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Topic: Using Mathematica
Replies: 2   Last Post: Aug 18, 2011 2:38 AM

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David Park

Posts: 1,560
Registered: 5/19/07
Using Mathematica
Posted: Aug 17, 2011 5:17 AM
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There are many postings to MathGroup related to problems of exporting to or
interfacing Mathematica with other applications. Although I recognize that
there may be some cases where this is really useful (acquisition of data or
interfacing with a supercomputer say), in most cases it is nothing more than
exporting to a far inferior medium, or finding ways to organize technical
work, which could be done perfectly well and even better within Mathematica
.



Too many users are ready to jump ship before they have even learned to sail
it. The problem with this is that it detracts from learning how to get the
most out of Mathematica. It is such a new and powerful medium that none of
us truly know how to use it to best advantage. How much time did it take us
to learn how to think and write decently in our own language? How much more
difficult is it to think about, develop and express technical ideas?



Mathematica has superb capabilities for computer algebra, graphics, active
calculation, dynamics and textual discussion, presentation and formatting as
coherent and elegant documents. With Workbench we have an excellent way to
generate, preserve, document and organize technical material - say within a
project or for a book. (Most day to day work can be done in Mathematica.)
WRI has reasonable purchase options for anyone interested in math and
science. Everyone should get it. If they don't want to, then it's "the happy
few". There is no reason to go to inferior and out-of-date media. There is
no reason to restrict Mathematica use to being a "super programmable
graphical calculator".



It's true that there are many ham-fisted features on the fringes of
Mathematica, Grid features that don't work properly, file saving in M8 that
seems to have been bollix up by the advent of CDF (which I consider
questionable and inadequate and now probably unnecessary) and Workbench has
a lot of ragged behavior. They don't seem to have fully embraced it use
outside of WRI documentation. But none of this is fatal and it can be fixed
- with a little pressure from users.



Yesterday there was a question about composing a "book cover" with
Mathematica. It's simple! We just lay down a piece of paper and write on
it.



Here is a sample graphic for the cover, in this case a contour plot for a
complex function. We only need to produce the primitives, not the entire
plot.



<< Presentations`



contourprimitives =

With[

{f = Function[z, (z (z - 1))/(z - I)],

zmin = -(1 + I),

zmax = 1.75 (1 + I),

contourlist = {0, 0.1, 0.2, .5, 1, 2, 3, 4, 5, 6, 10, 20, 100,

500}},

ComplexCartesianContour[f[z], {z, zmin, zmax}, Abs,

Contours -> contourlist,

ColorFunctionScaling -> False,

ColorFunction -> (ContourColors[contourlist,

ColorData["SolarColors"]][#] &),

ContourLabels -> None,

PlotRange -> {0, 500}]

];



Then we define a 6.75 by 9.5 piece of paper, write the various text items on
it, and place the contour primitives by scaling and translating them to
place. Finally we Magnify to the desired size.



Draw2D[

{Text[Style["My Wonderful Book", Bold, 28, FontFamily -> "Times"], {0.3,
8}, {-1, 0}],

Text[Style["Mr. Author", Bold, 14, FontFamily -> "Times"], {0.3, 7.2},
{-1, 0}],

contourprimitives // ScaleOp[1.5, {-1, -1}] // TranslateOp[{2.25, 3}],

Text[Style["Acme Publishing", Bold, 8, FontFamily -> "Helvetica"], {6,
0.5}, {1, 0}]},



PlotRange -> {{0, 6.75}, {0, 9.5}},

Background -> LightBlue,

ImageSize -> 300] // Magnify[#, 6.75 72/300] &







David Park

djmpark@comcast.net

<http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark/




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