## Posts tagged ‘software’

### 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.

### Experimental algebraic geometry I : the grassmannian

I just began playing with Macaulay 2 to see how it could help doing algebraic geometry without manual tedious computations. Let’s try with the grassmannian: fortunately, the program comes with lots of pre-written functions, including the generation of Grassmanians.

Macaulay provides a command-line interface using the readline library (like many other command-line programs) : here is what input/output looks like

i1 : V = Grassmannian(1,3)
o1 = ideal(p   p    - p   p    + p   p   )
1,2 0,3    0,2 1,3    0,1 2,3
o1 : Ideal of ZZ[p   , p   , p   , p   , p   , p   ]
0,1   0,2   1,2   0,3   1,3   2,3


When I type a command at i1, I get an output o1 with a value $\mathrm{ideal}(p_{1,2} p_{0,3} - p_{0,2} p_{1,3} + p_{0,1} p_{2,3})$ and a type: this output is an ideal of the ring $\mathbb{Z}[p_{0,1}, p_{0,2}, p_{1,2}, p_{0,3}, p_{1,3}, p_{2,3}]$. Many features of the Grassmannian as an algebraic variety are available: first define

i1 : V = Grassmannian(1,3,CoefficientRing => QQ);
o1 : Ideal of QQ[p   , p   , p   , p   , p   , p   ]
0,1   0,2   1,2   0,3   1,3   2,3
i2 : X = Proj(ring V / V)
o2 = X
o2 : ProjectiveVariety


the projective variety X over $\mathbb Q$ defined by the homogeneous ideal V : here ring V denotes the ambient ring of V. We see that $V$ is a non-singular quadric in 5-dimensional projective space, and check several well-known facts (more…)