Michael Monagan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=50
en-us2021 Maplesoft, A Division of Waterloo Maple Inc.Maplesoft Document SystemTue, 09 Mar 2021 08:49:12 GMTTue, 09 Mar 2021 08:49:12 GMTNew applications published by Michael Monaganhttps://www.maplesoft.com/images/Application_center_hp.jpgMichael Monagan: New Applications
https://www.maplesoft.com/applications/author.aspx?mid=50
Subgroup lattice plotting in 3-D
https://www.maplesoft.com/applications/view.aspx?SID=3907&ref=Feed
This routine is intended to show how one can program one's own plotting routines using the PLOT3D structure in Maple. The example we have chosen is to plot a subgroup lattice in 3-dimensions. But this code can serve as an example for how to plot an arbitrary graph G = V,E
<img src="https://www.maplesoft.com/view.aspx?si=3907//applications/images/app_image_blank_lg.jpg" alt="Subgroup lattice plotting in 3-D" style="max-width: 25%;" align="left"/>This routine is intended to show how one can program one's own plotting routines using the PLOT3D structure in Maple. The example we have chosen is to plot a subgroup lattice in 3-dimensions. But this code can serve as an example for how to plot an arbitrary graph G = V,E
https://www.maplesoft.com/applications/view.aspx?SID=3907&ref=FeedWed, 20 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganFORTRAN code generation with a linear algebra application
https://www.maplesoft.com/applications/view.aspx?SID=3888&ref=Feed
A discussion of the consequences that can arise from naive usage of symbolic computation when generating Fortran code. Given the following 3 by 3 symmetric matrix M (perhaps created in a symbolic computation system like Maple), and we want to evaluate numerically the inverse of M at particular values of the parameters q2, q3, p, m10, m30, j10y, j30x, j30y, j30z in a Fortran program. It is tempting to compute the inverse of the matrix M symbolically then use Maple's fortran function to generate the Fortran code. Does this produce the most efficient code? Let's see. <img src="https://www.maplesoft.com/view.aspx?si=3888//applications/images/app_image_blank_lg.jpg" alt="FORTRAN code generation with a linear algebra application" style="max-width: 25%;" align="left"/>A discussion of the consequences that can arise from naive usage of symbolic computation when generating Fortran code. Given the following 3 by 3 symmetric matrix M (perhaps created in a symbolic computation system like Maple), and we want to evaluate numerically the inverse of M at particular values of the parameters q2, q3, p, m10, m30, j10y, j30x, j30y, j30z in a Fortran program. It is tempting to compute the inverse of the matrix M symbolically then use Maple's fortran function to generate the Fortran code. Does this produce the most efficient code? Let's see. https://www.maplesoft.com/applications/view.aspx?SID=3888&ref=FeedWed, 20 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganDiatomic anharmonic oscillator
https://www.maplesoft.com/applications/view.aspx?SID=3878&ref=Feed
The calculation undertaken here employs perturbation theory of multiple orders; the extent of the calculation, according to the order, is adjustable by a user within limitations of machine capacity and acceptable duration of calculation.<img src="https://www.maplesoft.com/view.aspx?si=3878//applications/images/app_image_blank_lg.jpg" alt="Diatomic anharmonic oscillator" style="max-width: 25%;" align="left"/>The calculation undertaken here employs perturbation theory of multiple orders; the extent of the calculation, according to the order, is adjustable by a user within limitations of machine capacity and acceptable duration of calculation.https://www.maplesoft.com/applications/view.aspx?SID=3878&ref=FeedWed, 20 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganPlanck radiation
https://www.maplesoft.com/applications/view.aspx?SID=3818&ref=Feed
The Planck Radiation Formula is derived from Statistical Mechanics and Stefan's constant found.<img src="https://www.maplesoft.com/view.aspx?si=3818//applications/images/app_image_blank_lg.jpg" alt="Planck radiation" style="max-width: 25%;" align="left"/>The Planck Radiation Formula is derived from Statistical Mechanics and Stefan's constant found.https://www.maplesoft.com/applications/view.aspx?SID=3818&ref=FeedTue, 19 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganNumber of iterations in Collatz's problem
https://www.maplesoft.com/applications/view.aspx?SID=3644&ref=Feed
The 3n+1 sequence has probably consumed more CPU time than any other number theoretic conjecture. The reason being that its statement is so simple, that most amateurs will feel compelled to write programs to test it. This sequence, attributed to Lothar Collatz, has bee given various names, including Ulam's conjecture, Syracuse problem, Kakutani's problem and Hasse's algorithm. The conjecture is based on the iteration defined by:
n[i+1] = if n[i] is even then n[i]/2 else 3*n[i]+1 .
<img src="https://www.maplesoft.com/view.aspx?si=3644//applications/images/app_image_blank_lg.jpg" alt="Number of iterations in Collatz's problem" style="max-width: 25%;" align="left"/>The 3n+1 sequence has probably consumed more CPU time than any other number theoretic conjecture. The reason being that its statement is so simple, that most amateurs will feel compelled to write programs to test it. This sequence, attributed to Lothar Collatz, has bee given various names, including Ulam's conjecture, Syracuse problem, Kakutani's problem and Hasse's algorithm. The conjecture is based on the iteration defined by:
n[i+1] = if n[i] is even then n[i]/2 else 3*n[i]+1 .
https://www.maplesoft.com/applications/view.aspx?SID=3644&ref=FeedTue, 19 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganAn interesting 6x6 matrix
https://www.maplesoft.com/applications/view.aspx?SID=3631&ref=Feed
A highly structured symbolic matrix containing the six symbols "L-A-P-A-C-K" in various orders and signs is explored for interesting patterns, including its determinant, eigenvalues and inverse.<img src="https://www.maplesoft.com/view.aspx?si=3631//applications/images/app_image_blank_lg.jpg" alt="An interesting 6x6 matrix" style="max-width: 25%;" align="left"/>A highly structured symbolic matrix containing the six symbols "L-A-P-A-C-K" in various orders and signs is explored for interesting patterns, including its determinant, eigenvalues and inverse.https://www.maplesoft.com/applications/view.aspx?SID=3631&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganSymbolic eigenvalues & eigenvectors
https://www.maplesoft.com/applications/view.aspx?SID=3628&ref=Feed
How to compute exact symbolic values for eigenvalues and eigenvectors of both numeric and symbolic matrices, and computing with roots of polynomials.<img src="https://www.maplesoft.com/view.aspx?si=3628//applications/images/app_image_blank_lg.jpg" alt="Symbolic eigenvalues & eigenvectors " style="max-width: 25%;" align="left"/>How to compute exact symbolic values for eigenvalues and eigenvectors of both numeric and symbolic matrices, and computing with roots of polynomials.https://www.maplesoft.com/applications/view.aspx?SID=3628&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganAll terminal reliability polynomial for a graph G with probabilty of edge failure p
https://www.maplesoft.com/applications/view.aspx?SID=3519&ref=Feed
Routine for the all terminal reliability polynomial for a graph G with probability of edge failure<img src="https://www.maplesoft.com/view.aspx?si=3519//applications/images/app_image_blank_lg.jpg" alt="All terminal reliability polynomial for a graph G with probabilty of edge failure p" style="max-width: 25%;" align="left"/>Routine for the all terminal reliability polynomial for a graph G with probability of edge failurehttps://www.maplesoft.com/applications/view.aspx?SID=3519&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganMotion of a bullet under air resistance
https://www.maplesoft.com/applications/view.aspx?SID=3494&ref=Feed
This worksheet considers the problem of a ball or bullet thrown (shot) straight up into the air, with air resistance taken into account. We describe the trajectory of the ball / bullet as an ODE, plot the motion of the ball / bullet and solve for when the ball lands on the ground.<img src="https://www.maplesoft.com/view.aspx?si=3494//applications/images/app_image_blank_lg.jpg" alt="Motion of a bullet under air resistance" style="max-width: 25%;" align="left"/>This worksheet considers the problem of a ball or bullet thrown (shot) straight up into the air, with air resistance taken into account. We describe the trajectory of the ball / bullet as an ODE, plot the motion of the ball / bullet and solve for when the ball lands on the ground.https://www.maplesoft.com/applications/view.aspx?SID=3494&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganPrimitive trinomials
https://www.maplesoft.com/applications/view.aspx?SID=3464&ref=Feed
Computing primitive trinomials overfinite fields for error correcting codes and random number generators<img src="https://www.maplesoft.com/view.aspx?si=3464//applications/images/app_image_blank_lg.jpg" alt="Primitive trinomials" style="max-width: 25%;" align="left"/>Computing primitive trinomials overfinite fields for error correcting codes and random number generatorshttps://www.maplesoft.com/applications/view.aspx?SID=3464&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganCommutator package for Maple 6
https://www.maplesoft.com/applications/view.aspx?SID=123869&ref=Feed
This package provides for manipulation and simplification of commutators, expanding commutators in terms of &* Maple's non-commutatorive multiplication operator, and converting an expression in terms of &* to commutator form. <img src="https://www.maplesoft.com/view.aspx?si=3452//applications/images/app_image_blank_lg.jpg" alt="Commutator package for Maple 6" style="max-width: 25%;" align="left"/>This package provides for manipulation and simplification of commutators, expanding commutators in terms of &* Maple's non-commutatorive multiplication operator, and converting an expression in terms of &* to commutator form. https://www.maplesoft.com/applications/view.aspx?SID=123869&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganEuclid's algorithm for computing greatest common divisors, with a modern improvement
https://www.maplesoft.com/applications/view.aspx?SID=3451&ref=Feed
This worksheet is intended to show two things, firstly, how to write simple programs in Maple, and secondly, a expository study of Euclid's algorithm and how to compute the greatest common divisor of two integers a and b.
First, what is the greatest common divisor of two integers and why is this calculation important?<img src="https://www.maplesoft.com/view.aspx?si=3451//applications/images/app_image_blank_lg.jpg" alt="Euclid's algorithm for computing greatest common divisors, with a modern improvement" style="max-width: 25%;" align="left"/>This worksheet is intended to show two things, firstly, how to write simple programs in Maple, and secondly, a expository study of Euclid's algorithm and how to compute the greatest common divisor of two integers a and b.
First, what is the greatest common divisor of two integers and why is this calculation important?https://www.maplesoft.com/applications/view.aspx?SID=3451&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael MonaganFinite splitting fields
https://www.maplesoft.com/applications/view.aspx?SID=3450&ref=Feed
This worksheet is an application of Maple to doing some simple calculations over finite fields GF(p^k). The application is from error correcting codes and was brought to us by Nicolas Sendrier, INRIA, France, in May/90.
We were given a polynomial f(x) of the following form<img src="https://www.maplesoft.com/view.aspx?si=3450//applications/images/app_image_blank_lg.jpg" alt="Finite splitting fields" style="max-width: 25%;" align="left"/>This worksheet is an application of Maple to doing some simple calculations over finite fields GF(p^k). The application is from error correcting codes and was brought to us by Nicolas Sendrier, INRIA, France, in May/90.
We were given a polynomial f(x) of the following formhttps://www.maplesoft.com/applications/view.aspx?SID=3450&ref=FeedMon, 18 Jun 2001 00:00:00 ZMichael MonaganMichael Monagan