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Additional info for A Robust Embedded Data from Wavelet Coefficients
0 Sometimes the piecewise recognition requires some help, as in the following example (PrimePi x gives the number of primes less than or equal to x). Plot PrimePi x , x, 0, 50 , "SymbolicPiecewiseSubdivision" 3 7 13 19 29 37 True 43 15 12 9 6 3 0 2 5 11 17 23 31 41 47 In this case, it is simpler to just specify the discontinuities by adding the option Exclusions Range 50 . 6 ListPlot If one wishes to visualize a list of numbers quickly, then ListPlot is the command to use. Recall that the Fibonacci numbers are defined by F0 recursive formula Fn Fn 1 0, F1 1, and the Fn 2.
8 Algebraic Manipulations Here is a sampling of some functions available for algebraic manipulation. Together[3/x + x/3] 9 x2 3x Apart 3x x 2 2x 6 13 2 27 x 13 9 2x 2 y y2 Expand x x 2xy 9 x2 y 2 x y2 x2 y2 Simplify[%] x 2 x y 1 y Simplify accepts assumptions as an additional argument. Simplify Sin n Π , n Integers 18 Chapter 0 A Brief Introduction 0 Sometimes one must appeal to the more powerful FullSimplify to get results. For example, FullSimplify includes a factorization step. f Expand x Simplify f 6 11 x 1 6 x2 x 2 x 3 ; x3 FullSimplify f 1 x 2 x 3 x FunctionExpand is usually faster than FullSimplify and sometimes works when FullSimplify does not.
9 Customizing Mathematica The option inspector, available in the Format menu, allows easy customization of many features of notebooks. To make global changes, select Global Preferences in the upper left popup menu. To change the default grouping mechanism from Automatic to Manual, just look up CellGrouping, change the Automatic entry to Manual, and hit return. This is a choice I make because I prefer manual grouping. Another useful item has to do with initialization cells. If a notebook contains cells that have been declared to be initialization cells (Cell >> Cell Properties >> Initialization Cell menu item), then at the time of first evaluation of any input, a dialog box will appear asking the user if he or she wishes the initialization cells to be evaluated.