New Application Center Additions
https://www.maplesoft.com/applications
en-us2019 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemThu, 23 May 2019 15:16:14 GMTThu, 23 May 2019 15:16:14 GMTThe latest content added to the Application Centerhttps://www.maplesoft.com/images/Application_center_hp.jpgNew Application Center Additions
https://www.maplesoft.com/applications
Robot Arm Writing "Maplesoft" in Handwritten Cursive Script
https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=Feed
This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL><img src="https://www.maplesoft.com/view.aspx?si=154531/thumb.png" alt="Robot Arm Writing "Maplesoft" in Handwritten Cursive Script" style="max-width: 25%;" align="left"/>This application models a 3 DoF robot arm, with the motion of the tip writing "Maplesoft" in handwritten cursive script.
<BR><BR>
To model the arm, the worksheet:
<UL>
<LI>Analytically derives the Denavit & Hartenberg transformation matrix for each of the three joints
<LI>Lets the user specify a parametric path for the tip of the robot to follow. The default equations in the worksheet writes "Maplesoft" in cursive script
<LI>Animates the robot arm following the specified path
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154531&ref=FeedMon, 06 May 2019 04:00:00 ZBryon ThurBryon ThurGame of Thrones and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=Feed
Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.<img src="https://www.maplesoft.com/view.aspx?si=154529/thumb.png" alt="Game of Thrones and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the television series Game of Thrones, based upon the A Song of Ice and Fire books. With the judicious use of Maple, you can ask yourself really pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over each season?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the television series. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154530">A Song of Ice and Fire and Graph Theory</A> to ask these types of questions using data for the books.https://www.maplesoft.com/applications/view.aspx?SID=154529&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanA Song of Ice and Fire and Graph Theory
https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=Feed
Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.<img src="https://www.maplesoft.com/view.aspx?si=154530/thumb.png" alt="A Song of Ice and Fire and Graph Theory" style="max-width: 25%;" align="left"/>Graph theory can help you understand the social landscape of the books in the series A Song of Ice and Fire by G. R. R. Martin. With the judicious use of Maple, you can ask yourself <i>really</i> pressing questions like
<UL>
<LI>Who is the most influential person in Westeros? How has their influence changed over the five books?</LI>
<LI>How are Eddard Stark and Randyll Tarly connected?</LI>
<LI>What do eigenvectors have to do with the battle for the Iron Throne, anyway?</LI>
</UL>
This application uses data from the books. See <A HREF="https://www.maplesoft.com/applications/view.aspx?SID=154529">A Game of Thrones and Graph Theory</A> to ask these types of questions using data for the television series.https://www.maplesoft.com/applications/view.aspx?SID=154530&ref=FeedWed, 27 Mar 2019 04:00:00 ZSamir KhanSamir KhanSystem of Equations Determined Compatible 2x2
https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=Feed
This application solves a set of compatible equations of two variables. It also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. In Spanish.<img src="https://www.maplesoft.com/view.aspx?si=154520/sis_eq_dpd.png" alt="System of Equations Determined Compatible 2x2" style="max-width: 25%;" align="left"/>This application solves a set of compatible equations of two variables. It also graphs the intersection point of the variable "x" and "y". If we want to observe the intersection point closer we will use the zoom button that is activated when manipulating the graph. If we want to change the variable ("x" and "y") we enter the code of the button that solves and graphs. In Spanish.https://www.maplesoft.com/applications/view.aspx?SID=154520&ref=FeedTue, 19 Mar 2019 04:00:00 ZLenin Araujo CastilloLenin Araujo CastilloLomb-Scargle Spectral Analysis of Irregularly Sampled Data
https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=Feed
This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.<img src="https://www.maplesoft.com/view.aspx?si=154521/lomb-thumbnailbnail.jpg" alt="Lomb-Scargle Spectral Analysis of Irregularly Sampled Data" style="max-width: 25%;" align="left"/>This application
<UL>
<LI>generates an irregularly sampled signal of a sum of two sinusoids (i.e. a time vector at irregular intervals, and a signal vector containing a value at each of those times)
<LI>and then generates a Lomb-Scargle periodogram of that data.
</UL>
The periodogram correctly identifies the frequencies used to generate the irregularly sampled signal.https://www.maplesoft.com/applications/view.aspx?SID=154521&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanBlurring an Image in the Spatial Frequency Domain
https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=Feed
ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.<img src="https://www.maplesoft.com/view.aspx?si=154522/blurimage.jpg" alt="Blurring an Image in the Spatial Frequency Domain" style="max-width: 25%;" align="left"/>ere, we will blur in an image with a Gaussian Filter (effectively a low-pass filter) applied in the spatial frequency domain.
<UL>
<LI>First an image is imported
<LI>The fourier transform of the image is then computed, and the image periodogram plotted.
<LI>The fourier transform is multiplied by a Gaussian filter (this attenuates higher spatial frequencies - i.e. the finer detail is removed, leaving only the broad outline).
<LI>The resulted is inverted to the image domain, giving a blurry image
</UL>
This application uses the new Maple 2019 FFTShift function to swap data in a matrix or a vector into a different position. The Fourier transform of an image places lower frequency data near all four corners, with higher frequency data near the center. In this instance, FFTShift is typically applied to move the lowest frequencies to the center and the highest frequencies to the corners.
<BR><BR>
This results in a more meaningful visualization of the power spectrum where the lowest frequency data is contiguous, and simplifies the manipulation of image frequency data.https://www.maplesoft.com/applications/view.aspx?SID=154522&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanLocate a Signal in Audio in the Presence of Noise
https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=Feed
This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.<img src="https://www.maplesoft.com/view.aspx?si=154523/thumbnail.jpg" alt="Locate a Signal in Audio in the Presence of Noise" style="max-width: 25%;" align="left"/>This application demonstrates how you can estimate the location of a signal that might exist in a larger (perhaps noisy) measurement. In this instance, we find the location of a small segment of audio in a larger audio file.
<UL>
<LI>First, an audio file is first loaded, a small segment is extracted, and random Gaussian noise is added to both.
<LI>The cross-correlation of the full audio and the extract is computed, and the maximum lag computed.
</UL>
The maximum lag is the index at which the extract is predicted to exist in the audio.https://www.maplesoft.com/applications/view.aspx?SID=154523&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanFundamental Frequency and Harmonics of a Violin Note
https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=Feed
This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.<img src="https://www.maplesoft.com/view.aspx?si=154524/thumnbail.jpg" alt="Fundamental Frequency and Harmonics of a Violin Note" style="max-width: 25%;" align="left"/>This application finds the fundamental frequency and harmonics of a violin using information from the amplitude spectrum. Then, we generate a sinusoidal signal with the same frequency-amplitude characteristics of the violin note, and play the resulting sound.
The analysis uses the new Maple 2019 command for finding the peaks and valleys of a 1D data set - FindPeaks. This command offers several options that let you filter out peaks or valleys that are too close, what defines a peak or valley, and more.https://www.maplesoft.com/applications/view.aspx?SID=154524&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanFundamental Frequency of a Human Voice
https://www.maplesoft.com/applications/view.aspx?SID=154525&ref=Feed
This application predicts the fundamental frequency of a human voice using the ComplexCepstrum command.
<BR><BR>
After converting a small window of the audio to the cepstral domain, we find the pitch by noting the maximum "quefrency" in a carefully selected range.<img src="https://www.maplesoft.com/view.aspx?si=154525/thumbnail.jpg" alt="Fundamental Frequency of a Human Voice" style="max-width: 25%;" align="left"/>This application predicts the fundamental frequency of a human voice using the ComplexCepstrum command.
<BR><BR>
After converting a small window of the audio to the cepstral domain, we find the pitch by noting the maximum "quefrency" in a carefully selected range.https://www.maplesoft.com/applications/view.aspx?SID=154525&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanCompressing Audio with the Discrete Cosine Transform
https://www.maplesoft.com/applications/view.aspx?SID=154526&ref=Feed
This application demonstrates how you can compress a signal by discarding low-energy parts of its discrete cosine transform. Specifically, we only retain those coefficients that cumulatively sum to a large part of the signal energy.
<BR><BR>
Here, the signal is an audio file, where only 13% of the DCT coefficients are needed to represent 97% of the signal energy. After compression, the resulting audio is hissy but still legible.<img src="https://www.maplesoft.com/view.aspx?si=154526/thumbnail.jpg" alt="Compressing Audio with the Discrete Cosine Transform" style="max-width: 25%;" align="left"/>This application demonstrates how you can compress a signal by discarding low-energy parts of its discrete cosine transform. Specifically, we only retain those coefficients that cumulatively sum to a large part of the signal energy.
<BR><BR>
Here, the signal is an audio file, where only 13% of the DCT coefficients are needed to represent 97% of the signal energy. After compression, the resulting audio is hissy but still legible.https://www.maplesoft.com/applications/view.aspx?SID=154526&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanEcho Cancellation using Cepstrum Analysis
https://www.maplesoft.com/applications/view.aspx?SID=154527&ref=Feed
This application will
<UL>
<LI>import an audio file that has an echo
<LI>identify the start of the echo in the cepstral domain (using the RealCepstrum function)
<LI>use this information to generate and apply an IIR filter to remove the echo'
<LI>and write the de-echoed audio back to a sound file
</UL><img src="https://www.maplesoft.com/view.aspx?si=154527/thumbnail.jpg" alt="Echo Cancellation using Cepstrum Analysis" style="max-width: 25%;" align="left"/>This application will
<UL>
<LI>import an audio file that has an echo
<LI>identify the start of the echo in the cepstral domain (using the RealCepstrum function)
<LI>use this information to generate and apply an IIR filter to remove the echo'
<LI>and write the de-echoed audio back to a sound file
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154527&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanPredicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars
https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=Feed
Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081–1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL><img src="https://www.maplesoft.com/view.aspx?si=154528/thumbnail.jpg" alt="Predicting the Orbital Period of Exoplanets by Analyzing the Wobble of Stars" style="max-width: 25%;" align="left"/>Stars are pulled in a circle or ellipse in reponse to the gravity of orbiting planets. By analyzing the "wobble" (or radial velocity) of a star, astronomers can predict the presence and orbital period of exoplanets.
<BR><BR>
Radial velocity is recorded, often over months or years, with a spectrograph connected to a telescope. This data is used to generate a periodogram, in which a peak is evidence of an exoplanet; the orbital period of the exoplanet is given by the location of the peak.
<BR><BR>
However cloud cover, scheduling conflicts and other issues can often disrupt observations, so data is generally not regularly sampled. This means that standard Fourier techniques cannot be used to generate a periodogram, and other approaches are needed. A common method for the frequency analysis of irregularly sampled data is the Lomb-Scargle technique.
<BR><BR>
Fischer (2003) recorded the radial velocity of the star HD 3561 (also known as 54 Piscium), and generated a periodogram to show evidence of an exoplanet (now known as 54 Piscium b).
<BR><BR>
This application uses Maple 2019's new Lomb-Scargle tools to reproduce the analysis; the periodogram shows a periodicity of 62.2 days, agreeing with value given by Fischer (2003).
<BR><BR>
References:
<UL>
<LI>A Sub-Saturn Mass Planet Orbiting HD 3651, Fischer D.A. et al., The Astrophysical Journal, 590:1081–1087, 2003 June 20
<LI>Orbital velocity data found at http://astrostatistics.psu.edu/datasets/exoplanet_Doppler.html
</UL>https://www.maplesoft.com/applications/view.aspx?SID=154528&ref=FeedTue, 19 Mar 2019 04:00:00 ZSamir KhanSamir KhanMaplet pour creer des forteresses en Etoile
https://www.maplesoft.com/applications/view.aspx?SID=154513&ref=Feed
Cette maplet permet de rajouter sur chaque étoile imbriquée des "pointes" entre deux branches pour former des sortes de forteresses.
Le i eme "rapport1" x le rayon "interne" de la i eme etoile est egale a la distance et l'extremité d'une de ses pointes.
Le i eme "rapport2" x la longueur du coté d'une branche de la i eme etoile est egale à la longueur entre un point de base de la branche et le point de base de la "pointe".
"rapport-distance entre les etoiles" x le rayon "interne" de la i ème etoile est egale au rayon "externe" de la (i+1) ème etoile imbriquée.
"rapport1" et "rapport2" sont des sequences comme pour "angle des branches de l'étoiles".<img src="https://www.maplesoft.com/view.aspx?si=154513/forteresse-etoile.gif" alt="Maplet pour creer des forteresses en Etoile" style="max-width: 25%;" align="left"/>Cette maplet permet de rajouter sur chaque étoile imbriquée des "pointes" entre deux branches pour former des sortes de forteresses.
Le i eme "rapport1" x le rayon "interne" de la i eme etoile est egale a la distance et l'extremité d'une de ses pointes.
Le i eme "rapport2" x la longueur du coté d'une branche de la i eme etoile est egale à la longueur entre un point de base de la branche et le point de base de la "pointe".
"rapport-distance entre les etoiles" x le rayon "interne" de la i ème etoile est egale au rayon "externe" de la (i+1) ème etoile imbriquée.
"rapport1" et "rapport2" sont des sequences comme pour "angle des branches de l'étoiles".https://www.maplesoft.com/applications/view.aspx?SID=154513&ref=FeedSun, 03 Mar 2019 05:00:00 Zxavier cormierxavier cormierLinear Optimization Examples
https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=Feed
So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.<img src="https://www.maplesoft.com/view.aspx?si=154517/b0e3e02e0b878253dcb11a11a2b75fce.gif" alt="Linear Optimization Examples" style="max-width: 25%;" align="left"/>So, this was introduced into my son's high school Precalculus I class, and he really didn't understand it. After reading his textbook, I could understand why, the explanation was terrible. So, I decided to do a few examples for him, to show him how it would work. While I used Maple to do the computational pieces, I didn't use any built-in functions, I kept it as simple as possible.https://www.maplesoft.com/applications/view.aspx?SID=154517&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter SchochPlane flying through a thundercloud, calculating the E field
https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=Feed
This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.<img src="https://www.maplesoft.com/view.aspx?si=154519/b9715d1a184de2946329d1d396866539.gif" alt="Plane flying through a thundercloud, calculating the E field" style="max-width: 25%;" align="left"/>This problem models a thundercloud by a +40C charge at 10km height, -40C charge at 5km height and a 10C charge at a 2km height. It then has an airplane flying at 8km through the cloud. The crux of the problem is to calculate the Electric field on the plane beginning at the left of the cloud through to the right of the coud.
I placed the y axis along the charges within the cloud. his means the airplane has a fixed y value and just changes in x. I also numbered the charges from bottom to the top.https://www.maplesoft.com/applications/view.aspx?SID=154519&ref=FeedTue, 19 Feb 2019 05:00:00 ZProf. Peter SchochProf. Peter SchochStructured characteristic and bifurcation polynomials for polynomial maps
https://www.maplesoft.com/applications/view.aspx?SID=154515&ref=Feed
The worksheet computes linear transformation matrix T and its characteristic polynomial that belongs to a given polynomial map F (at least degree 2 in z) that can depend on parameters. The fastest computations are for the Mandelbrot map z^2+alpha, but other polynomial can be used. Matrix T represents multiplication by derivative of the map in a certain cyclic polynomial basis, the vector space that it works in is a cyclic polynomial factor ring according to ideal that belongs to k-cycles. The basis is chosen in a proper way to structure the matrix T into blocks that belong to cycle branches of known period d, d|k. The d-cycle branches degenerate at izolated parameter values with lambda = 1, where branches cross, so we can compute Guckenheimer's bifurcation points of a known type at connections of Mandelbrot bulbs and roots of newborn bulbs. Minimal bifurcation polynomials of d-cycles can be computed by this method. The characteristic polynomial for the Mandelbrot map transforms to the logistic map characteristic polynomial by a parameter change, since the maps are topologically equivalent. Fold bifurcation points of the logistic map are roots of the characteristic polynomials (more precisely their proper factors) for lambda = 1 and flip bifurcation points for lambda = -1. For k = 8 and lambda = -1 the worksheet computes the bifurcation polynomial for the B4 point of the logistic map. Since the basis have 36 cyclic polynomials, it computes determinant 36x36. Compared to the Groebner Basis method (see Kotsireas, Ilias S., and Kostas Karamanos. "Exact computation of the bifurcation point B4 of the logistic map and the Bailey-Broadhurst conjectures." International Journal of Bifurcation and Chaos 14.07 (2004): 2417-2423.) this method is relatively rapid (around 90 seconds, depending on the computer performance). The procedure matrixT with argument k (length of the cycle) is restricted to 150 polynomials in the cyclic basis to avoid time consuming operations, but you can change it. The same worksheet for the cubic Mandelbrot map z^3+alpha works analogously and computes the structure in the basis of dimension 130, but it takes more time to compute.<img src="https://www.maplesoft.com/view.aspx?si=154515/logisticMandelbrot.jpg" alt="Structured characteristic and bifurcation polynomials for polynomial maps" style="max-width: 25%;" align="left"/>The worksheet computes linear transformation matrix T and its characteristic polynomial that belongs to a given polynomial map F (at least degree 2 in z) that can depend on parameters. The fastest computations are for the Mandelbrot map z^2+alpha, but other polynomial can be used. Matrix T represents multiplication by derivative of the map in a certain cyclic polynomial basis, the vector space that it works in is a cyclic polynomial factor ring according to ideal that belongs to k-cycles. The basis is chosen in a proper way to structure the matrix T into blocks that belong to cycle branches of known period d, d|k. The d-cycle branches degenerate at izolated parameter values with lambda = 1, where branches cross, so we can compute Guckenheimer's bifurcation points of a known type at connections of Mandelbrot bulbs and roots of newborn bulbs. Minimal bifurcation polynomials of d-cycles can be computed by this method. The characteristic polynomial for the Mandelbrot map transforms to the logistic map characteristic polynomial by a parameter change, since the maps are topologically equivalent. Fold bifurcation points of the logistic map are roots of the characteristic polynomials (more precisely their proper factors) for lambda = 1 and flip bifurcation points for lambda = -1. For k = 8 and lambda = -1 the worksheet computes the bifurcation polynomial for the B4 point of the logistic map. Since the basis have 36 cyclic polynomials, it computes determinant 36x36. Compared to the Groebner Basis method (see Kotsireas, Ilias S., and Kostas Karamanos. "Exact computation of the bifurcation point B4 of the logistic map and the Bailey-Broadhurst conjectures." International Journal of Bifurcation and Chaos 14.07 (2004): 2417-2423.) this method is relatively rapid (around 90 seconds, depending on the computer performance). The procedure matrixT with argument k (length of the cycle) is restricted to 150 polynomials in the cyclic basis to avoid time consuming operations, but you can change it. The same worksheet for the cubic Mandelbrot map z^3+alpha works analogously and computes the structure in the basis of dimension 130, but it takes more time to compute.https://www.maplesoft.com/applications/view.aspx?SID=154515&ref=FeedSat, 02 Feb 2019 05:00:00 ZLenka PribylovaLenka PribylovaMaplet pour créer une Etoile
https://www.maplesoft.com/applications/view.aspx?SID=154511&ref=Feed
Cette Maplet permet de dessiner des étoiles en fonction du rayon de l'étoile,l'angle de ses branches,et le nombre de branches.On peut sauvegarder l'étoile en fichier .gif.C'est une application du théorème d'Al-Kashi.<img src="https://www.maplesoft.com/view.aspx?si=154511/etoile.gif" alt="Maplet pour créer une Etoile" style="max-width: 25%;" align="left"/>Cette Maplet permet de dessiner des étoiles en fonction du rayon de l'étoile,l'angle de ses branches,et le nombre de branches.On peut sauvegarder l'étoile en fichier .gif.C'est une application du théorème d'Al-Kashi.https://www.maplesoft.com/applications/view.aspx?SID=154511&ref=FeedTue, 15 Jan 2019 05:00:00 Zxavier cormierxavier cormierSolving the 15-puzzle
https://www.maplesoft.com/applications/view.aspx?SID=154509&ref=Feed
The 15-puzzle is a classic "sliding tile" puzzle that consists of tiles arranged in a 4 by 4 grid with one tile missing. The objective is to arrange the tiles in a sorted order only by making moves that slide a tile into the empty space. In this worksheet we demonstrate how this puzzle can be solved by encoding its rules into Boolean logic and using Maple's SAT solver.<img src="https://www.maplesoft.com/applications/images/app_image_blank_lg.jpg" alt="Solving the 15-puzzle" style="max-width: 25%;" align="left"/>The 15-puzzle is a classic "sliding tile" puzzle that consists of tiles arranged in a 4 by 4 grid with one tile missing. The objective is to arrange the tiles in a sorted order only by making moves that slide a tile into the empty space. In this worksheet we demonstrate how this puzzle can be solved by encoding its rules into Boolean logic and using Maple's SAT solver.https://www.maplesoft.com/applications/view.aspx?SID=154509&ref=FeedWed, 19 Dec 2018 05:00:00 ZCurtis BrightCurtis BrightInteractive Sudoku
https://www.maplesoft.com/applications/view.aspx?SID=154507&ref=Feed
This worksheet contains an interactive Sudoku game that allows one to play a game of Sudoku in Maple. New puzzles can be randomly generated, read from a file, or loaded an online source, and puzzles can be automatically solved.
No knowledge of Sudoku solving or puzzle generation was used in the implementation. Instead, the rules of Sudoku were encoded into Boolean logic and Maple's built-in SAT solver was used; source code and implementation details are included.<img src="https://www.maplesoft.com/view.aspx?si=154507/suduko.png" alt="Interactive Sudoku" style="max-width: 25%;" align="left"/>This worksheet contains an interactive Sudoku game that allows one to play a game of Sudoku in Maple. New puzzles can be randomly generated, read from a file, or loaded an online source, and puzzles can be automatically solved.
No knowledge of Sudoku solving or puzzle generation was used in the implementation. Instead, the rules of Sudoku were encoded into Boolean logic and Maple's built-in SAT solver was used; source code and implementation details are included.https://www.maplesoft.com/applications/view.aspx?SID=154507&ref=FeedMon, 03 Dec 2018 05:00:00 ZCurtis BrightCurtis BrightFord and Fulkerson's Max-Flow Algorithm
https://www.maplesoft.com/applications/view.aspx?SID=154503&ref=Feed
The Ford-Fulkerson algorithm is a method to solve the maximum flow problem in a connected weighted network. Proposes to look for routes in a network in which the flow can be increased, until the flow is reached maximum flow. The idea is to find a route of penetration with a net positive flow that links the origin and destination nodes.
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This work is part of a project in the master's degree in financial optimization destined to be used as didactic material in courses related to graph theory.<img src="https://www.maplesoft.com/view.aspx?si=154503/Imagen1.png" alt="Ford and Fulkerson's Max-Flow Algorithm" style="max-width: 25%;" align="left"/>The Ford-Fulkerson algorithm is a method to solve the maximum flow problem in a connected weighted network. Proposes to look for routes in a network in which the flow can be increased, until the flow is reached maximum flow. The idea is to find a route of penetration with a net positive flow that links the origin and destination nodes.
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This work is part of a project in the master's degree in financial optimization destined to be used as didactic material in courses related to graph theory.https://www.maplesoft.com/applications/view.aspx?SID=154503&ref=FeedFri, 30 Nov 2018 05:00:00 ZJorge Alberto CalvilloJorge Alberto Calvillo