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Here's a simple package for drawing knot diagrams and computing the Alexander polynomial. A typical usage case for the AlexanderPolynomial function is when a knot needs to be identified and only a visual representation of the knot is available. Then it's trivial to write down the Dowker sequence by hand and then the sequence can be used as an input for this package. The KnotDiagram function also takes the Dowker sequence as an input.


TorusKnot(p, q) and PretzelKnot(p, q, r) are accepted as an input as well and can also be passed to the DowkerNotation function.


The algorithm is fairly simple, it works as follows: represent each double point as a quadrilateral (two 'in' vertices and two 'out' vertices); connect the quads according to the Dowker specification; draw the result as a planar graph; erase the sides of each quad and draw its diagonals instead. This draws the intersections corresponding to the double points and guarantees that there are no other intersections. The knot polynomial is then computed from the diagram.


The diagrams work fairly well for pretzel knots, but for certain knots they can be difficult to read because some of the quads around the double points can become too small or too skewed. Also, the code doesn't check that the generated quadrilaterals are convex (which is an implicit assumption in the algorithm).



read "c:/math/prg/maple/knot.txt"




[AlexanderPolynomial, DowkerNotation, KnotDiagram]


AlexanderPolynomial([6, 8, 10, 2, 4], t)



AlexanderPolynomial([4, 10, 14, 12, 2, 8, 6], t)



AlexanderPolynomial([6, 18, 16, 14, -20, 4, 2, 22, 12, -8, -10], t)



KnotDiagram([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14])


AlexanderPolynomial([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14], t)



AlexanderPolynomial([4, 8, 10, 16, 2, 18, 20, 22, 6, 14, 12], t)



DowkerNotation(TorusKnot(5, 4))

[-24, -10, 20, -30, -16, 26, -6, -22, 2, -12, -28, 8, -18, -4, 14]


KnotDiagram(TorusKnot(5, 4))


AlexanderPolynomial(TorusKnot(p, q), t); 1; simplify(subs([p = 5, q = 4], %))





DowkerNotation(PretzelKnot(3, -4, 5))

[-16, -14, 20, 22, 24, 18, -4, -2, 10, 12, 6, 8]


KnotDiagram(PretzelKnot(3, -4, 5))


AlexanderPolynomial(PretzelKnot(p, q, r), t)

piecewise(p::odd and q::odd and r::odd, piecewise(p*q+p*r+q*r <> -1, (1/4)*signum(p*q+p*r+q*r+1)*((p*q+p*r+q*r)*(t^2-2*t+1)+t^2+2*t+1), 1), AlexanderPolynomial(PretzelKnot(p, q, r), t))


eval(%, [p = 3, q = -4, r = 5])






On the Physics Research and development page there are only 3 versions of the Physics package available.  What happened to the earlier final updates for Maple 16, 15 etc...

What is the latest one that can work on Maple12?  Was there one for M12?  What is the earliest versions of Maple the Research & Development Physics packages can work on?


Does any one have the package DESOLV not deslove , I need it with its help file.


Carl Love 9260


how can I download Fourier series package?

I have few packages downloaded from following link:

Following are packages that I need to install on Maple:

Rif: For differential elimination.

GeM: For computing symmetries and conservation laws for nonlinear PDEs.

wkptest: For symbolic computation of Painleve test for nonlinear PDEs.

My problem is to install these packages onto Maple, but I do not know how to do this. For example, the package Rif contains file like maple.hdb, maple.ind, maple.lib, but I do not know what to do with these files. I shall be grateful to auduience of Mapleprime if somebody can help me on this.

I created my own package and one procudure inside this package is to calculate the eigenvalues of a identity matrix, as shown below




Then, I use this package in another document, all other procedures work well except the procedure calculating egigenvalues, as shown below




How to solve this problem? Thank you.

I want to make a package that I have created work with the LinearAlgebra package that comes with Maple. My package loads into a worksheet fine, but when I try to use one of my procedures, most of which depend upon procedures in the Linear Algebra package, the executable part of my procedure from my package is simply echoed to the screen and not executed. If I then copy the echoed part to a command prompt then it executes fine. How do I make my package use the commands in the Linear Algebra package?

I have three procedures with calling struture:


    > call B (argseq)

    > call C (argseq)

     > etc code

     > return results

end A()

Procedures A, B, C are defined in a single MAPLE .mw worksheet, and each time I use them I have to reload them by pressing return.

Please can you suggest the best course of action?  I have been reading about modules but am not certain that A knows about B and C in the dame module when it calls them

Can anyone help please?




How can I stop this text from appearing in the worksheet output?

What is the purpose of this text as it's a GIANT DISTRACTION from my perspective?



> with(plots);

> with(geom3d);

outputs lots of blue text...


[Archimedean, AreCollinear, AreConcurrent, AreConjugate,

  AreCoplanar, AreDistinct, AreParallel, ArePerpendicular,

  AreSkewLines, DefinedAs, DirectionRatios, Equation, FindAngle,

  FixedPoint, GlideReflect, GlideReflection, GreatDodecahedron,

  GreatIcosahedron, GreatRhombicuboctahedron,

  GreatRhombiicosidodecahedron, GreatStellatedDodecahedron,

  HarmonicConjugate, HexakisIcosahedron, HexakisOctahedron,

  InRadius, IsArchimedean, IsEquilateral, IsFacetted, IsOnObject,

  IsQuasi, IsRegular, IsRightTriangle, IsStellated, IsTangent,

  MidRadius, NormalVector, OnSegment, ParallelVector,

  PentagonalHexacontahedron, PentagonalIcositetrahedron,

  PentakisDodecahedron, QuasiRegularPolyhedron, RadicalCenter,

  RadicalLine, RadicalPlane, RegularPolyhedron,

  RhombicDodecahedron, RhombicTriacontahedron, RotatoryReflect,

  RotatoryReflection, ScrewDisplace, ScrewDisplacement,

  SmallRhombicuboctahedron, SmallRhombiicosidodecahedron,

  SmallStellatedDodecahedron, SnubCube, SnubDodecahedron,

  StereographicProjection, StretchRotate, TangentPlane,

  TetrakisHexahedron, TrapezoidalHexecontahedron,

  TrapezoidalIcositetrahedron, TriakisIcosahedron,

  TriakisOctahedron, TriakisTetrahedron, TruncatedCuboctahedron,

  TruncatedDodecahedron, TruncatedHexahedron,

  TruncatedIcosahedron, TruncatedIcosidodecahedron,

  TruncatedOctahedron, TruncatedTetrahedron, altitude, area,

  center, centroid, coordinates, cube, cuboctahedron, detail,

  dilate, distance, dodecahedron, draw, dsegment, duality, faces,

  facet, form, gtetrahedron, hexahedron, homology, homothety,

  icosahedron, icosidodecahedron, incident, intersection,

  inverse, inversion, line, midpoint, octahedron, parallel,

  parallelepiped, plane, point, polar, pole, powerps, projection,

  radius, randpoint, reflect, reflection, rotate, rotation,

  schlafli, segment, sides, sphere, stellate, tetrahedron, tname,

  transform, translate, translation, transprod, triangle,

  vertices, volume, xcoord, xname, ycoord, yname, zcoord, zname] [animate, animate3d, animatecurve, arrow, changecoords,

  complexplot, complexplot3d, conformal, conformal3d,

  contourplot, contourplot3d, coordplot, coordplot3d,

  densityplot, display, dualaxisplot, fieldplot, fieldplot3d,

  gradplot, gradplot3d, implicitplot, implicitplot3d, inequal,

  interactive, interactiveparams, intersectplot, listcontplot,

  listcontplot3d, listdensityplot, listplot, listplot3d,

  loglogplot, logplot, matrixplot, multiple, odeplot, pareto,

  plotcompare, pointplot, pointplot3d, polarplot, polygonplot,

  polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus,

  semilogplot, setcolors, setoptions, setoptions3d, spacecurve,

  sparsematrixplot, surfdata, textplot, textplot3d, tubeplot]


Hi! I just started to use Maple and I play with some of its functions. I have seen in examples related to RegularChain package an output like  [regular_chain, [[-1, -1], [0, 0]]] and I wonder how I should read it. Thanks for any help and sorry if my question is very basic.

Hi, I know this has been asked ( and answered before) but when I installed this package and pressed ?globalsearch the help page is do I get it?

I am very new to Maple and am wondering how i would install a package. The package I am trying to install is located at 

I am using Maple 2015 on windows 8. Any advice would be useful

I need to minimize an Integration

Is there a package or an interactive package management utilities?


Dear all
I am using Physics[Vectors] package of Maple 17. I want to define an orthogonal curvilinear coordinates through alpha and beta independent variables. To define unit vectors of alpha and beta, I have to apply the derivatives of position vector r_ with respect to alpha and beta, respectively. Please help me to define the unit vectors in directions alpha and beta as derivatives of position vector r_ with respect to alpha and beta, respectively. Please see the below Code:

> restart;

> with(Physics[Vectors]);

> Setup(mathematicalnotation=true);

> r_:=X(alpha,beta)*_i+Y(alpha,beta)*_j+Z(alpha,beta)*_k;

The unit vectors in directions alpha and beta should be defined as:


It is worthwhile to mention that the following expression governs:

> diff(r_,alpha).diff(r_,beta)=0;


Please guide me.

Best wishes


The physics package is pretty awesome, but one thing that would be a big help is some functionality for entering and resolving vectors in angle/magnitude format (50 angle 45 degrees, or what have you.) Is there a way to do this?





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