ITC Research Computing Support Colloquia Fall, 2004 Mathematics on the Desktop Presented by Kathy Gerber of the ITC Research Computing Support Group (Kathy Gerber, Ed Hall, Katherine Holcomb, Tim F. Jost Tolson) E-Mail: Res-Consult@Virginia.EDU http://www.itc.virginia.edu/researchers Telephone: 243-8800 The Maple worksheet from this talk, as well as notes from previous talks will be available on ITCWeb at http://www.itc.virginia.edu/research/talks/

Strengths: - Interactive, easy to use, with extensive built in and on-line help - Nice interface with output in standard mathematical notation - Within a single document the user can -- perform computations -- manipulate mathematical expressions -- describe the problem-solving process - Easy to program - Integration of algebraic, numerical and graphical facilities - Extensive library of functions including packages in areas such as precalculus, calculus, linear algebra, polynomials, etc. Weakness: - For large numerical calculations, environments such as Maple, Mathematica are not as fast as Matlab, R or compiled languages. But they are better as a tool for teaching and developing numerical algorithms.

nextprime(1007898743453453465767945830458254303);

NiMiRl5XRGUvJGUlendsTVhgTXUpKnkrIg==

evalf(Pi,100);

NiMkIl9xb3E2VWAjWy5HJykqKjNpRzFrInlJI2ZXXCg0I2U1diQqUnByPiUpR116S1FWRVlRS3oqZWBFZlRKISMqKg==

- Not truly comprehensive.

Basic HowTo Help Introduction Examples

Dictionary

HTML: Use Export from the File Menu. When Sections are expanded, one page with internal links is created. When Sections are collapsed, a separate html page is created for each Section and linked back to the main page. RTF: can be converted to Word. LATEX: When creating dvi files in the Windows environment from exported *.tex documents, the *.sty files from the ..\Maple 8\etc directory (in Windows) or the ../maple8/etc directory (in unix) must be available either by modifying the PATH, or copying them into the appropriate directory. In Windows, MikTeX's latex and dvips commands are useful. If desired, the resulting ps file can be converted to pdf with Adobe Distiller. RedHat users may need to install the rpm for dvips. Use a current version of dvips. For RedHat 8.0 this is tetex-dvips-1.0.7-57.1.i386.rpm. A vulnerability in earlier version may allow local or remote attackers who have print access to carefully craft a print job that would allow them to execute arbitrary code as the user 'lp'.

Latex snippets are easily generated with the latex command in Maple.Int(1/(x^2+1), x) = int(1/(x^2+1), x);

NiMvLUkkSW50RzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2JCokLCYqJEkieEdGKSIiIyIiIkYwRjAhIiJGLi1JJ2FyY3RhbkdGJjYjRi4=

latex(Int(1/(x^2+1), x) = int(1/(x^2+1), x));

\int \! \left( {x}^{2}+1 \right) ^{-1}{dx}=\arctan \left( x \right)

MAPLE TEXT: can be opened by Maple PLAIN TEXT: can also be opened by Maple showing execution statements only

"Many proofs in Discrete Math are really algorithms in disguise." - Doron ZeilbergerAn ExampleRene - A Maple Package for Stating and Proving Theorems in Geometryhttp://www.math.rutgers.edu/~zeilberg/tokhniot/RENE

Code Generation

External Calling

Random Tools

The CurveFitting contains functions to fit various types of curves to given data points.

restart;The following command allows you to use the short form of the function names in the CurveFitting package. Note that the PolynomialInterpolation, RationalInterpolation, Spline, and ThieleInterpolation functions replace the obsolete functions interp, ratinterp, spline, and thiele, respectively.with(CurveFitting);

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A feature of the CurveFitting package is that the routines allow you to specify the data points in two ways. The points can be provided as two lists, the first containing the independent values and the second containing the dependent values. The following command computes a polynomial that interpolates the points {(0,1), (1,3), (2,-1), (3,2)}.PolynomialInterpolation([0,1,2,3], [1,3,-1,2], v);

NiMsKiokSSJ2RzYiIiIkIyIjOCIiJyokRiUiIiMjISM+RixGJSMiI0dGJyIiIkYx

The points can also be provided as a list of lists.PolynomialInterpolation([[0,1],[1,3],[2,-1],[3,2]], v);

NiMsKiokSSJ2RzYiIiIkIyIjOCIiJyokRiUiIiMjISM+RixGJSMiI0dGJyIiIkYx

The ability to specify the data as a list of lists facilitates plotting the original data with the result. Example plots are provided in the next section. The following command allows you to use the short form of the function names in the plots package.with(plots):

Warning, the name changecoords has been redefined

Below, we define a list of 8 points, then plot these points by using the plots[pointplot] function. (Note that the short form of the function name is used below.)points1 := [[0,1],[1,2.5],[3,2.3],[4.2,5],[5,3.5],[5.8,4.2],[7,7],[8,10]]: pntplot1 := pointplot(points1,symbol=BOX):The next command uses the PolynomialInterpolation function to compute the unique polynomial that interpolates the data points.polycurve := PolynomialInterpolation(points1, v):The plot command shown below generates a plot of the result. The plots[display] function displays both this plot and the previously computed plot of the data points. It can be seen that the degree 7 polynomial passes through each of the 8 data points.polyplot := plot(polycurve,v=0..8): display([pntplot1,polyplot]);

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If n data points are supplied, then the interpolating polynomial has degree less than or equal to n-1. One well-known problem with fitting an interpolating polynomial through a large set of data points is the undesirable oscillations produced by a high-degree polynomial. In the plot above, the function value for v=2 is far from the value for v=1 or v=3.A smoother curve can be obtained by using the Spline function. This function returns a piecewise polynomial of default degree 3 that passes through the 8 data points. The second derivative is set to zero at the endpoints, and this results in a "natural" spline. The degree of the spline can be controlled by the degree option, described on the Spline help page.splcurve := Spline(points1, v);

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

The plot below shows that a smoother curve, without the unwanted oscillations, is produced.splplot := plot(splcurve,v=0..8): display([pntplot1,splplot]);

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The LeastSquares function can be used to find a curve that best fits the data in a least-squares sense, that is, minimizes the sum of the squares of the differences between the estimated values and the actual data. Unlike the curves described in the previous section, the least-squares curve may not necessarily pass through the given points. The least-squares method is often used to fit models to experimental data.The commands below show how the LeastSquares function is used to compute the best linear fit through the points defined at the beginning of the previous section. In the resulting plot, it can be seen that the curve passes near but not necessarily through all the points. lscurve := LeastSquares(points1,v); lsplot := plot(lscurve,v=0..8): display([pntplot1,lsplot]);

NiM+SShsc2N1cnZlRzYiLCYkIitsYXglRyYhIzUiIiJJInZHRiUkIjMtdjRaISopKnAoPiohIz0=

LSUlUExPVEc2Ji0lJ1BPSU5UU0c2LDckJCIiIUYqJCIiIkYqNyRGKyQiI0QhIiI3JCQiIiRGKiQiI0JGMDckJCIjVUYwJCIiJkYqNyRGOSQiI05GMDckJCIjZUYwRjc3JCQiIihGKkZCNyQkIiIpRiokIiM1RiotSSdTWU1CT0xHNiRJKnByb3RlY3RlZEdGTEkoX3N5c2xpYkc2IjYjSSRCT1hHRkstRko2JEZQRkgtJSdDVVJWRVNHNiQ3UzckRikkIjMxKysrbGF4JUcmISM9NyQkIjNFTExMTEJ4VjxGWiQiM1NKMSRcI1xrKSlvRlo3JCQiM3ltbW07JD41RSRGWiQiMz10RzxtSjslRylGWjckJCIzTUxMTExBS25cRlokIjNDL2s5IlFwTiYpKkZaNyQkIjM9TExMTGMkXG8nRlokIjNDYl4jUid5TFY2ISM8NyQkIjMpZW1tbV4mUSVSKUZaJCIzVWhAKFIkemMrOEZpbzckJCIzd0tMTCRRayN6KipGWiQiMy1mY3ZOLk1ZOUZpbzckJCIzKSkqKioqKlxZSj87IkZpbyQiM2lLYUw5I3pzZiJGaW83JCQiMz9MTEw9Ilw8TCJGaW8kIjNlSkhbPS9RYDxGaW83JCQiMyIpKioqKipcW0E0XSJGaW8kIjNJIyoqKTMvNSkqMz5GaW83JCQiM3dtbW0nM1FcbiJGaW8kIjNVbXo3S2AucD9GaW83JCQiM09MTExCNkBHPUZpbyQiMy8jMyVRcjcsNUFGaW83JCQiMyYpKioqKioqZi13Kz9GaW8kIjNpbmcjKil5OyhvQkZpbzckJCIzJSoqKioqKioqKnksdUBGaW8kIjN4JD5ybCdSMkdERmlvNyQkIjMpKioqKioqKlJQKTRNI0ZpbyQiM19MIypSTlRrIm8jRmlvNyQkIjNJTExMPVpnI1wjRmlvJCIzTiQ+ISk0Yys2I0dGaW83JCQiM2NtbW1FbipHbiNGaW8kIjNdQS1eUngjcClIRmlvNyQkIjNUbW1tMXhpREdGaW8kIjM+dj5KNl5TRkpGaW83JCQiMyEpKioqKipcOSFILklGaW8kIjMlZSE+RiFwODNIJEZpbzckJCIzSW1tbTE6YmdKRmlvJCIzJnBlcDYoelhOTUZpbzckJCIzPCsrK1hANExMRmlvJCIzMTwnKj5zYzolZiRGaW83JCQiMzErKytOO1IoXCRGaW8kIjNNZ3RKN01GWFBGaW83JCQiM3dtbW07NCMpb09GaW8kIjNSaSNRMyMqW0ghUkZpbzckJCIzam1tbTZsQ0VRRmlvJCIzUVdyaWVVdVpTRmlvNyQkIjNFTExMJEdeZypSRmlvJCIzc1JKZyJmRFI/JUZpbzckJCIzb0tMTD0yVnNURmlvJCIzXUE3Zy1UOm1WRmlvNyQkIjNmKioqKipcYHBmSyVGaW8kIjMsRl1LKVx1dF0lRmlvNyQkIjMhSExMTG0meiJcJUZpbyQiM3kqKmVjJVInKilmWUZpbzckJCIzcyoqKioqKnotNmpZRmlvJCIzWTI1bVBrWTxbRmlvNyQkIjM8KioqKioqNCMzMiRbRmlvJCIzdUE5IVIpemhyXEZpbzckJCIzTyoqKioqXCN5J0cqXEZpbyQiMzRhUUBKdnc/XkZpbzckJCIzRyoqKioqKkglPUg8JkZpbyQiMy1HRT91RVAnRyZGaW83JCQiMzVtbW0xPnFNYEZpbyQiM1pIVndnaTxOYUZpbzckJCIzJSkqKioqKioqSFN1XSZGaW8kIjN1VSYzNCZlMCVmJkZpbzckJCIzJ0hMTCRlcCdSbSZGaW8kIjM4cyRIUFBDIVFkRmlvNyQkIjMnKSoqKioqKlI+NE5lRmlvJCIzLzJFQycqKj5hKmVGaW83JCQiMyNlbW07QDJoKmZGaW8kIjMiMygpKiozLDxOLydGaW83JCQiM10qKioqKlxjOVc7J0ZpbyQiMyl6Ij1WajVLKT4nRmlvNyQkIjNMbW1tbWQnKkdqRmlvJCIzJVtYJ1E/Lm5cakZpbzckJCIzaioqKioqXGlON10nRmlvJCIzS10pKTRtKj0iM2xGaW83JCQiM2FMTEx0PjpubUZpbyQiM01OIikpUiVRc2dtRmlvNyQkIjM1TExMLmEjbyRvRmlvJCIzJnoiMyVHUCV5O29GaW83JCQiM2FtbW1eUTQwcUZpbyQiMy9TOHNURWJycEZpbzckJCIzeSoqKioqKnpdcmZyRmlvJCIzJHokPkAyJ29QNihGaW83JCQiM2dtbW1jJUdwTChGaW8kIjNhUXdzX1R3d3NGaW83JCQiMy9MTEw4LVYmXChGaW8kIjMlUSkzczYkXERVKEZpbzckJCIzPSsrK1hoVWt3RmlvJCIzJ3kkKlF6cCcpemQoRmlvNyQkIjM9KysrOm88RXlGaW8kIjMxKj44KjQsd0V4RmlvNyRGRSQiM1kheXcpZXVqJyl5RmlvLSUmQ09MT1JHNiYlJFJHQkckRkhGMCRGKkYwRmldbC0lK0FYRVNMQUJFTFNHNiRRInZGTlEhRk4tJSVWSUVXRzYkO0ZpXWwkIiMhKUYwOyQiLFYoNFohUiQhIzYkIi4yXC9WKj01RmhebA==

In the previous example, the default curve used to fit the points is a linear polynomial av+b with parameters a and b. The LeastSquares function allows you to provide a different type of curve and to specify the parameters to optimize. In addition, weights associated with the data points can be defined. See the LeastSquares help page for more details about these options.The LeastSquares function requires that the model curve be linear in the parameters. In some cases, a nonlinear model can be transformed to allow a least-squares fit. For example, if you wish to use the model w=a*exp(b*v), you can take the logarithm of both sides of the equation and apply the transformation {y=log(w), c=log(a)} to obtain the model y=c+b*v, which is linear in the parameters c and b.newpoints1 := map(x->[x[1],evalf(log(x[2]))], points1); newlscurve := LeastSquares(newpoints1,v);

NiM+SStuZXdwb2ludHMxRzYiNyo3JCIiISRGKEYoNyQiIiIkIis+dCFIOyohIzU3JCIiJCQiK0g3NEgkKUYuNyQkIiNVISIiJCIrN3pWNDshIio3JCIiJiQiK29Id183Rjk3JCQiI2VGNiQiK0RYM045Rjk3JCIiKCQiK1wsImYlPkY5NyQiIikkIiskNCZlLUJGOQ==NiM+SStuZXdsc2N1cnZlRzYiLCYkIiskNG5RdSMhIzUiIiJJInZHRiUkIjNPaXUvYic+QlEjISM9

This result gives values for c and b. The following commands show the resulting plot, after transforming back to the original model.a := exp(coeff(newlscurve,v,0)); b := coeff(newlscurve,v,1); newlsplot := plot(a*exp(b*v),v=0..8): display([pntplot1,newlsplot]);

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The Optimization package provides commands to find the minimum or maximum of various types of functions subject to various types of constraints. This worksheet provides a few basic examples of each type of problem the package is capable of solving. Further information can be found on the help pages for the package and each of the individual package members. In this worksheet, we will be minimizing a function (referred to as the objective function) subject to a number of constraints. Certain maximize examples are included as well. In any of the examples, the maximize option can be added to the command to find the maximum instead of the minimum. Also note that in each case we are only finding a locally optimal value.

restart;The following command allows you to use the short form of the command names in the Optimization package. with(Optimization); with(plots):

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The commands in the Optimization package allow you to specify the objective function and the constraints in several different ways. This worksheet deals with the algebraic form of the objective function and constraints. The other forms are Matrix form and procedure form where Matrix form is covered in a separate example worksheet.In general, an optimization problem is of the formThe Optimization package handles several types of objective and constraint functions. Each type of problem is a subtype of the next one.Objective Function/Constraint/CommandLinear/Linear/LPSolveQuadratic/Linear/QPSolveNonlinear(General)/Nonlinear(General)/NLPSolve There is also a minimize command that will attempt to automatically select the best algorithm for a given problem. In addition, there is a command, LSSolve, which minimizes functions of the formNiMvLSUiZkc2IyUieEcqKCIiIkYpIiIjISIiLSUkU3VtRzYkKiQtJiUickc2IyUiaUdGJkYqL0Y0O0YpJSJuR0Yp

For a first example, we have a simplex two dimensional linear programming problem.subject toobj := -2*x-y;

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cnsts := [y<=4*x+1/2,y<=-5*x+2,x>=0,y>=0];

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The plot below shows the feasible region in yellow, the contours of the objective function, and the optimal solution as a green circle.p1 := inequal(cnsts, x=-0.5..2, y=-0.5..2, optionsexcluded=(colour=white), optionsfeasible=(colour=yellow)): p2 := contourplot(obj, x=-0.5..2, y=-0.5..2): p3 := pointplot({[0.1666,1.166]}, symbolsize=13, colour=green): display(p1, p2, p3);

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The command returns the optimal function values, as well as the point at which the optimal value occurs.LPSolve(obj, cnsts);

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Alternatively, we could use the first two constraints and the nonnegative option.LPSolve(obj, cnsts[1..2], assume=nonnegative);

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The first element of the solution is the minimum value that the objective function obtains, while satisfying the constraints. The second element indicates a point where the minimum is reached. This point is not necessarily unique.

We can also include equality constraint as the next example shows. This example also demonstrates the maximize option.obj := 2*x+y+z;

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cnsts := [y<=4*x+1/2,y<=-5*x+2,z=-2/3*x-2/3*y+20/3];

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LPSolve(obj, cnsts, assume=nonnegative, maximize);

NiM3JCQiL3l4eHh4eHMhIzg3JS9JInpHNiIkIjMrMnl4eHh4eGQhIzwvSSJ5R0YqJCIzX21tbW1tbW02Ri0vSSJ4R0YqJCIzZW1tbW1tbW07ISM9

For a first example of a quadratic program, we will use:obj := 4*x^2-y+x+5;

NiM+SSRvYmpHNiIsKiokSSJ4R0YlIiIjIiIlSSJ5R0YlISIiRigiIiIiIiZGLQ==

cnsts := [x+y-7*x>=-11, 11/2*x+y<=0,x>=-4];

NiM+SSZjbnN0c0c2IjclMSEjNiwmSSJ4R0YlISInSSJ5R0YlIiIiMSwmRiojIiM2IiIjRixGLSIiITEhIiVGKg==

The plot below shows the feasible region in yellow and the contours of the objective function. The green circle indicates the optimal point.p1 := contourplot(obj, x=-4..4, y=-10..10, contours=30): p2 := inequal(cnsts, x=-4..4, y=-10..10, optionsexcluded=(colour=white), optionsfeasible=(colour=yellow)): p3 := pointplot({[-0.8125,4.486]}, symbolsize=13, colour=green): display(p1,p2,p3);

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