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Transcript of SAGE software
software system Sage is mathematics software that combines the power of many existing open-source packages into a common Python-based interface. It covers many aspects of mathematics, including algebra, combinatorics, numerical mathematics, number theory, and calculus. Haneen AlSuradi
U00020619 Can be used either from "command line" or a GUI:
1. command line: >> sage
2. GUI: >>sage
>> notebook() *Ex2, solving equations:
>>S= solve(x^5 -11*x^4 + 43*x^3 - 73*x^2 +56*x -16 ==0,x) Sage as a calculator * Ex1, inverse of a matrix:
>> matrix([[1,2,-5],[3,4,1], [6,3,-2]])^(-1) Power Computing Ex1, finding the eigenvalues for 500x500 matrix.
code: >> m = random_matrix(RDF,500)
>>e = m.eigenvalues() #about 2 seconds Ex2, handling very large numbers, even numbers with millions or billions of digits:
code: >>factorial(100) Ex3, compute more than 100 digits of pi:
code: >> N(pi, digits=200) Symbolic computation Ex1: symbolic integration
>>integrate (e^-x *sqrt(x),x) Ex2: Expanding and factorizing functions
>>R.<x,y> = QQ
>>F= factor(x^33 +y^44); F
>>F= F.expand(); F Graphics and plotting Ex1: Plots drawn by sage: It is possible to call Sage commands from inside a LaTeX document.
The process goes as follows: Embedding Sage into LaTeX 1. SageTex package translate Sage code inside a LaTeX doc. into a Python file. 2. The python file is evaluated by Sage. 3. The result of each calculation is sent back to LaTeX. This even works for graphics, source-code and saved objects. To download Sagetex: http://www.ctan.org/pkg/sagetex Can be interfaced with many software packages: *Gnuplot (2D and 3D plots generator ) * R (Well-known package used for statistics ) *Mathematica (Computational Software used in science and Engineering) USER Friendly ! Ex3: Differentiating functions
f(x) = e^x * cos(x)
f_int(x) = integrate(f, x) Sage contains the
following packages: *CPython
*PyTable And 84 packages more! Solving ordinary diff, equations Code:
var('x, y, v')
f = desolve(x^2 * diff(y,x,2) + x*diff(y,x) + (x^2 - v^2) * y== 0,y, ivar=x) Analyzing Exp. data *MATLAB Sage Vs. MATLAB! 1. Sage is totally free, MATLAB is not. 2. Python packages can do nearly everything Matlab can do for signal processing. NumPy is like the Matlab core, SciPy is like Matlab toolboxes 3.Python is a general-purpose language. Matlab is purely for scientific computing,. 4. Sage supports symbolic computing. For MATLAB you have to purchase a toolbox "MuPAD", which even uses a different programming languages from MATLAB! It even knows special functions and polynomials. USE show() command to show the result printed as above! Start Using Sage? 1. Download it :
>>apt-add-repository -y ppa:aims/sagemath
>>apt-get install sagemath-upstream-binary 2. Go to:
www.sagemath.org 3. Check:
Documentation - Feature tour - Library. 4. ENJOY!