tag:blogger.com,1999:blog-3722233.post4707891720993336206..comments2020-02-19T03:43:18.369-05:00Comments on Computational Complexity: Two requets: A sum and a referenceLance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger12125tag:blogger.com,1999:blog-3722233.post-41519104033213828012009-06-26T04:06:20.858-04:002009-06-26T04:06:20.858-04:00The first lemma in your proof is a direct conseque...The first lemma in your proof is a direct consequence of the method of finite differences; it says that the nth forward difference of a polynomial of degree n-1 is identically zero.<br /><br />The inner summation in the second identity is basically computing the coefficients of the "Newton form" of the polynomial, although you seem to be using a slightly different basis. Nevertheless, these results are quite standard.Qiaochu Yuanhttp://qchu.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-77219194695412050142009-06-25T09:26:25.830-04:002009-06-25T09:26:25.830-04:00Bill,
FYI, the advantage of an article NOT appeari...Bill,<br />FYI, the advantage of an article NOT appearing in hardcopy on the UM system is that they'll get it interlibrary loan for you... and scan it in and email it to you. I've started hoping that they never have the articles I want in hardcopy...sorellehttp://kdphd.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-50839731917157481772009-06-25T07:18:23.477-04:002009-06-25T07:18:23.477-04:00I think this is the Newton series for the differe...I think this is the <a href="http://en.wikipedia.org/wiki/Difference_operator#Newton_series" rel="nofollow"> Newton series</a> for the difference operator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-72562978843710520152009-06-25T00:37:31.121-04:002009-06-25T00:37:31.121-04:00One of my readers emailed me the
paper. Actually i...One of my readers emailed me the<br />paper. Actually it was Lance<br />(I think he reads my blogs).<br /><br />Thanks Lance and thanks Anon who<br />offered to help.GASARCHnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-86793501400896529502009-06-24T18:11:44.836-04:002009-06-24T18:11:44.836-04:00No idea about prior art, but that looks an awful l...No idea about prior art, but that looks an awful lot like the discrete calculus analog of the fact that the $n$th degree Taylor expansion of a polynomial of degree $n$ is the polynomial.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90457548785102924632009-06-24T17:56:14.253-04:002009-06-24T17:56:14.253-04:00Anon who offered to try to get me the article I wa...Anon who offered to try to get me the article I want- Nobody has<br />gotten me the article yet, so yes<br />please do so.<br /><br />Thanks<br /><br />BIll Gasarch<br />(logged in to a dif person so it<br />will look like its Anon but its not)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-48924840385764196342009-06-24T17:04:31.067-04:002009-06-24T17:04:31.067-04:00sep322,
Yup, that's why you use a conversion ...sep322,<br /><br />Yup, that's why you use a conversion script rather than writing MathML by hand.<br /><br />Anonymous,<br /><br />itex2mml is great, but for a blog where you just want to write short snippets of math it is easier to go with a javascript solution that you can just add into the HTML header of your blog. That's why I would recommend <a href="http://math.etsu.edu/LaTeXMathML/" rel="nofollow">LaTeXMathML</a>. It is not perfect, but until a better solution comes along it is the best that I know of.<br /><br />Of course, if you are using Wordpress or Moveable Type then you can use <a href="http://golem.ph.utexas.edu/~distler/blog/itex2MML.html" rel="nofollow">Jacques Distler's plugin</a> based on itex2Mmml, but there isn't one for Blogger as far as I know.<br /><br />Another thing worth mentioning is that there are a few graphical MathML editors available (a bit like Microsoft Equation Editor) that produce MathML directly. They may be suitable if you only need to do this sort of thing occasionally.<br /><br />Finally, it is also the case that you can find several plugins for converting LaTeX equations into .png images if you feel like you absolutely have to (but don't because you don't).Matt Leiferhttp://mattleifer.infonoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-51657289642915365962009-06-24T16:53:22.731-04:002009-06-24T16:53:22.731-04:00the e-version of the article is available from UCB...the e-version of the article is available from UCB library. My UC campus cannot access it. but if you dont get it please leave a note here and I will try through the library.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-66677713323574129172009-06-24T16:41:51.646-04:002009-06-24T16:41:51.646-04:00This identity is not new. There is a procedure cal...This identity is not new. There is a procedure called the method of difference due to pascal in order to compute/approximate functions. It is known to work exactly for polynomials and that boils down to this identity.Sushhttps://www.blogger.com/profile/02681534412045681372noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84712639148987339762009-06-24T16:35:38.880-04:002009-06-24T16:35:38.880-04:00<?xml version="1.0" encoding="UT...<?xml version="1.0" encoding="UTF-8"?><br /><!DOCTYPE math:math PUBLIC "-//OpenOffice.org//DTD Modified W3C MathML 1.01//EN" "math.dtd"><br /><math:math xmlns:math="http://www.w3.org/1998/Math/MathML"><br /> <math:semantics><br /> <math:mfenced math:open="" math:close=""><br /> <math:mtable><br /> <math:mtr><br /> <math:mrow><br /> <math:mi>x</math:mi><br /> <math:mo math:stretchy="false">−</math:mo><br /> <math:mn>1</math:mn><br /> </math:mrow><br /> </math:mtr><br /> <math:mtr><br /> <math:mi>x</math:mi><br /> </math:mtr><br /> </math:mtable><br /> </math:mfenced><br /> </math:semantics><br /></math:math>sep332https://www.blogger.com/profile/15089674288837329342noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-21142135191089257142009-06-24T15:42:40.484-04:002009-06-24T15:42:40.484-04:00I Recommend itex2mml for translation. It'll c...I Recommend itex2mml for translation. It'll change itex (a subset of LaTeX) into MathML. See:<br /><a href="http://pear.math.pitt.edu/mathzilla/itex2mml.html" rel="nofollow">itex2mml</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-21100595890409819312009-06-24T13:55:27.926-04:002009-06-24T13:55:27.926-04:00"(Side Request: How do you do a choose-sign i..."(Side Request: How do you do a choose-sign in html?)"<br /><br />You don't. Instead you install a LaTeX script on your blog, e.g. LaTeXMathML.Matt Leiferhttp://mattleifer.infonoreply@blogger.com