How to calculate a polynomial of (s+1)(s+2)…(s+10) in a short time?
Instead of calculate them one by one, we can do it with the help of Python library – Numpy.
1. Make sure you have installed Numpy for your Python interpreter. In Ubuntu, you may just want to install python-scipy as it contains all the scientific calculation tools.
2. Try the following example in your python interpreter:
from numpy import * p1 = poly1d(1, 1 ) #(S+1) p2 = poly1d(1, 2 ) #(S+2) p3 = poly1d(1, 3 ) #(S+3) p4 = poly1d(1, 4 ) #(S+4) p5 = poly1d(1, 5 ) #(S+5) p6 = poly1d(1, 6 ) #(S+6) p7 = poly1d(1, 7 ) #(S+7) p8 = poly1d(1, 8 ) #(S+8) p9 = poly1d(1, 9 ) #(S+9) p10 = poly1d(1, 10) #(S+10) print p1*p2*p3*p4*p5*p6*p7*p8*p9*p10
3. Then, you will an get an output like:
10 9 8 7 6 5 4 3 2 1 x - 10 x + 45 x - 120 x + 210 x - 252 x + 210 x - 120 x + 45 x - 10 x + 1
That is the answer:
x^10 - 10x^9 +45x^8 - 120x^7 + 210x^6 - 252x^5 + 210x^4 - 120x^3 + 45x^2 - 10x + 1
4. Say, we need to find the root of this polynomial. With the help of Python, we can get the roots by feeding these line into the interpreter.
(p1*p2*p3*p4*p5*p6*p7*p8*p9*p10).r #.r means root.
And, we will get an output like this:
array([ 1.04405137+0.0143565j , 1.04405137-0.0143565j , 1.02709855+0.03755416j, 1.02709855-0.03755416j, 0.99974141+0.04619473j, 0.99974141-0.04619473j, 0.97275208+0.03706564j, 0.97275208-0.03706564j, 0.95635659+0.01406697j, 0.95635659-0.01406697j])
The polynomial has 5 complex conjugates: 1.04405137 +/- 0.0143565j, 1.02709855 +/- 0.03755416j, 0.99974141+/- 0.04619473j, 0.97275208 +/-0.03706564j, 0.97275208 +/- 0.03706564j and 0.95635659 +/- 0.01406697j .
<With Love> is the first Japanese drama that I watched in my secondary school. Seeing this youtube brings me back to my sentimental high school puppy love. @_+
The storyline goes as follows:
Takashi (Takenouchi), a talented composer, who could not write a love song ever since his girlfriend Rina left him suddenly. Accidentally, Takashi sent an uncompleted piece of his latest work to Amane (Tanaka) via email.
Deeply touched by his music, Amane wrote back to him, without getting a reply. Amane continued writing to him, pouring out her thoughts, with the nickname of “Teru Teru Bozu”. One day, Takashi responded with a mail saying “WHO ARE YOU?” because what Rina left him as a farewell gift was a teru teru bozu!
(Quoted from http://jdorama.com/drama.445.htm)
February 2008 – Edison Chan, a Hong Kong artist is found to be in troubles after his sex photo scandal circulates the world through Internet. He claimed that the photos were stolen after sending his laptop to a repair shop.
Edison did a mistake that we do, that is, storing files nakedly in machine.
Some files like docs and spreadsheets can be encrypted with the tool provided by OpenOffice itself. However, pictures and MP4 are left nakedly in hard disk. A baddie may possess these files by overriding the user privilege (E.g. using live-CD to bypass).
To overcome this, we encrypt our partitions. Most of the Linux users will have two partitions in their machine. One for for the root (/, /root, /bin,…) and another one for users home directory (/home). To avoid performance impact, we can encrypt the the partition of the home directory.
In the following example, Ubuntu 9.10 will be the targeted Linux OS, and LUKS is used as the encryption system.
A good calculus book for beginners and advanced readers. The calculus concepts are explained nicely. Not too technical, but suite me very well.
This book is available at Amazon.
Drawing in Linux is a pain to (most*) newbie users .
Sometimes, we just want to draw a simple circle in the picture and GIMP is found to be too complicated to be used.
If you are fine to be ms-slave, perhaps we can just run mspaint in Linux (Ubuntu 9.10) as well.
Running mspaint in Ubuntu 9.10 is not hard. All you need is:
- mspaint.exe (just google to get it)
- mfc42u.dll (just google to get it)
- and, wine (download-able with apt-get).
I have tested this with Ubuntu 9.10 and it can edit/save BMP images with no issue.