Don't get a DEplot 

Download uitzoeken_ode_lesmateriaal_betounes_of_het_werkt.mw

Dear maple users,

Greetings.

When converting the maple figure into EPS format (for latex) which shows white patches.

How to avoid such patches.

does maple provide a way to programatically get the name of the "current" worksheet file?

I'm looking for something analogous to
interface(worksheetdir);

which gives the directory the worksheet file is in.

thanks.

Hello everyone.

I am not really sure how to solve the following problem:

Given a parametriaztion of a surface as an interpolation in terms of given nodes as:
X(ξ,η)= Σ Νi(ξ,η) Xi, it is possible to calculate tangent and normal vectors as:
α1(ξ,η)= Σ Νi,ξ(ξ,η) Xi     α2(ξ,η)= Σ Νi,η(ξ,η) Xi  and a3(ξ,η)= cross(a1,a2) and their derivatives
α1,ξ α1,η α2,ξ α2,η etc.
For a variation of Xi i.e.  a variation of X can be calculated δX(ξ,η)= Σ Νi(ξ,η) δXi in terms of 
intermediate quantities that are as simple as  Σ Νi(ξ,η) for the position vector but get quite complicate
for the normal vector (δα3 that depends on a cross product) of given vectors  and for higher order derivatives,
or for the second variation. These variations can be also expressed with a directional derivative in the direction 
X,Y, or Z of a node i with initial position Xi.

To calculate those more complicate derivations I try to express them in terms of known less complicate ones.
Symbolizing r and s the first and second variation, and α,β firs and second derivative withh respect to ξ οr h or ξ,η.

Regarding the variation of the normal vector "a3_t" as known (i.e. a3_t,r)
and the variation of its norm "a3_n" (i.e. a3_n,r) as known too we can get the variation of
the of unit normal using the following commands:

a3 := a3_t(a, s, r)*(1/a3_n(a, s, r)): (vector-scalar operation) (1)
diff(a3, r):

the second variation
diff(a3, r):
diff(diff(a3, r), s) (2)

and even variations of its derivatives 
diff(diff(diff(a3, a), r), s): (3) 

That yield the results of the posted picture.

The problem is that if we want to calculate in the same way the variation of the derivative 
of expressions that involve the vector-vector operations i.e  variation of diff(a3_t, a)
where a3_t = CrossProduct(a1(a,r,s),a2(a,r,s)) it is not possible to do that as in (1)
we cannot substitute CrossProduct or dot product operation  with simple multiplication.

If we use the same strategy in VectorCalculus package we can get some results:
using the following commands: 

a1 := PositionVector([a1x(a, s, r), a1y(a, s, r), a1z(a, s, r)], cartesian[x, y, z])
a2 := PositionVector([a2x(a, s, r), a2y(a, s, r), a2z(a, s, r)], cartesian[x, y, z])
a3T := CrossProduct(a1, a2)
diff(a3T, r)

but then (as it is shown in the upload picture 2) the calculations are performed component-wise
are very lengthy so it is impossible to get second derivative or second derivation.

So I would like to ask is it possible to declare a1 as a vector but not give its components a1x, a1y etc explicitely but instead
declare it as a vector valued function of (a, r, s). so that it yields simpler expressions 
as "a3_t,r= a1,r(x)a2 + a1(x)a2,r".

I would also like to know if those calculations can be made simpler with and another package and if so is there an appropriate example
or a book that explains how to do that.

I would really appreciate  any idea.
Because this is a difficult problem Maple can make it very easy.

Thank you in advance.

upload1.mw

with(plots,implicitplot3d);with(plots, display3d);
                        [implicitplot3d]

Error, (in with) package plots does not export display3d

------------------------------
As i understand it correct: there is no display3d command in the plots package to find.

Someone is using this display3d in Maple ,but is doesn't matter , because display and display3d  working both the same 
Example : 

p1:=implicitplot3d(x^2+y^2-1=0,x=-2..2,y=-2..2,z=-2..2):
p2:=implicitplot3d(y^2+z^2-1=0,x=-2..2,y=-2..2,z=-2..2):
display({p1,p2});
display3d({p1,p2});
or even

display3DA({p1,p2}); gives 2 3d pics ?

Is there a special display3d command in Maple ?, because (one or more)  plot3d plotstructures with display should show all 3d pics in Maple  ?
 

If I have a tensor  in 3-dimensions which is symmetric on  and anti-symmetric on , then the number of independent components should be zero. However, if I put this into Maple, using  followed by  it returns .

Any insight into why it does this would be great, thanks.

Hi,

I have been  working on a Maple code written almost 17 years back. The code generates a 3D model input for modelling analysis in ABAQUS software. The input file generated is different from the usual ABAQUS input files. I am seeking help with how to make changes to the input file generated to import into the  ABAQUS. I am uploading the notepad version of the input file as the Maple does not allow .inp files. Please do find the below attachment.

wucell.txt

How can I find the corresponding group for the Lie algebra given in the picture (using Maplesoft software)?

Also, the command Lies Third Theorem works only for Solvable representations. What to for unsolvable representation.

Given two sets of lie algebra data, How to check, using maple software, that these lie algebras are isomorphic?

for example : 

The two sets of lie algebras are given as : L1 := [[e1, e4] = e1, [e2, e3] = e1, [e2, e4] = e2]

and

L2 := [[e1, e2] = e1].

Hi there,

Could you help me with Harley's norm computation algorithm that is based on the Fast Extended Euclidean Algorithm that was suggested by Harley in an email to NMBRTHRY list in 2002 and that described in Vercauteren's thesis pp 87-90:

https://pdfs.semanticscholar.org/c945/c98267db064b272c87a885fc5eeb764b0b2d.pdf

My implementation working correctly and fast for low degree polynomials without modulo and for high degree polynomials with modulo M, where M is a prime number greater than 2^N. But all I need - it's a resultant modulo 2^N (or 2^(Nc) due to Vercauteren's Remark 3.10.3) of two large polynomials. So I should include in routine mod 2^N (or mod 2^(Nc)...) instructions to avoid exponential coefficients' growing. But since the 2^N is not prime it's a problem - polynomials contain even coefficients and this leads to some even denominators - and for example multiplicative inverse 1/2 mod 2^N doesn't exist. Please tell me how to solve this problem?

How to adapt XGCD routine for correct mod 2^N calculation of resultant (norm)?

Thank you.

mod prime version of XGCD:

XGCD.mw

Suppose that a function f  has derivatives of all orders at a.  The the series

∑=(f(k)(a)/(k!))*(x−a)^k (limits are infinity and k=0, i donot how to insert that)

is called the Taylor series for f  about  a, where  f(n) is the n th order derivative of  f.

Suppose that the Taylor series for e2 x sin(5 x) about 0 is

a0+a1x+a2x2+⋯+a8x8+⋯

Enter the exact values of a0 and a8  in the boxes below.

      a0=      

     a8=      

Use Maple to find the solution of the initial value problem

y*(d^(2)*y/d*x^2)+(dy/dx)^2=0 0 with initial conditions y(0)=5and y'(0)=8.

Using Maple syntax, type in your answer in the box below, or copy (Ctrl-C) from your Maple worksheet and paste (Ctrl-V) in the answer box the solution. Do NOT enter the y(x)= part of the Maple output.

Why is pdsolve's 'generalsolution' option giving the particular solution u(x, y) = 0 instead of the general solution u(x, y) = A sin(x) sin(2 y) + B sin(2 x) sin(y) for the attached problem?

Problem.mw

A is a 2 x 2 matrix with eigenvalue, eigenvector pairs:

5,<4,1> and 1,<3,4>.

1. Find an invertible matrix M and a diagonal matrix D such that A=MDM^(-1).

M=                                          D=      

2. For any integer n, find the matrix A^n   as a single matrix (i.e. explicitly entry-by-entry). Use Maple notation for a matrix.

   An=       

(Hint: compose your answer in Maple to make sure your syntax is correct and your answer is what you think it should be.)

Let A be an m×n matrix. The image of A  is the set of vectors

im(A)={y:y=Ax for some x∈Rn} ,

which is a vector space.

The dimension of im(A)  is called the rank of A, denoted by rank(A) .

(a)  Find the rank of the matrix 

v1:=<-146, -84, 28, -154>

v2:=<-203, 106, 34, -181>

v3:=<-94, -4, 106, -154>

v4:=<-36, 152, -86, 50>

v5:=< 173, 122, -390, 435>

A:=<v1|v2|v3|v4|v5>;

and enter in the box below.

rank(A)=    

(b) For the matrix A in (a), select all the statements below which are true.

(1) <97,-8,-49,-66> is in im(A)

(2) <-65,74,10,-52> is in im(A)

(3)im(A) is subspace of R^4

(4) <2,-2,-4,4,-2> is in im(A)

(5) <0,0,0,0> is in im(A)

(6) <0,0,0,0,0> is in im(A)

(7) <-1,-2,1,-2,1> is in im(A)

(8) im(A) is a subspace of R^5