Mathematica Programming Language–An Introduction
- by JoshReuben
The Mathematica http://www.wolfram.com/mathematica/ programming model consists of a kernel computation engine (or grid of such engines) and a front-end of notebook instances that communicate with the kernel throughout a session. The programming model of Mathematica is incredibly rich & powerful – besides numeric calculations, it supports symbols (eg Pi, I, E) and control flow logic. obviously I could use this as a simple calculator: 5 * 10 --> 50 but this language is much more than that! for example, I could use control flow logic & setup a simple infinite loop: x=1; While [x>0, x=x,x+1] Different brackets have different purposes: square brackets for function arguments: Cos[x] round brackets for grouping: (1+2)*3 curly brackets for lists: {1,2,3,4} The power of Mathematica (as opposed to say Matlab) is that it gives exact symbolic answers instead of a rounded numeric approximation (unless you request it): Mathematica lets you define scoped variables (symbols): a=1; b=2; c=a+b --> 5 these variables can contain symbolic values – you can think of these as partially computed functions: use Clear[x] or Remove[x] to zero or dereference a variable. To compute a numerical approximation to n significant digits (default n=6), use N[x,n] or the //N prefix: Pi //N -->3.14159 N[Pi,50] --> 3.1415926535897932384626433832795028841971693993751 The kernel uses % to reference the lastcalculation result, %% the 2nd last, %%% the 3rd last etc –> clearer statements: eg instead of: Sqrt[Pi+Sqrt[Sqrt[Pi+Sqrt[Pi]]] do: Sqrt[Pi]; Sqrt[Pi+%]; Sqrt[Pi+%] The help system supports wildcards, so I can search for functions like so: ?Inv* Mathematica supports some very powerful programming constructs and a rich function library that allow you to do things that you would have to write allot of code for in a language like C++. the Factor function – factorization: Factor[x^3 – 6*x^2 +11x – 6] --> (-3+x) (-2+x) (-1+x) the Solve function – find the roots of an equation: Solve[x^3 – 2x + 1 == 0] --> the Expand function – express (1+x)^10 in polynomial form: Expand[(1+x)^10] --> 1+10x+45x^2+120x^3+210x^4+252x^5+210x^6+120x^7+45x^8+10x^9+x^10 the Prime function – what is the 1000th prime? Prime[1000] -->7919 Mathematica also has some powerful graphics capabilities: the Plot function – plot the graph of y=Sin x in a single period: Plot[Sin[x], {x,0,2*Pi}] you can also plot 3D surfaces of functions using Plot3D function
