Maple Programming: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=226
en-us2014 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemWed, 16 Apr 2014 16:51:48 GMTWed, 16 Apr 2014 16:51:48 GMTNew applications in the Maple Programming categoryhttp://www.mapleprimes.com/images/mapleapps.gifMaple Programming: New Applications
http://www.maplesoft.com/applications/category.aspx?cid=226
Generalized, byte-oriented, to reverse engineering resistant, fast stream-cipher
http://www.maplesoft.com/applications/view.aspx?SID=153499&ref=Feed
<p>A new numerous family of strong, to reverse engineering resistant, and fast byte-oriented stream-ciphers has been presented. One ought to unpack the file gbosc.zip, open the worksheet gbosc.mw in the Maple session, read it and test the application described.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Generalized, byte-oriented, to reverse engineering resistant, fast stream-cipher" align="left"/><p>A new numerous family of strong, to reverse engineering resistant, and fast byte-oriented stream-ciphers has been presented. One ought to unpack the file gbosc.zip, open the worksheet gbosc.mw in the Maple session, read it and test the application described.</p>153499Tue, 28 Jan 2014 05:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyClassroom Tips and Techniques: Slider-Control of Parameters in an ODE
http://www.maplesoft.com/applications/view.aspx?SID=152112&ref=Feed
Several ways to provide slider-control of parameters in a differential equation are considered. In particular, the cases of one and two parameters are illustrated, and for the case of two parameters, a 2-dimensional slider is constructed.<img src="/view.aspx?si=152112/thumb.jpg" alt="Classroom Tips and Techniques: Slider-Control of Parameters in an ODE" align="left"/>Several ways to provide slider-control of parameters in a differential equation are considered. In particular, the cases of one and two parameters are illustrated, and for the case of two parameters, a 2-dimensional slider is constructed.152112Mon, 23 Sep 2013 04:00:00 ZDr. Robert LopezDr. Robert LopezHohmann Elliptic Transfer Orbit with Animation
http://www.maplesoft.com/applications/view.aspx?SID=151351&ref=Feed
<p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p><img src="/view.aspx?si=151351/Elliptic_image1.jpg" alt="Hohmann Elliptic Transfer Orbit with Animation" align="left"/><p>Abstract<br /><br />The main purpose of this article is to show how to use Hohmann elliptic transfer in two situations:<br />a- When one manned spaceship is trying to catch up with an other one <br />on the same circular orbit around Earth.<br />b- When delivering a payload from Earth to a space station on a circular <br />orbit around Earth using 2-stage rocket .<br /><br />The way we set up the problem is as follows:<br />Consider two manned spaceships with astronauts Sally & Igor , the latter<br />lagging behind Sally by a given angle = 4.5 degrees while both are on the same<br />circular orbit C2 about Earth. A 2d lower circular orbit C1 is given. <br />Find the Hohmann elliptic orbit that is tangent to both orbits which allows<br />Sally to maneuver on C1 then to get back to the circular orbit C2 alongside Igor.<br /><br />Though the math was correct , however the final result we found was not !! <br />It was somehow tricky to find the culprit!<br />We have to restate the problem to get the correct answer. <br />The animation was then set up using the correct data. <br />The animation is a good teaching help for two reasons:<br />1- it gives a 'hand on' experience for anyone who wants to fully understand it,<br />2- it is a good lesson in Maple programming with many loops of the type 'if..then'.<br /><br />Warning<br /><br />This particular animation is a hog for the CPU memory since data accumulated <br />for plotting reached 20 MB! This is the size of this article when animation is <br />executed. For this reason and to be able to upload it I left the animation <br />procedure non executed which drops the size of the article to 300KB.<br /><br />Conclusion<br /><br />If I can get someone interested in the subject of this article in such away that he or <br />she would seek further information for learning from other sources, my efforts<br />would be well rewarded.</p>151351Wed, 04 Sep 2013 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyMaple `Keyless` Base b Encryption Scheme
http://www.maplesoft.com/applications/view.aspx?SID=149026&ref=Feed
In this submission it will be shown that the convert/base built-in function can be used to create many new tools which can encrypt or decrypt any file selected. Such a tool, named Maple "keyless` base b encryption scheme, allows to determine the admissible number of elements of the set of ASCII decimals which will be present in the encrypted file, and to choose all the elements of this set.<img src="/applications/images/app_image_blank_lg.jpg" alt="Maple `Keyless` Base b Encryption Scheme" align="left"/>In this submission it will be shown that the convert/base built-in function can be used to create many new tools which can encrypt or decrypt any file selected. Such a tool, named Maple "keyless` base b encryption scheme, allows to determine the admissible number of elements of the set of ASCII decimals which will be present in the encrypted file, and to choose all the elements of this set.149026Mon, 01 Jul 2013 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyBase 64 "Keyless" File Encryption
http://www.maplesoft.com/applications/view.aspx?SID=145918&ref=Feed
Abstract: A "keyless" cipher not using complex mathematical formulas but applying non-linear transformations of base 64 encoding scheme has been described. The word "keyless" means that the encrypting/decrypting application itself fulfills the role of the secret key and should be carefully watched and stored. Presented tool is mainly suitable for cryptographic protection of e-mail enclosures.<BR>
<P>
Note: For proper functioning of this application, this application must be saved in a location with no spaces in the path name, e.g. C:\keyless.<img src="/applications/images/app_image_blank_lg.jpg" alt="Base 64 "Keyless" File Encryption" align="left"/>Abstract: A "keyless" cipher not using complex mathematical formulas but applying non-linear transformations of base 64 encoding scheme has been described. The word "keyless" means that the encrypting/decrypting application itself fulfills the role of the secret key and should be carefully watched and stored. Presented tool is mainly suitable for cryptographic protection of e-mail enclosures.<BR>
<P>
Note: For proper functioning of this application, this application must be saved in a location with no spaces in the path name, e.g. C:\keyless.145918Mon, 15 Apr 2013 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyGems 26-30 from the Red Book of Maple Magic
http://www.maplesoft.com/applications/view.aspx?SID=141091&ref=Feed
<p>In 2011, this column published five "Maple Magic" articles, each containing five "gems" gleaned from interactions with Maple and the Maplesoft programmers. Here are five more recent additions to the Red Book, every one of which contained something about Maple that was a surprise to me, experienced Maple user that I am.</p><img src="/view.aspx?si=141091/thumb.jpg" alt="Gems 26-30 from the Red Book of Maple Magic" align="left"/><p>In 2011, this column published five "Maple Magic" articles, each containing five "gems" gleaned from interactions with Maple and the Maplesoft programmers. Here are five more recent additions to the Red Book, every one of which contained something about Maple that was a surprise to me, experienced Maple user that I am.</p>141091Tue, 04 Dec 2012 05:00:00 ZDr. Robert LopezDr. Robert LopezObject-Oriented Programming in Maple 16
http://www.maplesoft.com/applications/view.aspx?SID=132199&ref=Feed
The Maple language is a full programming language designed for mathematical computation, combining the best principles from procedural, functional, and object-oriented programming. Maple 16 adds support for light-weight objects for enhanced object-oriented programming. Such objects integrate closely with Maple using operator overloading, making your objects almost indistinguishable from built-in Maple types. This example illustrates the use of light-weight objects.<img src="/view.aspx?si=132199/thumb.jpg" alt="Object-Oriented Programming in Maple 16" align="left"/>The Maple language is a full programming language designed for mathematical computation, combining the best principles from procedural, functional, and object-oriented programming. Maple 16 adds support for light-weight objects for enhanced object-oriented programming. Such objects integrate closely with Maple using operator overloading, making your objects almost indistinguishable from built-in Maple types. This example illustrates the use of light-weight objects.132199Tue, 27 Mar 2012 04:00:00 ZMaplesoftMaplesoftSpherical Pendulum with Animation
http://www.maplesoft.com/applications/view.aspx?SID=132143&ref=Feed
<p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br /> " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations & programming as I did.<br /><br /></p><img src="/view.aspx?si=132143/433082\Spherical_Pendulum_p.jpg" alt="Spherical Pendulum with Animation" align="left"/><p>Some years ago I have written a Maple document ( already on Maple's online) on the subject of animating a simple pendulum for large angles of oscillation. This gave me the chance to test Maple command JacobiSN(time, k). I was very much pleased to see Maple do a wonderful job in getting these Jacobi's elliptic functions without a glitch.<br />Today I am back to these same functions for a similar purpose though much more sophisticated than the previous one.<br />The idea is:<br />1- to get the differential equations of motion for the Spherical Pendulum (SP),<br />2- to solve them,<br />3- to use Maple for finding the inverse of these Elliptic Integrals i.e. finding the displacement z as function of time,<br />4- to get a set of coordinates [x, y, z] for the positions of the bob at different times for plotting,<br />5- finally to work out the necessary steps for the purpose of animation.<br />It turns out that even with only 3 oscillations where each is defined with only 20 positions of the bob for a total of 60 points on the graph, the animation is so overwhelming that Maple reports:<br /> " the length of the output exceeds 1 million".<br />Not withstanding this warning, Maple did a perfect job by getting the animation to my satisfaction. <br />Note that with only 60 positions of the bob, the present article length is equal to 11.3 MB! To be able to upload it, I have to save it without running the last command related to the animation. Doing so I reduced it to a mere 570 KB.<br /><br />It was tiring to get through a jumble of formulas, calculations and programming so I wonder why I have to go through all this trouble to get this animation and yet one can get the same thing with much better animation from the internet. I think the reason is the challenge to be able to do things that others have done before and secondly the idea of creating something form nothing then to see it working as expected, gives (at least to me) a great deal of pleasure and satisfaction.<br />This is beside the fact that, to my knowledge, no such animation for (SP) has been published on Maple online with detailed calculations & programming as I did.<br /><br /></p>132143Mon, 26 Mar 2012 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyCBC Mode Fast AES Directory Encryption/Decryption
http://www.maplesoft.com/applications/view.aspx?SID=129039&ref=Feed
<p>The application shows how to implement a Maple wrapper for a binary file executing the AES algorithm about 5 000 times faster than two Maple implementations of this algorithm published in Maple Application Center.</p><img src="/view.aspx?si=129039/CBCdirect_sm.jpg" alt="CBC Mode Fast AES Directory Encryption/Decryption" align="left"/><p>The application shows how to implement a Maple wrapper for a binary file executing the AES algorithm about 5 000 times faster than two Maple implementations of this algorithm published in Maple Application Center.</p>129039Fri, 23 Dec 2011 05:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyMaple User's Calendar Generators
http://www.maplesoft.com/applications/view.aspx?SID=129018&ref=Feed
<p>In the application the user-friendly interactive tool for creating calendars for any year has been presented. The application is an example of programming using strongly system dependent Components palette.</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Maple User's Calendar Generators" align="left"/><p>In the application the user-friendly interactive tool for creating calendars for any year has been presented. The application is an example of programming using strongly system dependent Components palette.</p>129018Thu, 22 Dec 2011 05:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyBase64 Format Encoding/Decoding
http://www.maplesoft.com/applications/view.aspx?SID=128969&ref=Feed
<p>Base64 format is useful for encoding arbitrary binary information as, for example, *.exe files, encrypted messages, cryptographic keys, audio and image files, for transmission by electronic mail. The application applies the freeware executable published by John Walker (<a href="http://www.fourmilab.ch">http://www.fourmilab.ch</a>) and allows to encode list of bytes, containing arbitrary values, 0 including, to base64 string format and decode obtained string again into list of bytes. Similarly it is possible to encode/decode arbitrary files. File encoded to base64 format has original file name with the added extension *.b64. For safety reasons, name of the decoded file is the concatenation of an original file name and dash character (_).</p><img src="/applications/images/app_image_blank_lg.jpg" alt="Base64 Format Encoding/Decoding" align="left"/><p>Base64 format is useful for encoding arbitrary binary information as, for example, *.exe files, encrypted messages, cryptographic keys, audio and image files, for transmission by electronic mail. The application applies the freeware executable published by John Walker (<a href="http://www.fourmilab.ch">http://www.fourmilab.ch</a>) and allows to encode list of bytes, containing arbitrary values, 0 including, to base64 string format and decode obtained string again into list of bytes. Similarly it is possible to encode/decode arbitrary files. File encoded to base64 format has original file name with the added extension *.b64. For safety reasons, name of the decoded file is the concatenation of an original file name and dash character (_).</p>128969Mon, 19 Dec 2011 05:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyUsing Maple to Solve a Peg Board Puzzle Game
http://www.maplesoft.com/applications/view.aspx?SID=119107&ref=Feed
With the addition of Maple 15's new parallel multi-process features, and beefed up Grid Computing package, I was recently thinking about big examples that could show off how fast Maple can run on modern multi-core computers. My mind turned back to this toy game, and I wondered just how long it would take to find a solution in Maple.<img src="/view.aspx?si=119107/thumb.jpg" alt="Using Maple to Solve a Peg Board Puzzle Game" align="left"/>With the addition of Maple 15's new parallel multi-process features, and beefed up Grid Computing package, I was recently thinking about big examples that could show off how fast Maple can run on modern multi-core computers. My mind turned back to this toy game, and I wondered just how long it would take to find a solution in Maple.119107Thu, 21 Apr 2011 04:00:00 ZPaul DeMarcoPaul DeMarcoTracking Data in Maple
http://www.maplesoft.com/applications/view.aspx?SID=119105&ref=Feed
This application is partially inspired by the BMI tracker in Nintendo's WiiFit application. It could be easily used to track a weight loss goal, but could also be used to track other quantifiable goals. It also takes advantage of two new features in Maple 15, specifically the Finance package, and the DataTable document component.<img src="/view.aspx?si=119105/thumb.jpg" alt="Tracking Data in Maple" align="left"/>This application is partially inspired by the BMI tracker in Nintendo's WiiFit application. It could be easily used to track a weight loss goal, but could also be used to track other quantifiable goals. It also takes advantage of two new features in Maple 15, specifically the Finance package, and the DataTable document component.119105Thu, 21 Apr 2011 04:00:00 ZJohn MayJohn MayInteractive Applications in Maple 15
http://www.maplesoft.com/applications/view.aspx?SID=103810&ref=Feed
With Maple 15, you can quickly build sophisticated applications that include interactive elements such as sliders, buttons, and dials in your document. Simply drag and drop these interface components into your document, and then define their behavior using a few simple Maple commands. In Maple 15, the new data table is part of this collection of interactive components, so you can build even more powerful applications that receive, display, and use tabular data. After creating an application, you can use it within Maple or share it on the web using MapleNet. Saving the unmodified document onto the MapleNet server is all it takes to deploy and share your work.<img src="/view.aspx?si=103810/thumb.jpg" alt="Interactive Applications in Maple 15" align="left"/>With Maple 15, you can quickly build sophisticated applications that include interactive elements such as sliders, buttons, and dials in your document. Simply drag and drop these interface components into your document, and then define their behavior using a few simple Maple commands. In Maple 15, the new data table is part of this collection of interactive components, so you can build even more powerful applications that receive, display, and use tabular data. After creating an application, you can use it within Maple or share it on the web using MapleNet. Saving the unmodified document onto the MapleNet server is all it takes to deploy and share your work.103810Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftVisualizing an Optimization Problem
http://www.maplesoft.com/applications/view.aspx?SID=103815&ref=Feed
In this example we want to optimize a nonlinear constraint problem. Instead of just getting a final number from a black-box routine, we want to look at the constraints and visualize partial solutions. The following problem is described by Rakesh Angira and B.V. Babu in section 6 of the paper "Optimization of Non-Linear Chemical Processes using Modified Differential Evolution" ( http://discovery.bits-pilani.ac.in/~bvbabu/RB_IICAI-05_147.pdf). The goal is to determine the optimal operation of an alkylation unit, commonly used in the petroleum industry.<img src="/view.aspx?si=103815/thumb.jpg" alt="Visualizing an Optimization Problem" align="left"/>In this example we want to optimize a nonlinear constraint problem. Instead of just getting a final number from a black-box routine, we want to look at the constraints and visualize partial solutions. The following problem is described by Rakesh Angira and B.V. Babu in section 6 of the paper "Optimization of Non-Linear Chemical Processes using Modified Differential Evolution" ( http://discovery.bits-pilani.ac.in/~bvbabu/RB_IICAI-05_147.pdf). The goal is to determine the optimal operation of an alkylation unit, commonly used in the petroleum industry.103815Wed, 06 Apr 2011 04:00:00 ZMaplesoftMaplesoftTerminator circle with animation
http://www.maplesoft.com/applications/view.aspx?SID=100509&ref=Feed
<p>The idea of writing this article came to me on the 25th of June 2003 when I was listening to Cairo radio announcing that Maghrib prayer is due in Cairo city while I was sitting in my home town at 400 miles North East of Cairo. What is interesting is that at exactly the same time a next door mosque, in my home town, was also calling for the Maghrib prayer. This makes me wonder : how could it be that sunset is simultaneous at two locations separated by a distance of 400 miles from each other and at different Latitudes & Longitudes. As a reminder Maghrib prayer time occurs everywhere at sunset. <br />In what follows we explore this issue and try to prove or disprove the simultaneity of sunset at two different locations. In so doing we are led to some interesting conclusions and as a bonus we got ourselves an animation of the Terminator circle on the surface of the globe. <br />Aside from its modest value and its originality ( I am not aware of anything similar to it ) this article is a good exercise in Maple programming. <br />May this article be a stimulus for some readers to get interested in Astronomy which is a science as ancient as the early human civilizations. <br /><br /></p><img src="/view.aspx?si=100509/thumb.jpg" alt="Terminator circle with animation" align="left"/><p>The idea of writing this article came to me on the 25th of June 2003 when I was listening to Cairo radio announcing that Maghrib prayer is due in Cairo city while I was sitting in my home town at 400 miles North East of Cairo. What is interesting is that at exactly the same time a next door mosque, in my home town, was also calling for the Maghrib prayer. This makes me wonder : how could it be that sunset is simultaneous at two locations separated by a distance of 400 miles from each other and at different Latitudes & Longitudes. As a reminder Maghrib prayer time occurs everywhere at sunset. <br />In what follows we explore this issue and try to prove or disprove the simultaneity of sunset at two different locations. In so doing we are led to some interesting conclusions and as a bonus we got ourselves an animation of the Terminator circle on the surface of the globe. <br />Aside from its modest value and its originality ( I am not aware of anything similar to it ) this article is a good exercise in Maple programming. <br />May this article be a stimulus for some readers to get interested in Astronomy which is a science as ancient as the early human civilizations. <br /><br /></p>100509Tue, 28 Dec 2010 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyTwo Bodies Revolving Around Their Center of Mass with ANIMATION
http://www.maplesoft.com/applications/view.aspx?SID=99587&ref=Feed
<p>For any isolated system of two bodies revolving around each other by virtue of the gravitational attraction that each one exerts on the other, the general motion is best described by using a frame of reference attached to their common Center of Mass (CM). The reason is that their motion is in fact around their CM as we shall see. <br />For an isolated system the momentum remains constant so that the CM is either moving along a straight line or is at rest.<br />For an Earth's satellite we can always take the motion of the satellite relative to Earth using a geocentric frame of reference. <br />The reason is that:<br /> the mass of the satellite being insignificant compared to Earth's <br /> mass, the revolving satellite doesn't affect Earth at all so<br /> that the CM of Earth-satellite system is still the center of the Earth.<br /> Hence we use the center of the Earth as the origin of a rectangular<br /> coordinates system.<br /> <br />In this article we use Maple powerful animation routines to study the motion of two bodies having comparable masses revolving about each other by showing: <br />1- their combined motion as seen from their common Center of Mass,<br />2- their relative motion as if one of them is fixed and the other one is moving. <br />In this last instance the frame of reference is attached to the the body that is supposed to be at rest.<br /><br /></p><img src="/view.aspx?si=99587/thumb.jpg" alt="Two Bodies Revolving Around Their Center of Mass with ANIMATION" align="left"/><p>For any isolated system of two bodies revolving around each other by virtue of the gravitational attraction that each one exerts on the other, the general motion is best described by using a frame of reference attached to their common Center of Mass (CM). The reason is that their motion is in fact around their CM as we shall see. <br />For an isolated system the momentum remains constant so that the CM is either moving along a straight line or is at rest.<br />For an Earth's satellite we can always take the motion of the satellite relative to Earth using a geocentric frame of reference. <br />The reason is that:<br /> the mass of the satellite being insignificant compared to Earth's <br /> mass, the revolving satellite doesn't affect Earth at all so<br /> that the CM of Earth-satellite system is still the center of the Earth.<br /> Hence we use the center of the Earth as the origin of a rectangular<br /> coordinates system.<br /> <br />In this article we use Maple powerful animation routines to study the motion of two bodies having comparable masses revolving about each other by showing: <br />1- their combined motion as seen from their common Center of Mass,<br />2- their relative motion as if one of them is fixed and the other one is moving. <br />In this last instance the frame of reference is attached to the the body that is supposed to be at rest.<br /><br /></p>99587Mon, 29 Nov 2010 05:00:00 ZDr. Ahmed BaroudyDr. Ahmed BaroudyUsing Command Completion
http://www.maplesoft.com/applications/view.aspx?SID=6517&ref=Feed
Maple's command completion feature helps you avoid typos, reduces the need to memorize exact command names, provides an easy keyboard method for entering symbols, and as of Maple 12, provides guidance for calling sequences of commands.
The command completion feature allows you to type the first few characters in the command or symbol name, and then ask Maple to provide a list of possible endings. You then choose the appropriate ending from the list provided. In this Tips and Techniques, you will learn how to use command completion to finish command names, obtain fill-in-the-blank command templates, and enter mathematical symbols straight from the keyboard.<img src="/view.aspx?si=6517/Untitled-1.jpg" alt="Using Command Completion" align="left"/>Maple's command completion feature helps you avoid typos, reduces the need to memorize exact command names, provides an easy keyboard method for entering symbols, and as of Maple 12, provides guidance for calling sequences of commands.
The command completion feature allows you to type the first few characters in the command or symbol name, and then ask Maple to provide a list of possible endings. You then choose the appropriate ending from the list provided. In this Tips and Techniques, you will learn how to use command completion to finish command names, obtain fill-in-the-blank command templates, and enter mathematical symbols straight from the keyboard.6517Tue, 29 Jul 2008 04:00:00 ZMaplesoftMaplesoftAnimation of Dudeney's Dissection Transforming an Equilateral Triangle to a Square
http://www.maplesoft.com/applications/view.aspx?SID=6499&ref=Feed
In 1902, Henry Ernest Dudeney posed the problem of cutting an equilateral triangular region into 4 pieces that can be rearranged to form a square region. His published solution notes that the pieces can be hinged so as to smoothly rotate from one form to the other. We use Maple packages in linear algebra, geometry, and plotting to construct a picture of the pieces, and then animate the construction.<img src="/view.aspx?si=6499/1.gif" alt="Animation of Dudeney's Dissection Transforming an Equilateral Triangle to a Square" align="left"/>In 1902, Henry Ernest Dudeney posed the problem of cutting an equilateral triangular region into 4 pieces that can be rearranged to form a square region. His published solution notes that the pieces can be hinged so as to smoothly rotate from one form to the other. We use Maple packages in linear algebra, geometry, and plotting to construct a picture of the pieces, and then animate the construction.6499Thu, 24 Jul 2008 00:00:00 ZProf. Mark MeyersonProf. Mark MeyersonMaple, C, and Assembly Language - Performance Comparison
http://www.maplesoft.com/applications/view.aspx?SID=5837&ref=Feed
We show how to utilize Maple with an external calling mechanism to speed up function execution by coding them in C and assembly language. Techniques were demonstrated on Jonesâ€™ algorithm for finding the n-th prime number.<img src="/view.aspx?si=5837/Maple_C_and_Assembly_Langua.gif" alt="Maple, C, and Assembly Language - Performance Comparison" align="left"/>We show how to utilize Maple with an external calling mechanism to speed up function execution by coding them in C and assembly language. Techniques were demonstrated on Jonesâ€™ algorithm for finding the n-th prime number.5837Tue, 15 Apr 2008 00:00:00 ZMilorad Pop-TosicMilorad Pop-Tosic