Maple Toolboxes Questions and Posts

These are Posts and Questions associated with the product, Maple Toolboxes
 

 

 

Maple 2019 has a new add-on package Maple Quantum Chemistry Toolbox from RDMChem for computing the energies and properties of molecules.  As a member of the team at RDMChem that developed the package, I would like to tell the story of its origins and provide a brief demonstration of the package.  

 

Thinking about Quantum Chemistry at Harvard

 

The story of the Maple Quantum Chemistry Toolbox begins with my graduate studies in Chemical Physics at Harvard University in the late 1990s.  Even in 1998 programs for computing the energies and properties of molecules were extremely complicated and nonintuitive.  Many of the existing programs had begun in the 1970s on computers whose programs would be recorded on punchcards.

Fig. 1: Used Punchcard by Pete Birkinshaw from Manchester, UK CC BY 2.0

 

Even today some of these programs have remnants of their early versions such as input files that must start on the second column to account for the margin of the now non-existent punchcards.  As a student, I made a bound copy of one of these manuals at a local Kinkos photocopy shop and later found myself in Harvard Yard, thinking that there must be a better way to present quantum chemistry computations.  The idea for a Maple-like package for quantum chemistry was born in that moment.

 

At the same time I was learning about something called the two-electron reduced density matrix (2-RDM).  The basic variable in quantum chemistry is the wave function which is the probability amplitude for finding each of the electrons in a molecule.  Because electrons are indistinguishable with pairwise interactions, the wave function contains much more information than is needed for computing the energies and electronic properties of molecules.  The energies and properties of any molecule with any number of electrons can be expressed as a function of a 2 electron matrix, the 2-RDM [1-3].  A quantum chemistry based on the 2-RDM, it was known, would have potentially significant advantages over wave function calculations in terms of accuracy and computational cost, especially for molecules far from the mean-field limit.  A 2-RDM approach to quantum chemistry became the focus of my Ph.D. thesis.

 

Representing Many Electrons with Only Two Electrons

 

The idea of using the 2-RDM in quantum chemistry can be attributed to four scientists: two physicists Kodi Husimi and Joseph Mayer, a chemist Per-Olov Lowdin, and a mathematician John Coleman [1-3].  In the early 1940s Husimi first published the idea in a Japanese physics journal, but in the midst of World War II the paper was not widely disseminated in the West.  In the summer of 1951 John Coleman, which attending a physics conference at Chalk River, realized that the ground-state energy of any atom or molecule could be expressed as functional of the 2-RDM, and similar ideas later occurred to Per-Olov Lowdin and Joseph Mayer who published their ideas in Physical Review in 1955.  It was soon recognized that computing the ground-state energy of an atom or molecule with the 2-RDM was potentially difficult because not every two-electron density matrix corresponds to an N-electron density matrix or wave function.  The search for the appropriate constraints on the 2-RDM, known as N-representability conditions, became known as the N-representability problem [1-3].  

 

Beginning in the late 1990s and early 2000s, Carmela Valdemoro and Diego Alcoba at the Consejo Superior de Investigaciones Científicas (Madrid, Spain), Hiroshi Nakatsuji, Koji Yasuda, and Maho Nakata at Kyoto University (Kyoto, Japan), Jerome Percus and Bastiaan Braams at the Courant Institute (New York, USA), John Coleman and Robert Erdahl at Queens University (Kingston, Canada), and my research group and I at The University of Chicago (Chicago, USA) began to make significant progress in the computation of the 2-RDM without computing the many-electron wave function [1-3].  Further contributions were made by Eric Cances and Claude Le Bris at CERMICS, Ecole Nationale des Ponts et Chaussées (Marne-la-Vallée, France), Paul Ayers at McMaster University (Hamilton, Canada), and Dimitri Van Neck at the University of Ghent (Ghent, Belgium) and their research groups.  By 2014 several powerful 2-RDM methods had emerged for the computation of molecules.  The Army Research Office (ARO) issued a proposal call for a company to develop a modern, built-from-scratch package for quantum chemistry that would contain two newly developed 2-RDM-based methods from our group: the parametric 2-RDM method [1] and the variational 2-RDM method with a fast algorithm for solving the semidefinite program [4,5,6].   The company RDMChem LLC was founded to work with the ARO to develop such a package built around RDMs, and hence, the name of the company RDMChem was selected as a hybrid of the RDM abbreviation for Reduced Density Matrices and the Chem colloquialism for Chemistry.  To achieve a really new design for an electronic structure package with access to numeric and symbolic computations as well as advanced visualizations, the team at RDMChem and I developed a partnership with Maplesoft to build something new that became the Maple Quantum Chemistry Package (or Toolbox), which was released with Maple 2019 on Pi Day.

 

Maple Quantum Chemistry Toolbox

 The Maple Quantum Chemistry Toolbox provides a powerful, parallel platform for quantum chemistry calculations that is directly integrated into the Maple 2019 environment.  It is optimized for both cutting-edge research as well as chemistry education.  The Toolbox can be used from the worksheet, document, or command-line interfaces.  Plus there is a Maplet interface for rapid exploration of molecules and their properties.  Figure 2 shows the Maplet interface being applied to compute the ground-state energy of 1,3-dibromobenzene by density functional theory (DFT) in a 6-31g basis set.           

Fig. 2: Maplet interface to the Quantum Chemistry Toolbox 2019, showing a density functional theory (DFT) calculation         

After entering a name into the text box labeled Name, the user can click on: (1) the button Web to import the geometry from an online database containing more than 96 million molecules,  (2) the button File to read the geometry from a standard XYZ file, or (3) the button Input to enter the geometry.  As soon the geometry is entered, the Maplet displays a 3D picture of the molecule in the window on the right of the options.  Dropdown menus allow the user to select the basis set, the electronic structure method, and a boolean for geometry optimization.  The user can click on the Compute button to perform the computation.  When the quantum computation completes, the total energy appears in the box labeled Total Energy.  The dropdown menu Analyze contains a list of data tables, plots, and animations that can be selected and then displayed by clicking the Analyze button.  The Maplet interface contains nearly all of the options available in the worksheet interface.   The Help Pages of the Toolbox include extensive curricula and lessons that can be used in undergraduate, graduate, and even high school chemistry courses.  Next we look at some sample calculations in the worksheet interface.     

 

Reproducing an Early 2-RDM Calculation

 

One of the earliest variational calculations of the 2-RDM was performed in 1975 by Garrod, Mihailović,  and  Rosina [1-3].  They minimized the electronic ground state of the 4-electron atom beryllium as a functional of only two electrons, the 2-RDM.  They imposed semidefinite constraints on the particle-particle (D), hole-hole (Q), and particle-hole (G) metric matrices.  They solved the resulting optimization problem of minimizing the energy as a linear function of the 2-RDM subject to the semidefinite constraints, known as a semidefinite program, by a cutting-plane algorithm.  Due to limitations of the cutting-plane algorithm and computers circa 1975, the calculation was a difficult one, likely taking a significant amount of computer time and memory.

 

With the Quantum Chemistry Toolbox we can use the command Variational2RDM to reproduce the calculation on a Windows laptop.  First, in a Maple 2019 worksheet we load the commands of the Add-on Quantum Chemistry Toolbox:

with(QuantumChemistry);

[AOLabels, ActiveSpaceCI, ActiveSpaceSCF, AtomicData, BondAngles, BondDistances, Charges, ChargesPlot, CorrelationEnergy, CoupledCluster, DensityFunctional, DensityPlot3D, Dipole, DipolePlot, Energy, FullCI, GeometryOptimization, HartreeFock, Interactive, Isotopes, MOCoefficients, MODiagram, MOEnergies, MOIntegrals, MOOccupations, MOOccupationsPlot, MOSymmetries, MP2, MolecularData, MolecularGeometry, NuclearEnergy, NuclearGradient, Parametric2RDM, PlotMolecule, Populations, RDM1, RDM2, ReadXYZ, SaveXYZ, SearchBasisSets, SearchFunctionals, SkeletalStructure, Thermodynamics, Variational2RDM, VibrationalModeAnimation, VibrationalModes, Video]

(1.1)

Then we define the atom (or molecule) using a Maple list of lists that we assign to the variable atom:

atom := [["Be",0,0,0]];

[["Be", 0, 0, 0]]

(1.2)

 

We can then perform the variational 2-RDM method with the Variational2RDM command to compute the ground-state energy and properties of beryllium in a minimal basis set like the one used by Rosina and his collaborators.  By default the method uses the D, Q, and G N-representability conditions and the minimal "sto-3g" basis set.  The calculation, which completes in seconds, contains a wealth of information in the form of a convenient Maple table that we assign to the variable data.

data := Variational2RDM(atom);

table(%id = 18446744313704784158)

(1.3)

 

The table contains the total ground-state energy of the beryllium atom in the atomic unit of energy (hartrees)

data[e_tot];

HFloat(-14.40370016681039)

(1.4)

 

We also have the atomic orbitals (AOs) employed in the calculation

data[aolabels];

Vector(5, {(1) = "0 Be 1s", (2) = "0 Be 2s", (3) = "0 Be 2px", (4) = "0 Be 2py", (5) = "0 Be 2pz"})

(1.5)

 

as well as the Mulliken populations of these orbitals

data[populations];

Vector(5, {(1) = 1.9995807710723152, (2) = 1.7913484714571852, (3) = 0.6969023822632789e-1, (4) = 0.6969026475511847e-1, (5) = 0.6969029119010149e-1})

(1.6)

 

We see that 2 electrons are located in the 1s orbital, 1.8 electrons in the 2s orbital, and about 0.2 electrons in the 2p orbitals.  By default the calculation also returns the 1-RDM

data[rdm1];

Matrix(5, 5, {(1, 1) = 1.9999258249189755, (1, 2) = -0.37784860208539793e-2, (1, 3) = 0., (1, 4) = 0., (1, 5) = 0., (2, 1) = -0.37784860208539793e-2, (2, 2) = 1.7910034176105256, (2, 3) = 0., (2, 4) = 0., (2, 5) = 0., (3, 1) = 0., (3, 2) = 0., (3, 3) = 0.6969023822632789e-1, (3, 4) = 0., (3, 5) = 0., (4, 1) = 0., (4, 2) = 0., (4, 3) = 0., (4, 4) = 0.6969026475511847e-1, (4, 5) = 0., (5, 1) = 0., (5, 2) = 0., (5, 3) = 0., (5, 4) = 0., (5, 5) = 0.6969029119010149e-1})

(1.7)

 

The eigenvalues of the 1-RDM are the natural orbital occupations

LinearAlgebra:-Eigenvalues(data[rdm1]);

Vector(5, {(1) = 1.9999941387490443+0.*I, (2) = 1.7909351037804568+0.*I, (3) = 0.6969023822632789e-1+0.*I, (4) = 0.6969026475511847e-1+0.*I, (5) = 0.6969029119010149e-1+0.*I})

(1.8)

 

We can display the density of the 2s-like 2nd natural orbital using the DensityPlot3D command providing the atom, the data, and the orbitalindex keyword

DensityPlot3D(atom,data,orbitalindex=2);

 

 

Similarly,  using the DensityPlot3D command, we can readily display the 2p-like 3rd natural orbital

DensityPlot3D(atom,data,orbitalindex=3);

 

 

By using Maple keyword arguments in the Variational2RDM command, we can readily change the basis set, use point-group symmetry, add active orbitals with or without self-consistent-field, change the N-representability conditions, as well as explore many other options.  Having reenacted one of the first variational 2-RDM calculations ever, let's examine a more complicated molecule.

 

Explosive TNT

 

We consider the molecule TNT that is used as an explosive. Using the command MolecularGeometry, we can import the experimental geometry of TNT from the online PubChem database.

mol := MolecularGeometry("TNT");

[["O", .5454, -3.514, 0.12e-2], ["O", .5495, 3.5137, 0.8e-3], ["O", 2.4677, -2.4539, -0.5e-3], ["O", 2.4705, 2.4513, 0.3e-3], ["O", -3.5931, -1.0959, 0.4e-3], ["O", -3.5922, 1.0993, 0.6e-3], ["N", 1.2142, -2.454, 0.2e-3], ["N", 1.217, 2.4527, 0], ["N", -2.9846, 0.15e-2, 0.1e-3], ["C", 1.2253, -0.6e-3, -0.9e-3], ["C", .5271, -1.2082, -0.8e-3], ["C", .5284, 1.2078, -0.8e-3], ["C", -1.5646, 0.8e-3, -0.4e-3], ["C", -.8678, -1.2074, -0.6e-3], ["C", -.8666, 1.2084, -0.6e-3], ["C", 2.7239, -0.16e-2, 0.11e-2], ["H", -1.4159, -2.1468, -0.3e-3], ["H", -1.4137, 2.1483, -0.3e-3], ["H", 3.1226, .2418, -.9891], ["H", 3.0863, .6934, .7662], ["H", 3.3154, -.8111, .4109]]

(1.9)

 

The command PlotMolecule generates a 3D ball-and-stick plot of the molecule

PlotMolecule(mol);

 

 

We perform a variational calculation of the 2-RDM of TNT in an active space of 10 electrons and 10 orbitals by setting the keyword active to the list [10,10].  The keyword casscf is set to true to optimize the active orbitals during the calculation.  The keyword basis is used to set the basis set to a minimal basis set sto-3g for illustration.   

data := Variational2RDM(mol, active=[10,10], casscf=true, basis="sto-3g");

table(%id = 18446744493271367454)

(1.10)

 

The ground-state energy of TNT in hartrees is

data[e_tot];

HFloat(-868.8629631593426)

(1.11)

 

Unlike beryllium, the electric dipole moment of TNT in debyes is nonzero

data[dipole];

Vector(3, {(1) = .5158925019252739, (2) = -0.5985274393363119e-1, (3) = .1277528280025474})

(1.12)

 

We can easily visualize the dipole moment relative to the molecule's ball-and-stick model with the DipolePlot command

DipolePlot(mol,method=Variational2RDM, active=[10,10], casscf=true, basis="sto-3g");

 

 

The 1-RDM is returned by default

data[rdm1];

_rtable[18446744313709602566]

(1.13)

 

The natural molecular-orbital (MO) occupations are the eigenvalues of the 1-RDM

data[mo_occ];

_rtable[18446744313709600150]

(1.14)

 

All of the occupations can be viewed at once by converting the Vector to a list

convert(data[mo_occ], list);

[HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(2.0), HFloat(1.9110133620349001), HFloat(1.8984139688344246), HFloat(1.6231436866358906), HFloat(1.6158489471020905), HFloat(1.6145310163161273), HFloat(0.38920731792133734), HFloat(0.387039366894289), HFloat(0.37786347287813526), HFloat(0.09734187094597906), HFloat(0.08559699476985069), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0), HFloat(0.0)]

(1.15)

 

We can visualize these occupations with the MOOccupationsPlot command

MOOccupationsPlot(mol,method=Variational2RDM, active=[10,10], casscf=true, basis="sto-3g");

 

 

The occupations, we observe, show significant deviations from 0 and 2, indicating that the electrons have substantial correlation beyond the mean-field (Hartree-Fock) limit.  The blue lines indicate the first N/2 spatial orbitals where N is the total number of electrons while the red lines indicate the remaining spatial orbitals.  We can visualize the highest "occupied" molecular orbital (58) with the DensityPlot3D command

DensityPlot3D(mol,data, orbitalindex=58);

 

 

Similarly, we can visualize the lowest "unoccupied" molecular orbital (59) with the DensityPlot3D command

DensityPlot3D(mol,data, orbitalindex=59);

 

 

Comparison of orbitals 58 and 59 reveals an increase in the number of nodes (changes in the phase of the orbitals denoted by green and purple), which reflects an increase in the energy of the orbital.

 

Looking Ahead

 

The Maple Quantum Chemistry Toolbox 2019, an new Add-on for Maple 2019 from RDMChem, provides a easy-to-use, research-grade environment for the computation of the energies and properties of atoms and molecules.  In this blog we discussed its origins in graduate research at Harvard, its reproduction of an early 2-RDM calculation of beryllium, and its application to the explosive molecule TNT.  We have illustrated only some of the many features and electronic structure methods of the Maple Quantum Chemistry package.  There is much more chemistry and physics to explore.  Enjoy!    

 

Selected References

 

[1] D. A. Mazziotti, Chem. Rev. 112, 244 (2012). "Two-electron Reduced Density Matrix as the Basic Variable in Many-Electron Quantum Chemistry and Physics"

[2]  Reduced-Density-Matrix Mechanics: With Application to Many-Electron Atoms and Molecules (Adv. Chem. Phys.) ; D. A. Mazziotti, Ed.; Wiley: New York, 2007; Vol. 134.

[3] A. J. Coleman and V. I. Yukalov, Reduced Density Matrices: Coulson’s Challenge (Springer-Verlag,  New York, 2000).

[4] D. A. Mazziotti, Phys. Rev. Lett. 106, 083001 (2011). "Large-scale Semidefinite Programming for Many-electron Quantum Mechanics"

[5] A. W. Schlimgen, C. W. Heaps, and D. A. Mazziotti, J. Phys. Chem. Lett. 7, 627-631 (2016). "Entangled Electrons Foil Synthesis of Elusive Low-Valent Vanadium Oxo Complex"

[6] J. M. Montgomery and D. A. Mazziotti, J. Phys. Chem. A 122, 4988-4996 (2018). "Strong Electron Correlation in Nitrogenase Cofactor, FeMoco"

 

Download QCT2019_PrimesV17_05.05.19.mw

It is my pleasure to announce the return of the Maple Conference! On October 15-17th, in Waterloo, Ontario, Canada, we will gather a group of Maple enthusiasts, product experts, and customers, to explore and celebrate the different aspects of Maple.

Specifically, this conference will be dedicated to exploring Maple’s impact on education, new symbolic computation algorithms and techniques, and the wide range of Maple applications. Attendees will have the opportunity to learn about the latest research, share experiences, and interact with Maple developers.

In preparation for the conference we are welcoming paper and extended abstract submissions. We are looking for presentations which fall into the broad categories of “Maple in Education”, “Algorithms and Software”, and “Applications of Maple” (a more extensive list of topics can be found here).

You can learn more about the event, plus find our call-for-papers and abstracts, here: https://www.maplesoft.com/mapleconference/

Hello,

I try to install MapleToolbox2018.0LinuxX64Installer.run I run it as root or with sudo command, but everytime I finish with below message:

Choose Maple 2018 Folder

Please specify the path to your existing Maple 2018 Installation.

 [/opt/maple2018]:  /opt/exp_soft/local/generic/maple/2018

----------------------------------------------------------------------------
Choose MATLAB Folder

Select your MATLAB installation.

 []: /opt/exp_soft/local/generic/matlab/R2016b

Warning: The installer has detected a previous version of the Maple Toolbox in
your MATLAB installation.
Press [Enter] to continue:
Warning: The directory
/opt/exp_soft/local/generic/matlab/R2016b
is not writable by the current user

I'm not sure what to do with it.

---
Regards,

Bartek

 

I've got Maple 2017 linked to MATLAB R2017a but I can't get MATLAB R2017a linked to Maple 2017.

I've got MATLAB R2016b linked to Maple 2017.

Any ideas? (Or do I just need to wait for an update?)

I have an important question regarding the symbolic toolbox from maple for matlab

I have declared three symbolic variables:

syms t;

x = sym('x(t)', 'real');

y = sym('y(t)', 'real');

z = sym('z(t)', 'real'); 

f = x + y + z;

Now i want to  calculate the derivation of f regarding the variable t:

df = diff (f, t);

The result should be 

df = dx(t) / dt + dy(t) / dt + dz(t) / dt

but  instead i get the result df = 0. If i use the command diff (f) i get the result

df = dx(t) / dt 

Does anyone know how to fix this problem?

 

I was looking to see if anyone has come across a Maple routine for a savings algorithm - specifically, Clarke and Wright. In fact, any classical savings heuristic would also be interesting.

Any guidance would be truly appreciated.

 

I have proposed a SE site for maple.

This will help to put maple on SE.

Please follow this site.

http://area51.stackexchange.com/proposals/107315/maple

 Update

We have moved to the next phase Commitment. Come and join us.

Hi,

Ive been trying to use the global optimization toolbox to optimize a model I extract from the maplesim environment.
It works fine with the regular Optimization toolbox. but when I run the optimization on the Global toolbox I get this error:

Warning, Error at t=0.0000000000000000e+000: index-1 and derivative evaluation failure

to explain a little,
I use the getCompiledProc command to turn the maplesim model into a module to be used in maple.

pjf

I  encountered a non-integrable integral in the process of solving the following process, . How to achieve its numerical solution? Such as in a looping   code:

#######
pa[i] := pa[i-1]-(Int(subs(t = tau, Lpa[i-1]+Na1[i-1]-Na2[i-1]), tau = 0 .. t)); 

pw[i] := pw[i-1]-(Int(subs(t = tau, Lpw[i-1]+Nw1[i-1]-Nw2[i-1]), tau = 0 .. t)); u[i] := u[i-1]-(Int(subs(t = tau, Lu[i-1]+Nu1[i-1]+Nu2[i-1]), tau = 0 .. t));

######
Detailed code see annexBC2.mw

Hello

I have a procedure that builds an ideal from a specific set of polynomials and then calls the Groebner basis package to eliminate some of the variables.  Even though the procedure is running on a machine with 2 processors, 24 cores and 72 GB of ram, only one core has been used (and is always on a 100% usage).  Would the Grid Computing Toolbox be of some hope in this case?  If so,  how to insert the Grid commands so that Maple sends the calculations to the other cores (I find the document rather confusing)?   If I am talking non sense,  please let me know.

Many thanks

Ed

 

 

 

Hi everyone,

For my first question, I am looking for some help about the following. I have the opportunity to run a worksheet in parallel on a cluster of sixteen workstations, each one endowed with twelve CPUs, through the GRID Computing Toolbox. However, I have troubles concerning how to do that.

I join the worksheet at issue: abmm_ma_1.mw The aim is to run large-scale numerical simulations of a dynamic system, depending on the values given to the initial conditions and to the parameters. The worksheet is organized in four execution groups:

  1. The required packages (combinat and LinearAlgebra).
  2. Calibration of the parameters and initial conditions.
  3. The system, which is embedded into a procedure called SIM.
  4. The activation of SIM, whose outputs are nine .mla files, each one being made of a real-number matrix.

The truth is, I do not clearly see how to modify the worksheet with some elements of the GRID package. Besides, the cluster operates under HTCondor so that running the worksheet requires beforehand the creation of a .sub file. This should be done in consistency with the aforesaid modification.

Any help is welcome, thanks a lot.

We have just released a new version of the Multivariate Calculus Study Guide.  It provides a new section on Vector Calculus, with over 100 additional worked problems, and makes extensive use of Maple’s Clickable Math tools as well as commands.

Existing study guide customers can get the new content via a free update, available through the Check for Updates system or from our website. See Multivariate Calculus Study Guide 2016 Update for details.

For more information about this guide, including a full table of contents, visit Multivariate Calculus Study Guide.

 

eithne

How to random generate 2 integer number with condition x must be less than y ?

I had tried the coding below. But the output shown not what i want.

x:=RandomTools[Generate](integer(range=1..7);

y:=RandomTools[Generate](integer(range=1..7);

if x>= y then x:=RandomTools[Generate](integer(range=1..7); y:=RandomTools[Generate](integer(range=1..7); end if;

 

Example:

I get x:= 5 , y:=1, then i need to regenerate the value of x and y using the last statemet above. but the problem is sometime i might still get the value of x>= y for example on second generate x:3, y=2. I need a code that x and y must be regerate until it get x<y. Can someone help ? Thank you in advance.

 

Hi all

I need to convert int matrix into matrix over finite field.

E.g: Convert inform integer number

      A := <140, 155, 162, 64;

               218, 12, 245, 50;

                36, 251, 34, 253;

                171, 251, 184, 37>;

 into B = <x^7+x^3+x^2,x^7+x^4+x^3+x+1,x^7+x^5+x, x^6;

             x^7+x^6+x^4+x^3+x, x^3+x^2, x^7+x^6+x^5+x^4+x^2+1, x^5+x^4+x;

            x^5+x^2, x^7+x^6+x^5+x^4+x^3+x+1, x^5+x, x^7+x^6+x^5+x^4+x^3+x^2+1;

            x^7+x^5+x^3+x+1, x^7+x^6+x^5+x^4+x^3+x+1, x^7+x^5+x^4+x^3, x^5+x^2+1>;

 

(Matrix B over finite field GF(2^8)/f(x) =x^8 + x^6 +x^5 +x^3 +1) 

Thanks alot.

I got a code file and i dont know how to load it in Linux. In Windows i just type:

read "E:/code.txt"

But thing now i change to use Linux and cant do the same (Maple 2015 64bit Linux ver), try to load

read "/root/Desktop/code.txt"

It show me that:

I click Cancel and it show me:

Hope can help me another ways to use and load my code to run.

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