Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

How to convert maple file into the pdf file?For example the attacahed file is maple file.I want to convert this to a pdf file.

conservation_of_wave_eq.mw

I posted this earlier on a question I asked more than a month ago due to the similarity of the problem.  However, I got no response.  So I will post this as a new question in an effort to get a response.

I get the following error when working with the "INERT" Sum?

Warning, solutions may have been lost

I do not get the message when working with the "ACTIVE" sum.  I tried the AllSolutions option, but still get the same message.  How can I get the proper output working with the "INERT" form?

lost_solutions.mw

How can I install GeM software from the link http://cpc.cs.qub.ac.uk/?

I have tried many times but I didn't get.

 

@mskalsi

I was trying the direct method for conservation law of wave equation.But the fluxes and conserved density are not coming correct in eq.(4)(see attached file) because (1) and (6) are not same.What mistake have I done?

 

 

wave_eq_3.mws

Thought it would be a neat way to create identation for loops and if branches in a text editor and copy the code into Maple. But Maple inserts a new prompt at the beginning of every line.

Is there a solution in 2018?

with(Physics[Vectors]);

This should  equal Dirac delta function

I know this must have been addressed somewhere previously.  However I have searched extensively and not been able to find an answer.  Sorry for asking again.

The set and list produced by map (see below) contain duplicates.  How to remove duplicates?
 

p := (1+5^(1/2))*(1/2)

1/2+(1/2)*5^(1/2)

(1)

with(Bits)

[And, FirstNonzeroBit, GetBits, Iff, Implies, Join, Nand, Nor, Not, Or, Settings, Split, String, Xor]

(2)

with(LinearAlgebra)

[`&x`, Add, Adjoint, BackwardSubstitute, BandMatrix, Basis, BezoutMatrix, BidiagonalForm, BilinearForm, CARE, CharacteristicMatrix, CharacteristicPolynomial, Column, ColumnDimension, ColumnOperation, ColumnSpace, CompanionMatrix, CompressedSparseForm, ConditionNumber, ConstantMatrix, ConstantVector, Copy, CreatePermutation, CrossProduct, DARE, DeleteColumn, DeleteRow, Determinant, Diagonal, DiagonalMatrix, Dimension, Dimensions, DotProduct, EigenConditionNumbers, Eigenvalues, Eigenvectors, Equal, ForwardSubstitute, FrobeniusForm, FromCompressedSparseForm, FromSplitForm, GaussianElimination, GenerateEquations, GenerateMatrix, Generic, GetResultDataType, GetResultShape, GivensRotationMatrix, GramSchmidt, HankelMatrix, HermiteForm, HermitianTranspose, HessenbergForm, HilbertMatrix, HouseholderMatrix, IdentityMatrix, IntersectionBasis, IsDefinite, IsOrthogonal, IsSimilar, IsUnitary, JordanBlockMatrix, JordanForm, KroneckerProduct, LA_Main, LUDecomposition, LeastSquares, LinearSolve, LyapunovSolve, Map, Map2, MatrixAdd, MatrixExponential, MatrixFunction, MatrixInverse, MatrixMatrixMultiply, MatrixNorm, MatrixPower, MatrixScalarMultiply, MatrixVectorMultiply, MinimalPolynomial, Minor, Modular, Multiply, NoUserValue, Norm, Normalize, NullSpace, OuterProductMatrix, Permanent, Pivot, PopovForm, ProjectionMatrix, QRDecomposition, RandomMatrix, RandomVector, Rank, RationalCanonicalForm, ReducedRowEchelonForm, Row, RowDimension, RowOperation, RowSpace, ScalarMatrix, ScalarMultiply, ScalarVector, SchurForm, SingularValues, SmithForm, SplitForm, StronglyConnectedBlocks, SubMatrix, SubVector, SumBasis, SylvesterMatrix, SylvesterSolve, ToeplitzMatrix, Trace, Transpose, TridiagonalForm, UnitVector, VandermondeMatrix, VectorAdd, VectorAngle, VectorMatrixMultiply, VectorNorm, VectorScalarMultiply, ZeroMatrix, ZeroVector, Zip]

(3)

with(VectorCalculus)

[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, Compatibility, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, Tangent, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]

(4)

b := proc (x, w) options operator, arrow; (-1)^GetBits(x, w, output = number) end proc

proc (x, w) options operator, arrow; (-1)^Bits:-GetBits(x, w, output = number) end proc

(5)

l := proc (x, t, u, v) options operator, arrow; frac(x)*Vector([b(floor(x), 0)*t, b(floor(x), 1)*u, b(floor(x), 2)*v])+(1-frac(x))*Vector([b(floor(x), 0)*v, b(floor(x), 1)*t, b(floor(x), 2)*u]) end proc

proc (x, t, u, v) options operator, arrow; VectorCalculus:-`+`(VectorCalculus:-`*`(frac(x), VectorCalculus:-Vector([VectorCalculus:-`*`(b(floor(x), 0), t), VectorCalculus:-`*`(b(floor(x), 1), u), VectorCalculus:-`*`(b(floor(x), 2), v)])), VectorCalculus:-`*`(VectorCalculus:-`+`(1, VectorCalculus:-`-`(frac(x))), VectorCalculus:-Vector([VectorCalculus:-`*`(b(floor(x), 0), v), VectorCalculus:-`*`(b(floor(x), 1), t), VectorCalculus:-`*`(b(floor(x), 2), u)]))) end proc

(6)

map(l, {0, 1, 2, 3, 4, 5, 6, 7, 8}, 0, 1, p)

{Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian])}

(7)

map(l, [0, 1, 2, 3, 4, 5, 6, 7, 8], 0, 1, p)

[Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian])]

(8)

q := ListTools:-MakeUnique(%)

q := [Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian])]

(9)

Equal(q[1], q[9])

true

(10)

qq := [op({q[]})]

qq := [Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = -1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = -1/2-(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian]), Vector(3, {(1) = 1/2+(1/2)*5^(1/2), (2) = 0, (3) = 1}, attributes = [coords = cartesian])]

(11)

LinearAlgebra:-Equal(qq[1], qq[5])

true

(12)

NULL


 

Download cp.mw

To restrict the domain of a vector field, I have multiplied a coordinate with a non-real complex number (namely a sqrt(of negative expression)). This does work, as shown in this Maple 2017 worksheet program (below). My question is whether this is the best technique of accomplishing this result, or else how to do it better? Would be interested in suggestions for improvements. Here is my program so far:

restart;
#
with(plots):
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(` Vector Field inside Torus`);
print(` ------- ------- ------- ------- ------- ------- -------`);
print(` Assignment:  `);
print(` In a circular pipe of radius (my2r), water is flowing in the direction `);
print(` of the pipe, with speed (my2r)^2-(mya)^2, where (mya) is the distance  `);
print(` to the axis of the pipe.  `);
print(` Depict the vector field describing the flow if the pipe goes around in `);
print(` the shape of a torus with major radius (my1r).  `);
print(`   `);
print(`   `);
print(`   `);
print(` ------- ------- ------- ------- ------- ------- -------`);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 1) major radius of torus:`);
#
my1r  := 5;     
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 2) minor radius of torus (pipe radius):`);
#
my2r := 4; 
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 3) definition of torus (polar coordinates):`);
#
c00 := [(my1r+my2r*cos(s))*cos(t),(my1r+my2r*cos(s))*sin(t),my2r*sin(s)];
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 4) 3D plot of solid torus (polar coordinates):`);
#
plot3d({c00},scaling=constrained,color=red);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 5) 3D plot of wireframe torus (polar coordinates):`);
#
P1 := plot3d({c00},scaling=constrained,style=wireframe);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 6) implicit definition of torus (cartesian coordinates):`);
#
c01 := (sqrt(x^2+y^2)-my1r)^2+z^2-my2r^2;
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 7) implicit 3D plot of solid torus (cartesian coordinates):`);
#
gx := my1r+my2r; # min and max of each coordinate
#
implicitplot3d(c01,x=-gx..gx,y=-gx..gx,z=-gx..gx,numpoints=9000);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 8) vector field definition (cartesian coordinates):`);
#
my1vfx := -y;
my1vfy := x;
my1vfz := 0;
#
my1fld := [my1vfx,my1vfy,my1vfz];
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 9) 3D plot of vector field (cartesian coordinates):`);

#
fieldplot3d(my1fld,x=-gx..gx,y=-gx..gx,z=-gx..gx);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 10) definition of vector field with unit length vectors (cartesian coordinates):`);
#
my1vl := sqrt(my1vfx^2+my1vfy^2+my1vfz^2); # vector length
#
my2fld := [my1vfx/my1vl,my1vfy/my1vl,my1vfz/my1vl];
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 11) 3D plot of vector field with unit length vectors (cartesian coordinates):`);
#
fieldplot3d(my2fld,x=-gx..gx,y=-gx..gx,z=-gx..gx);
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 12) definition of vector field with asked for length vectors (cartesian coordinates):`);
#
mya := sqrt((sqrt(x^2+y^2)-my1r)^2+z^2);
c01r := sqrt(my2r^2-mya^2); # also used for domain restricting vector field below
#
my1tsz := solve([c01],[z]);
#
assign(my1tsz[1][1]);
my1tz := z;
unassign('z');
#
assign(my1tsz[2][1]);
my2tz := z;
unassign('z');
#
my1vp := c01r/my2r; # vector length (maximum one unit)
#
my3fld := [my1vp*my1vfx/my1vl,my1vp*my1vfy/my1vl,my1vp*my1vfz/my1vl];
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 13) 3D plot of vector field with asked for length vectors (cartesian coordinates):`);
#
fieldplot3d(my3fld,x=-gx..gx,y=-gx..gx,z=-gx..gx);
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n(Section 14) same asked for vector field with 3-D arrow vectors:`);
print(`   `);
print(` (to get this to display properly it was necessary to do:  `);
print(` -> Maple 2017 -> Preferences... -> Precision ->   `);
print(`   [unselect] Limit expression length to   `);
print(`   Apply to Session`);
print(`   `);
#
gr := 15;
#
P3 := fieldplot3d(my3fld,x=-gx..gx,y=-gx..gx,z=-gx..gx,arrows=`3-D`,grid=[gr,gr,gr]);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);
print(`\n display asked for vector field within wireframe torus:`);
#
display([P1,P3]);
#
#
print(` ------- ------- ------- ------- ------- ------- -------`);

I got decimal places problem,

not known correct or not

the value are different but difference is constant 

i do not know how many places needed to get exact result

i do not believe the difference is constant

because the matrix are different

but even if using 36 decimal places still constant, 

i notice increasing decimal places , the constant difference is changed

is it possible  to output fraction when calculate eigenvector?

Ok embarassing I posted this one and now it outputs this java error file log and yep i dont know that much about java at all. 

 

Sometimes it works, sometimes it closes maple automatically and spits out the .txt error log i have attached if thats any help... MAPLE_EXAMPLE_16.mw  i honestly have never ever seen maple behave this way in more than a decade of playing around in it with stuff like this.

EDIT: Here is a version with smaller plot components that seems to be working.... MAPLE_EXAMPLE_17.mw

It says i am not allowed to upload a log file but this is what it looks like:

#
# A fatal error has been detected by the Java Runtime Environment:
#
# java.lang.OutOfMemoryError: requested 1024000 bytes for GrET in C:\BUILD_AREA\jdk6_18\hotspot\src\share\vm\utilities\growableArray.cpp. Out of swap space?
#
 
V  [jvm.dll+0x15df8a]
V  [jvm.dll+0x1e1e14]
V  [jvm.dll+0x1a1aad]
V  [jvm.dll+0xc834f]
V  [jvm.dll+0xca01c]
V  [jvm.dll+0xca370]
V  [jvm.dll+0xce42a]
V  [jvm.dll+0x1d8592]
V  [jvm.dll+0xc9398]
V  [jvm.dll
Java Threads: ( => current thread )
  0x522e7c00 JavaThread "Timer-28" [_thread_blocked, id=23236, stack(0x5f2f0000,0x5f6f0000)]
  0x522e7400 JavaThread "Timer-22" [_thread_blocked, id=24248, stack(0x6b440000,0x6b840000)]
  0x522e2c00 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=11140, stack(0x6a2d0000,0x6a6d0000)]
  0x522e7000 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=6792, stack(0x64d30000,0x65130000)]
  0x522e6400 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=20280, stack(0x6a6d0000,0x6aad0000)]
  0x522e4400 JavaThread "Timer-18" daemon [_thread_blocked, id=23888, stack(0x63f20000,0x64320000)]
  0x522e6800 JavaThread "Timer-17" [_thread_blocked, id=17320, stack(0x69ed0000,0x6a2d0000)]
  0x522e5000 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=13480, stack(0x69ad0000,0x69ed0000)]
  0x522e4800 JavaThread "Timer-16" daemon [_thread_blocked, id=18184, stack(0x68ed0000,0x692d0000)]
  0x522e3000 JavaThread "Timer-15" [_thread_blocked, id=23296, stack(0x692d0000,0x696d0000)]
  0x522e3800 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=16388, stack(0x66820000,0x66c20000)]
  0x522e1400 JavaThread "Timer-14" daemon [_thread_blocked, id=24500, stack(0x61c50000,0x62050000)]
  0x522e0c00 JavaThread "Timer-13" [_thread_blocked, id=15848, stack(0x659b0000,0x65db0000)]
  0x522e0000 JavaThread "WMI:MapleClientSocket:Kernel Connection " daemon [_thread_blocked, id=7260, stack(0x655b0000,0x659b0000)]
  0x466cb000 JavaThread "Timer-12" daemon [_thread_blocked, id=1112, stack(0x64320000,0x64720000)]
  0x4699b800 JavaThread "Timer-11" [_thread_blocked, id=24540, stack(0x64930000,0x64d30000)]
  0x4699b400 JavaThread "Timer-10" daemon [_thread_blocked, id=21144, stack(0x60bf0000,0x60ff0000)]
  0x4699d400 JavaTh
 
How to translate the elliptic curve from the 4th to the 3rd curve with maple?

thanks.

Is there any way to get random numbers in Maple with the Sobol method?

Thank you.

can anyone tell me the difference between subs and eval and  evalf ?

The  partition function is geven as'

Zvib(Beta)"=integrate(exp^Beta*alpha^2*h^2/4*units*m *(B-2A)+Beta*alpha^2*h^2*B^/8*units*m*(n+c)^2+Beta*alpha^2*h^2*rho^2*drho,rho=(c+n) from to lambda+c

I need to find the intersection points of two circles (x-7)^2+(y-2)^2=100 and (x-11)^2+(y-5)^2=75 using the modified Newton secant method. 

I have already done this by using these two equations to make one in terms of x. But, i am looking for suggestions on how to make a multiple variable version of the secant method.

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