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Text of the page (random words):
embûches tissues because mathematics often look like a web of logs embûches tissues home about me mathkaba my tool for managing bibliography i recently decided to systematically conserve a backup copy of articles i am downloading but what if i want to use these backup copy i usually only remember the title of the article or the name of the author if i was not really working on the article i may forget the author or even the title if i only remember that somewhere it is written that you may know mendeley i tried to use it for some time but it is not open source has too many features for what i need and could be better suited to a mathematical use by supporting for example the msc classification or by having specific interfaces with mathscinet or zentralblatt hence i decided writing my own program to do the job for the moment it may probably crash at any time and seriously lack essential features but it satisfies my daily purposes which are have a quick overview of the articles i have on my computer have a way of opening them without having to know where it is in case it is not stored on my computer open a suitable url without having to search through mathscinet the result is called mathkaba and is hosted on github for the moment it works by reading metadata which is not stored in a database as usual i hate databases but in plain text files along with the pdf files which should have the same syntax as the ascii output of zentralblatt mathscinet can also output entries in the endnote format which seems equally interesting any comments are welcome 5 march 2010 at 9 55 am 4 comments creating executables for windows from a linux box when writing a program especially a graphical one you may feel some compassion towards windows users and wonder whether it would be possible to give them a chance of using it famous toolkits like gtk and qt provide good support for windows and an abstraction layer for os dependent vital functions so it becomes easier to write os independant code next you need a cross compiler it s just a compiler except that instead of creating executable files you could run it creates executables in another format e g win32 exe files but since windows is very different from gnu linux some code or one of its dependencies has to use windows specific functions so you need source headers and maybe additional libraries more 3 march 2010 at 3 34 pm leave a comment changing default applications for developers when not using those uber featured desktop environments such as kde or gnome out there it can sometimes be challenging to find a simple text based way of configuring things for example i am currently writing a gtk2 program which uses the method gtk_show_uri to open files using default programs on the computer i am using at work this results in opening acrobat reader over an xdmcp connection which is really distasteful even using gnome s control center there does not seem to be a way to change that what should i look at more 24 february 2010 at 7 33 pm leave a comment merry christmas from a dying blog to anyone still reading me i wish a merry christmas may it be free from any gratuitous consumerist madness and proprietary software i may still have several things to talk about in the near future 25 december 2009 at 10 58 am 1 comment operads in haskell mikael vejdemo johansson who was at the operads conference in luminy which i also attended wrote in only one week a haskell module computing gröbner bases for operads nice work 11 may 2009 at 8 25 pm leave a comment elliptic curves for high school students i had to give a talk to high school students about some mathematical notion i decided to tell them something about elliptic curves but not the usual speech about cryptography finite fields and the group law on a cubic curve instead i talked about the perhaps less known appearances of elliptic functions as solutions of classical odes even if i don t really know much about these myself the simplest mechanical system whose motion is governed by an elliptic curve is the pendulum the reason for this is that the ode which classically describes the time evolution of the angle of the pendulum is best rewritten in terms of the altitude of the pendulum the law of energy conservation is then written as where 0 and 2l are the extremal values of the altitude is the highest altitude which can be reached with a given energy even if which corresponds to the pendulum make full rotations around its axis and is the vertical momentum of the pendulum in this setting there are classical hamilton relations so the differential form turns out to be the canonical non vanishing abelian differential on the elliptic curve this explains why the period of the pendulum is an elliptic integral which can be calculed by an arithmetic geometric mean and why the position of the pendulum at can be deduced from its position at times and by the classical secant tangent law the notes for the talk in french are available here 11 may 2009 at 8 08 pm leave a comment cardboard associahedron after the dodecahedron comes the cardboard associahedron it represents the combinatorics of moving parentheses to calculate an associative product of five things step by step the vertices of the associahedron are thus the 14 different binary trees with 5 leaves given four factors there are exactly five ways of multiplying them using a binary operation by moving parentheses according to the associativity rule you go through five different trees in a cyclic way this is known as maclane s pentagon coherence rule which states that in not too weak notions of monoid checking coherence for pentagon diagrams ensures that the definition of the product is well behaved more 8 april 2009 at 12 11 am leave a comment cardboard dodecahedron i made a cardboard dodecahedron for the needs of a talk if you draw 5 coloured stars on all facets by choosing smartly the colours you can get five coloured cubes whose vertices are vertices of the dodecahedron this trick can be used to show that the symmetry group of the dodecahedron is the alternate symmetric group it replaces a star by a star with a different arrangement of colours since there are 12 facets and 5 ways of rotating each of them 60 colourings can be seen by rotating the dodecahedron by direct isometries however it is not true that you can see the 120 possible colourings by allowing also reflections the full isometry group of the dodecahedron is the symmetric group on five colours an easy reason for this is that the colouring is invariant under symmetry through the central point which is a determinant 1 transformation you can also argue that reflections act as double transpositions of the colours of a star people also talk about five tetrahedra in a isocahedron which can also be obtained in the dodecahedron by choosing a tetrahedron in each cube in a consistent way the tetrahedra have faithful action of the isometry group there are two sets of five tetrahedron which are exchanged under signature 1 transformations and even permutations of the tetrahedra correspond to direct isometries 6 april 2009 at 12 01 am leave a comment computing gröbner bases in haskell i wrote a small package to compute gröbner bases in haskell with the buchberger algorithm with applications to variable elimination performance is quite bad compared to specialised software like macaulay but it seems to work i put a cabal package here maybe i ll add several functions afterwards a testcase import data polynomial import data ring import algebra groebnerbasis import algebra elimination type r polynom qq varxyz x y z t u v map returnp x y z t u v r projection from a point on the intersection of quadrics main do print step_eliminate t makeideal x 2 3 y z z t 2 x t z 2 5 y 2 z x 2 t z the output should be x y 2 2 5 x 2 z 1 2 y 2 z 3 10 x z 2 3 5 y z 2 1 10 z 3 20 march 2009 at 7 47 pm leave a comment schemes in algebraic geometry 3 glued schemes and sheaves andré weil was among the first ones to point out the importance of having a local description of varieties especially projective spaces which can always locally be described as an affine space with completion by a hyperplane at infinity and projective varieties which similarly look like varieties in affine space the use of sheaves in local description of spaces was magnified by cartan and serre in the context of complex analytic spaces and generalised to the algebraic setting by serre in faisceaux algébriques cohérents the projective space is the simplest example of an algebro geometric object which cannot be described by the prime spectrum or the functor of points of a ring for example there is no obvious ring whose ideals describe varieties in projective space which come from homogeneous equations we would like to give a correct definition of gluing affine lines with coordinates and to define the projective line as the gluing of with given by for functors of points the latest article by alain connes and caterina consani gives a definition for prime spectra one has to be aware that gluing only topological spaces do not give meaningful information on algebraic properties this is illustrated by the case of differentiable manifolds which are not the same as topological manifolds gluing differentiable manifolds has to induce a correspondance between differentiable functions this is equivalent to the requirement that gluing maps between charts be differentiable more 17 march 2009 at 12 35 am leave a comment older posts pages about me abelian category adjunction algebra algebraic geometry arithmetic geometric mean baer sum barycentre book calculus category circle circular curve cohomology combinatorics commutative algebra conic ellipse elliptic function elliptic integral euclidean geometry extension extensions fft free algebra functor geometry gerbes godement grassmannian group gröbner basis handcrafted mathematics haskell highest weight inauguration inversion jacobian language laver table lie algebra line local logic macaulay manifold monad monads in mathematics newton method operad plücker coordinates prime ideal prime spectrum projective plane projective space qed quadrics quartic rational map representation riemann sphere scheme schubert condition sheaves simson software spectral sequence square root stacks tensor product topology translation triangle undecidable variety verma module computer blogs arch linux and haskell language blogs bradshaw of the future motivated grammar math and physics blogs éléments des sciences concrete nonsense math goes pop motivic stuff not even wrong rigourous trivialities secret blogging seminar the everything seminar the n category café what s new terence tao not blogs ma page web au labo my web page at university of nice xkcd top posts extensions of sheaves and the local global spectral sequence ten constructions of the cohomology of varieties monads in mathematics 4 the bar and cobar constructions schemes in algebraic geometry 3 glued schemes and sheaves categories algebra commutative algebra homological algebra blabber calculus categories combinatorics curves english français geometry algebraic geometry euclidean geometry projective geometry group theory language logic representation theory review series monads in mathematics schemes in algebraic geometry software macaulay sysadmin topology algebraic topology undergraduate archives march 2010 february 2010 december 2009 may 2009 april 2009 march 2009 february 2009 january 2009 december 2008 recent comments rodney price on mathkaba my tool for managin carmine napolitano on merry christmas from a dying remyoudompheng on mathkaba my tool for managin alberto on mathkaba my tool for managin gaetan bisson on mathkaba my tool for managin meta create account log in entries feed comments feed wordpress com blog at wordpress com embûches tissues blog at wordpress com subscribe subscribed embûches tissues join 25 other subscribers sign me up already have a 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