices [nist.gov] (the (C) 2010 NIST link at the bottom of the pages) gives the answer:

        Pursuant to Title 17 USC 105, the National Institute of Standards and Technology (NIST), United States Department of Commerce, is authorized to receive and hold copyrights transferred to it by assignment or otherwise. Authors of the works appearing in the Digital Library of Mathematical Functions (DLMF) have assigned copyright to the works to NIST, United States Department of Commerce, as represented by t

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