Maple Programming: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=211
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemSun, 01 Aug 2021 06:49:46 GMTSun, 01 Aug 2021 06:49:46 GMTNew applications in the Maple Programming categoryhttps://www.maplesoft.com/images/Application_center_hp.jpgMaple Programming: New Applications
https://www.maplesoft.com/applications/category.aspx?cid=211
Bee-Cell Structure.mw
https://www.maplesoft.com/applications/view.aspx?SID=154603&ref=Feed
Nature, in general, affords many examples of economy of space and time for anyone who is curious enough to stop for a while and think.
Pythagoras (6th Century BC) was reported to have known the fact that the circle is the figure that has the greatest surface area among all plane figures having the same perimeter which is obviously an example of economy of space.
Heron (2d Century BC) deduced the fact that light after reflection follows the shortest path, hence an example of economy of space.
Fermat (1601-1665) was seeking a way to put the law of light refraction under a form similar to that given by Heron for the light reflection but this time he was looking for an economy of time rather than space.
Huygens (1629-1695), building on Fermat finding, considered the path of light not as a straight line but rather as a curve when passing through mediums where its velocity is variable from one point to an other. Hence economy of time.
Jean Bernoulli (1667-1748) he too was building on Huygens concept when he solved the problem of the brachystochron which is based on economy of time.
This is not to say that nature economy is concerned with only physical phenomena but examples taken from living creatures abound around us. To take one example that many researches have examined very carefully and in many details in the past is that of the honeycomb building in a bee hive.
It turns out, as we shall soon prove, that the bottom of any bee-cell has the form of a trihedron with 3 equal rhombi (rhombotrihedron) which, once added to the hexagonal right prism, will make the total surface area smaller resulting in economy on the precious wax that is secreted and used by worker bee in the construction of the entire cell.
Our plan in this article has a double purpose:
1- to prove the minimal surface we referred to above using a classical proof.
2- To start with no preconceived idea about the bee-cell then
A- to consider a trihedron having 90 degrees dihedral angle between all 3 planes.
B- To get an equation relating dihedral angle with the larger angle in a rhombus that, once
solved, gives exactly the dihedral angle of 120 degrees along with the larger angle in each
rhombus as 109.47122 degrees which are the exact data one can find at the bottom end of a
honey-cell.
This configuration which is that of a minimal surface of the cell is the only one that our
equation can give for all 3 planes to have in common these two angles . All others have
different dihedral and larger angles.
I believe that the neat and simple equation I arrived at is somehow original and so far I have no idea if anyone else has found it before me.<img src="https://www.maplesoft.com/view.aspx?si=154603/3b4238cc9e7aeb803a42872bde31a350.gif" alt="Bee-Cell Structure.mw" style="max-width: 25%;" align="left"/>Nature, in general, affords many examples of economy of space and time for anyone who is curious enough to stop for a while and think.
Pythagoras (6th Century BC) was reported to have known the fact that the circle is the figure that has the greatest surface area among all plane figures having the same perimeter which is obviously an example of economy of space.
Heron (2d Century BC) deduced the fact that light after reflection follows the shortest path, hence an example of economy of space.
Fermat (1601-1665) was seeking a way to put the law of light refraction under a form similar to that given by Heron for the light reflection but this time he was looking for an economy of time rather than space.
Huygens (1629-1695), building on Fermat finding, considered the path of light not as a straight line but rather as a curve when passing through mediums where its velocity is variable from one point to an other. Hence economy of time.
Jean Bernoulli (1667-1748) he too was building on Huygens concept when he solved the problem of the brachystochron which is based on economy of time.
This is not to say that nature economy is concerned with only physical phenomena but examples taken from living creatures abound around us. To take one example that many researches have examined very carefully and in many details in the past is that of the honeycomb building in a bee hive.
It turns out, as we shall soon prove, that the bottom of any bee-cell has the form of a trihedron with 3 equal rhombi (rhombotrihedron) which, once added to the hexagonal right prism, will make the total surface area smaller resulting in economy on the precious wax that is secreted and used by worker bee in the construction of the entire cell.
Our plan in this article has a double purpose:
1- to prove the minimal surface we referred to above using a classical proof.
2- To start with no preconceived idea about the bee-cell then
A- to consider a trihedron having 90 degrees dihedral angle between all 3 planes.
B- To get an equation relating dihedral angle with the larger angle in a rhombus that, once
solved, gives exactly the dihedral angle of 120 degrees along with the larger angle in each
rhombus as 109.47122 degrees which are the exact data one can find at the bottom end of a
honey-cell.
This configuration which is that of a minimal surface of the cell is the only one that our
equation can give for all 3 planes to have in common these two angles . All others have
different dihedral and larger angles.
I believe that the neat and simple equation I arrived at is somehow original and so far I have no idea if anyone else has found it before me.https://www.maplesoft.com/applications/view.aspx?SID=154603&ref=FeedThu, 13 Feb 2020 17:34:36 ZAhmed BaroudyAhmed BaroudyGift Exchange Helper
https://www.maplesoft.com/applications/view.aspx?SID=154372&ref=Feed
The "pick a name" style of gift exchange is an important part of many group celebrations, but can be complicated to arrange, especially if your group has rules like “you cannot pick your partner”. If you could do without the "this didn't work, let's try it again" aspect of your gift exchange, you can use this application to do the matching for you. You give it a list of names, and any "person A cannot pick person B" restrictions you might have, and it puts them into a virtual hat and then tells you who picked who.To read more about this application, see the MaplePrimes post <A HREF="https://www.mapleprimes.com/posts/208779-Gift-Exchange-Helper">Gift Exchange Helper</A>.<img src="https://www.maplesoft.com/view.aspx?si=154372/gifts-sm.jpg" alt="Gift Exchange Helper" style="max-width: 25%;" align="left"/>The "pick a name" style of gift exchange is an important part of many group celebrations, but can be complicated to arrange, especially if your group has rules like “you cannot pick your partner”. If you could do without the "this didn't work, let's try it again" aspect of your gift exchange, you can use this application to do the matching for you. You give it a list of names, and any "person A cannot pick person B" restrictions you might have, and it puts them into a virtual hat and then tells you who picked who.To read more about this application, see the MaplePrimes post <A HREF="https://www.mapleprimes.com/posts/208779-Gift-Exchange-Helper">Gift Exchange Helper</A>.https://www.maplesoft.com/applications/view.aspx?SID=154372&ref=FeedMon, 04 Dec 2017 05:00:00 ZEithne MurrayEithne MurrayFibonacci Numbers
https://www.maplesoft.com/applications/view.aspx?SID=154362&ref=Feed
Many programming language tutorials have an example about computing Fibonacci numbers to illustrate recursion. Usually, however, these simple examples exhibit an abysmal runtime behaviour, namely, exponential in the index.
<BR><BR>
In this presentation, several more efficient ways of computing Fibonacci numbers, using Maple, are discussed. The best algorithm presented is based on doubling formulae for the Fibonacci numbers, which we also prove using Maple.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Fibonacci Numbers" style="max-width: 25%;" align="left"/>Many programming language tutorials have an example about computing Fibonacci numbers to illustrate recursion. Usually, however, these simple examples exhibit an abysmal runtime behaviour, namely, exponential in the index.
<BR><BR>
In this presentation, several more efficient ways of computing Fibonacci numbers, using Maple, are discussed. The best algorithm presented is based on doubling formulae for the Fibonacci numbers, which we also prove using Maple.https://www.maplesoft.com/applications/view.aspx?SID=154362&ref=FeedTue, 21 Nov 2017 05:00:00 ZDr. Jürgen GerhardDr. Jürgen GerhardVector Force
https://www.maplesoft.com/applications/view.aspx?SID=154245&ref=Feed
This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154245/vecfza.png" alt="Vector Force" style="max-width: 25%;" align="left"/>This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. This is an easy-to-use interactive application. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154245&ref=FeedTue, 09 May 2017 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloCombining Multiple Animations in Maple
https://www.maplesoft.com/applications/view.aspx?SID=154222&ref=Feed
In this document, we show to build up complex animations by showing different ways to combine existing animations. We illustrate this using three animations, however, the techniques are general and can be applied to any number of animations.
<BR><BR>
This application is also the subject of a post on MaplePrimes: <A HREF="http://www.mapleprimes.com/posts/207840-Combinations-Of-Multiple-Animations">Combinations of multiple animations</A><img src="https://www.maplesoft.com/view.aspx?si=154222/multipleAnimations.jpg" alt="Combining Multiple Animations in Maple" style="max-width: 25%;" align="left"/>In this document, we show to build up complex animations by showing different ways to combine existing animations. We illustrate this using three animations, however, the techniques are general and can be applied to any number of animations.
<BR><BR>
This application is also the subject of a post on MaplePrimes: <A HREF="http://www.mapleprimes.com/posts/207840-Combinations-Of-Multiple-Animations">Combinations of multiple animations</A>https://www.maplesoft.com/applications/view.aspx?SID=154222&ref=FeedTue, 07 Feb 2017 05:00:00 ZYury ZavarovskyYury ZavarovskyAplicativo de Ecuaciones en primer orden
https://www.maplesoft.com/applications/view.aspx?SID=154139&ref=Feed
With this application you can develop your equations without the need to worry about the difficult calculation. Save calculation time and you will increase the time in interpreting the results. It was developed in Maple 2016 and can be executed in maple player.
In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154139/appec.png" alt="Aplicativo de Ecuaciones en primer orden" style="max-width: 25%;" align="left"/>With this application you can develop your equations without the need to worry about the difficult calculation. Save calculation time and you will increase the time in interpreting the results. It was developed in Maple 2016 and can be executed in maple player.
In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154139&ref=FeedSun, 07 Aug 2016 04:00:00 ZProf. Lenin Araujo CastilloProf. Lenin Araujo CastilloCryptographic Protection of E-Mail Attachment with Filename Extensions `txt`, `doc`, `docx`, `rtf` or `mw` Using the Secret Key of Length 1980 Bits
https://www.maplesoft.com/applications/view.aspx?SID=154109&ref=Feed
This worksheet contains an easy-to-use applications for encrypting and decrypting email attachments to ensure the security of confidential information. It can be used with Word, text, RTF, and Maple documents. The key space used by the algorithms is huge (1980 bits), therefore, the encrypted contents of the file is in practice unbreakable.<img src="https://www.maplesoft.com/view.aspx?si=154109/tk1980b64.jpg" alt="Cryptographic Protection of E-Mail Attachment with Filename Extensions `txt`, `doc`, `docx`, `rtf` or `mw` Using the Secret Key of Length 1980 Bits" style="max-width: 25%;" align="left"/>This worksheet contains an easy-to-use applications for encrypting and decrypting email attachments to ensure the security of confidential information. It can be used with Word, text, RTF, and Maple documents. The key space used by the algorithms is huge (1980 bits), therefore, the encrypted contents of the file is in practice unbreakable.https://www.maplesoft.com/applications/view.aspx?SID=154109&ref=FeedMon, 23 May 2016 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyStatically Indeterminate Structure
https://www.maplesoft.com/applications/view.aspx?SID=153940&ref=Feed
The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.<img src="https://www.maplesoft.com/view.aspx?si=153940/391e24e981ea8d11454375def604a185.gif" alt="Statically Indeterminate Structure" style="max-width: 25%;" align="left"/>The application allows you to determine the constraint reactions, build diagrams of the normal forces N, shear forces Q and bending moments M for beams and frames with any number of sections and degree of static indefinability.
The application calculates the deformation (displacements) of the structure in millimeters and displays the displacements of nodes in the horizontal and vertical. It is also possible to calculate the displacement of any point of the structure.https://www.maplesoft.com/applications/view.aspx?SID=153940&ref=FeedWed, 09 Mar 2016 05:00:00 ZDr. Aleksey ShirkoDr. Aleksey ShirkoByte Frequency Analyzer
https://www.maplesoft.com/applications/view.aspx?SID=153920&ref=Feed
In the cryptographic research an important operation is to determine the byte-frequency of non-encrypted and encrypted files. This action allows us to appraise the quality of the cryptographic algorithms. This application implements a `byte-frequency analyzer` in Maple. Results are displayed in column graphs, using both linear and logarithmic scales on the y-axis. The logarithmic y-axis is very useful if the differences between the byte values are large. The displayed column graphs can be exported in six formats (Bitmap, PNG, GIF, JPEG, Encapsulated Postcript, PDF and Windows Metafile) for use in documents concerning cryptography and file processing tools.<img src="https://www.maplesoft.com/view.aspx?si=153920/bytefreq.png" alt="Byte Frequency Analyzer" style="max-width: 25%;" align="left"/>In the cryptographic research an important operation is to determine the byte-frequency of non-encrypted and encrypted files. This action allows us to appraise the quality of the cryptographic algorithms. This application implements a `byte-frequency analyzer` in Maple. Results are displayed in column graphs, using both linear and logarithmic scales on the y-axis. The logarithmic y-axis is very useful if the differences between the byte values are large. The displayed column graphs can be exported in six formats (Bitmap, PNG, GIF, JPEG, Encapsulated Postcript, PDF and Windows Metafile) for use in documents concerning cryptography and file processing tools.https://www.maplesoft.com/applications/view.aspx?SID=153920&ref=FeedThu, 12 Nov 2015 05:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnySending Emails from the Maple Command Line
https://www.maplesoft.com/applications/view.aspx?SID=153912&ref=Feed
You can send emails from the Maple command line via Mailgun (http://mailgun.com) a free email delivery service with an web-based API. The code in this application communicates with this API to send an email; you'll need to replace certain parts with details from your own Mailgun account.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Sending Emails from the Maple Command Line" style="max-width: 25%;" align="left"/>You can send emails from the Maple command line via Mailgun (http://mailgun.com) a free email delivery service with an web-based API. The code in this application communicates with this API to send an email; you'll need to replace certain parts with details from your own Mailgun account.https://www.maplesoft.com/applications/view.aspx?SID=153912&ref=FeedFri, 30 Oct 2015 04:00:00 ZSamir KhanSamir KhanThe SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions
https://www.maplesoft.com/applications/view.aspx?SID=153903&ref=Feed
The National Institute of Standards and Technology (NIST) has released the final version of its "Secure Hash Algorithm-3" (SHA-3) standard in August 2015. The new standard ("Federal Information Processing Standard (FIPS) 202") specifies four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, as well as two Extendable-Output Functions (XOFs), called SHAKE128 and SHAKE256. These functions are based on the Keccak sponge function, designed by G. Bertoni, J. Daemen, M. Peeters and G. Van Assche. The hash functions are an essential tool for securing the integrity of electronic information and the XOFs offer the added flexibility of having a variable output length. This application contains an implementation of these functions and also of the SHA-3-based Message Authentication Code HMAC.<img src="https://www.maplesoft.com/view.aspx?si=153903/keccak.jpg" alt="The SHA-3 Family of Cryptographic Hash Functions and Extendable-Output Functions" style="max-width: 25%;" align="left"/>The National Institute of Standards and Technology (NIST) has released the final version of its "Secure Hash Algorithm-3" (SHA-3) standard in August 2015. The new standard ("Federal Information Processing Standard (FIPS) 202") specifies four cryptographic hash functions, called SHA3-224, SHA3-256, SHA3-384 and SHA3-512, as well as two Extendable-Output Functions (XOFs), called SHAKE128 and SHAKE256. These functions are based on the Keccak sponge function, designed by G. Bertoni, J. Daemen, M. Peeters and G. Van Assche. The hash functions are an essential tool for securing the integrity of electronic information and the XOFs offer the added flexibility of having a variable output length. This application contains an implementation of these functions and also of the SHA-3-based Message Authentication Code HMAC.https://www.maplesoft.com/applications/view.aspx?SID=153903&ref=FeedFri, 16 Oct 2015 04:00:00 ZJosé Luis Gómez PardoJosé Luis Gómez PardoMaple Implementation of the Secure Transport Encryption Scheme
https://www.maplesoft.com/applications/view.aspx?SID=153863&ref=Feed
An easy-to-use interactive Maple implementation of transport encryption scheme has been presented. It allows to encrypt any file with arbitrary extension stored in the used computer system and in portable memory devices. The encrypted file may contain all 7-bit characters. Therefore, the encrypted file can be securely transmitted over the internet as an e-mail enclosure. The application encrypts also the name of the plaintext file: this way, the kind of content of the plaintext file is hidden. The encrypted file is saved in the same folder as the plaintext file. On encryption/decryption in the GUI Text Area the user will see an exhaustive information about the performed task. On decryption, the encrypted file is removed. The presented applications sm128b.mw must have permission to save and remove the processed files. It is worth to know that the secret key in the application is embedded. Thus, any user can embed his own secret key in the application in many ways.<img src="https://www.maplesoft.com/view.aspx?si=153863/transport.png" alt="Maple Implementation of the Secure Transport Encryption Scheme" style="max-width: 25%;" align="left"/>An easy-to-use interactive Maple implementation of transport encryption scheme has been presented. It allows to encrypt any file with arbitrary extension stored in the used computer system and in portable memory devices. The encrypted file may contain all 7-bit characters. Therefore, the encrypted file can be securely transmitted over the internet as an e-mail enclosure. The application encrypts also the name of the plaintext file: this way, the kind of content of the plaintext file is hidden. The encrypted file is saved in the same folder as the plaintext file. On encryption/decryption in the GUI Text Area the user will see an exhaustive information about the performed task. On decryption, the encrypted file is removed. The presented applications sm128b.mw must have permission to save and remove the processed files. It is worth to know that the secret key in the application is embedded. Thus, any user can embed his own secret key in the application in many ways.https://www.maplesoft.com/applications/view.aspx?SID=153863&ref=FeedWed, 09 Sep 2015 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyMaple Implementation of Transport Encryption Scheme Using the Secret Key of Length 479 Bits
https://www.maplesoft.com/applications/view.aspx?SID=153841&ref=Feed
An easy-to-use Maple implementation of transport encryption has been presented. It allows encrypting any file with arbitrary extension stored in the used computer system. The encrypted file contains space, alphabetic and decimal digit characters and the following special characters !#$%&'()*+,-./:;<=>?@[]^_`{|}~. These 93 printable characters can be defined by the set {32, 33, 35, seq(i, i=36 .. 91), seq(i, i=93 .. 126)} of byte values. Therefore, the encrypted file can be not only securely transmitted over the internet as an e-mail enclosure, but also protected effectively against unauthorized access. The application encrypts the name of the plaintext file as well: this way, the kind of content of the plaintext file is hidden. The encrypted file is saved in the same folder as the plaintext file. The size of the encrypted file is about 22.3% greater than the size of the plaintext file. On encryption/decryption in the GUI Text Area the user will see exhaustive information about the performed task. On decryption, the encrypted file is removed. It is worth knowing that the secret key in the application is embedded. Thus, any user can install his own secret key in the application in many ways. For example, he can change the value of the variable skc and the value of the variable seed in the procedures fne and fnd. The presented applications fed479k.mw must have permission to save and to remove the processed files. For security reason the application worksheet fed479k.mw ought to be stored in the meticulously watched over pen drive.<img src="https://www.maplesoft.com/view.aspx?si=153841/im.jpg" alt="Maple Implementation of Transport Encryption Scheme Using the Secret Key of Length 479 Bits" style="max-width: 25%;" align="left"/>An easy-to-use Maple implementation of transport encryption has been presented. It allows encrypting any file with arbitrary extension stored in the used computer system. The encrypted file contains space, alphabetic and decimal digit characters and the following special characters !#$%&'()*+,-./:;<=>?@[]^_`{|}~. These 93 printable characters can be defined by the set {32, 33, 35, seq(i, i=36 .. 91), seq(i, i=93 .. 126)} of byte values. Therefore, the encrypted file can be not only securely transmitted over the internet as an e-mail enclosure, but also protected effectively against unauthorized access. The application encrypts the name of the plaintext file as well: this way, the kind of content of the plaintext file is hidden. The encrypted file is saved in the same folder as the plaintext file. The size of the encrypted file is about 22.3% greater than the size of the plaintext file. On encryption/decryption in the GUI Text Area the user will see exhaustive information about the performed task. On decryption, the encrypted file is removed. It is worth knowing that the secret key in the application is embedded. Thus, any user can install his own secret key in the application in many ways. For example, he can change the value of the variable skc and the value of the variable seed in the procedures fne and fnd. The presented applications fed479k.mw must have permission to save and to remove the processed files. For security reason the application worksheet fed479k.mw ought to be stored in the meticulously watched over pen drive.https://www.maplesoft.com/applications/view.aspx?SID=153841&ref=FeedThu, 13 Aug 2015 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyMaple Implementation of Transport Encoding Scheme Using the Base Value Equal to 93
https://www.maplesoft.com/applications/view.aspx?SID=153817&ref=Feed
In the `RFC 4648` document (http://www.rfc-base.org/rfc-4648.html) the commonly used base 64, base 32, and base 16 encoding schemes are decribed. The output file, encoded according to this document, is about 33%, 60% and 100% greater than the input file, respectively. The presented application uses the base value equal to 93, and now the encoded file is only about 22% greater than the input file. The application must have a permission to save and to remove the files processed. It is easy to use - the reader is informed which tasks are being performed for any selected option, namely, he will know the input file size and name, the output file size and name, the encoding/decoding rates.In the `RFC 4648` document (http://www.rfc-base.org/rfc-4648.html) the commonly used base 64, base 32, and base 16 encoding schemes are decribed. The output file, encoded according to this document, is about 33%, 60% and 100% greater than the input file, respectively. The presented application uses the base value equal to 93, and now the encoded file is only about 22% greater than the input file. The application must have a permission to save and to remove the files processed. It is easy to use - the reader is informed which tasks are being performed for any selected option, namely, he will know the input file size and name, the output file size and name, the encoding/decoding rates.https://www.maplesoft.com/applications/view.aspx?SID=153817&ref=FeedThu, 25 Jun 2015 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyComputational Performance with evalhf and Compile: A Newton Fractal Case Study
https://www.maplesoft.com/applications/view.aspx?SID=153683&ref=Feed
<p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p><img src="https://www.maplesoft.com/view.aspx?si=153683/thumb.jpg" alt="Computational Performance with evalhf and Compile: A Newton Fractal Case Study" style="max-width: 25%;" align="left"/><p>This Tips and Techniques article focuses on the relative performance of Maple's various modes for floating-point computations. The example used here is the computation of a particular Newton fractal, which is easily parallelizable. We compute an image representation for this fractal under several computational modes, using both serial and multithreaded computation schemes.</p>
<p>This article is a follow up to a previous Tips and Techniques, <a href="http://www.maplesoft.com/applications/view.aspx?SID=153645">evalhf, Compile, hfloat and all that</a>, which discusses functionality differences amongst Maple's the different floating-point computation modes available in Maple.</p>https://www.maplesoft.com/applications/view.aspx?SID=153683&ref=FeedFri, 26 Sep 2014 04:00:00 ZDave LinderDave LinderGenerating random numbers efficiently
https://www.maplesoft.com/applications/view.aspx?SID=153662&ref=Feed
Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.<img src="https://www.maplesoft.com/view.aspx?si=153662/thumb.jpg" alt="Generating random numbers efficiently" style="max-width: 25%;" align="left"/>Generating (pseudo-)random values is a frequent task in simulations and other programs. For some situations, you want to generate some combinatorial or algebraic values, such as a list or a polynomial; in other situations, you need random numbers, from a distribution that is uniform or more complicated. In this article I'll talk about all of these situations.https://www.maplesoft.com/applications/view.aspx?SID=153662&ref=FeedMon, 18 Aug 2014 04:00:00 ZDr. Erik PostmaDr. Erik Postmaevalhf, Compile, hfloat and all that
https://www.maplesoft.com/applications/view.aspx?SID=153645&ref=Feed
Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="evalhf, Compile, hfloat and all that" style="max-width: 25%;" align="left"/>Users sometimes ask how to make their floating-point (numeric) computations perform faster in Maple. The answers often include references to special terms such as evalhf, the Compiler, and option hfloat. A difficulty for the non-expert lies in knowing which of these can be used, and when. This Tips and Techniques attempts to clear up some of the mystery of these terms, by discussion and functionality comparison.https://www.maplesoft.com/applications/view.aspx?SID=153645&ref=FeedTue, 22 Jul 2014 04:00:00 ZDave LinderDave LinderElGamal E-mail Encryption Scheme
https://www.maplesoft.com/applications/view.aspx?SID=153538&ref=Feed
<p>The submission shows how to implement the user-friendly, but mathematically sophisticated strong e-mail encryption scheme using the ElGamal algorithm working in the multiplicative group of GF(p^m) (http://www.maplesoft.com/applications/view.aspx?SID=4403, J. L. G. Pardo - Introduction to Cryptography with Maple). On unpacking the file `elgmail.zip` the user will see three public key files: `ElGpub_Eve_Flower.m`, `ElGpub_Jack_Herod.m`, `ElGpub_Michele_Lazy.m` and three application worksheets: `ElGedm_Flower.mw`, `ElGedm_Herod.mw`, `ElGedm_Lazy.mw` in which the proper private keys are embedded. Each of the three users can encrypt an e-mail letter and can send the encrypted message to the required addressee, knowing its public key. Evidently, any user can also decrypt the proper encrypted message, addressed to him. The way of generating the public and private keys demonstrates the worksheet ElGkg.mw. The data contained in the names of the computed keys using the worksheet ElGkg.mw is evident. In the presented example the e-mail message should contain no more than 782 printable characters with byte values less than 127. The scheme can be accepted for any e-mail system: the public keys and encrypted messages are Maple `*.m` format files containing characters with 91 byte values from the set {10, 33 .. 122}. The user can also observe the time needed for encryption, decryption and the computation of keys, and the encryption scheme redundancy. An example test message and its cryptogram is also presented and the user can check for which the encrypted test message ought to be sent.</p><img src="https://www.maplesoft.com/view.aspx?si=153538/image.PNG" alt="ElGamal E-mail Encryption Scheme" style="max-width: 25%;" align="left"/><p>The submission shows how to implement the user-friendly, but mathematically sophisticated strong e-mail encryption scheme using the ElGamal algorithm working in the multiplicative group of GF(p^m) (http://www.maplesoft.com/applications/view.aspx?SID=4403, J. L. G. Pardo - Introduction to Cryptography with Maple). On unpacking the file `elgmail.zip` the user will see three public key files: `ElGpub_Eve_Flower.m`, `ElGpub_Jack_Herod.m`, `ElGpub_Michele_Lazy.m` and three application worksheets: `ElGedm_Flower.mw`, `ElGedm_Herod.mw`, `ElGedm_Lazy.mw` in which the proper private keys are embedded. Each of the three users can encrypt an e-mail letter and can send the encrypted message to the required addressee, knowing its public key. Evidently, any user can also decrypt the proper encrypted message, addressed to him. The way of generating the public and private keys demonstrates the worksheet ElGkg.mw. The data contained in the names of the computed keys using the worksheet ElGkg.mw is evident. In the presented example the e-mail message should contain no more than 782 printable characters with byte values less than 127. The scheme can be accepted for any e-mail system: the public keys and encrypted messages are Maple `*.m` format files containing characters with 91 byte values from the set {10, 33 .. 122}. The user can also observe the time needed for encryption, decryption and the computation of keys, and the encryption scheme redundancy. An example test message and its cryptogram is also presented and the user can check for which the encrypted test message ought to be sent.</p>https://www.maplesoft.com/applications/view.aspx?SID=153538&ref=FeedWed, 02 Apr 2014 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnySimon Tatham's 5 Puzzle Games
https://www.maplesoft.com/applications/view.aspx?SID=152142&ref=Feed
<p>It has been shown how to implement one-worksheet application containing six *.exe files. The files, embedded in the presented statham5mp.mw Maple worksheet, allow the Maple user to play Simon Tatham's five one-player puzzle games</p>
<p>(<a href="http://www.chiark.greenend.org.uk/~sgtatham/puzzles/">http://www.chiark.greenend.org.uk/~sgtatham/puzzles/</a>).</p>
<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:\games.</p><img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Simon Tatham's 5 Puzzle Games" style="max-width: 25%;" align="left"/><p>It has been shown how to implement one-worksheet application containing six *.exe files. The files, embedded in the presented statham5mp.mw Maple worksheet, allow the Maple user to play Simon Tatham's five one-player puzzle games</p>
<p>(<a href="http://www.chiark.greenend.org.uk/~sgtatham/puzzles/">http://www.chiark.greenend.org.uk/~sgtatham/puzzles/</a>).</p>
<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:\games.</p>https://www.maplesoft.com/applications/view.aspx?SID=152142&ref=FeedTue, 24 Sep 2013 04:00:00 ZCzeslaw KoscielnyCzeslaw KoscielnyHohmann Elliptic Transfer Orbit with Animation
https://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="https://www.maplesoft.com/view.aspx?si=151351/24030360191a26b4d767de35f843bbd8.gif" alt="Hohmann Elliptic Transfer Orbit with Animation" style="max-width: 25%;" 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>https://www.maplesoft.com/applications/view.aspx?SID=151351&ref=FeedWed, 04 Sep 2013 04:00:00 ZDr. Ahmed BaroudyDr. Ahmed Baroudy