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

I am not geting value of F3.

question_1.mw
 

Download question_1.mw

Hello Everyone
My maple is evaluating the following provided in figure. I have  attached MAPLE file. Kindly help me to solve this. Thanks in advance.

question.mw

what is the best way to "extract" a list of terms from a sum of terms.

So something like this::

split_expr(a+b+3) should return [a,b,3]

split_expr(diff(x(t),t)) should return  [ diff(x(t),t)]

split_expr(Int(abc(t), t=2..3) + 3) should return [Int(abc(t), t=2..3) , 3]

I very often have expressions with sums of many terms, and need to run some command on each element (say simplify, or collect, etc)... i've been using convert(expr, list) to split things up, apply a command and recombine, but the convert command breaks on some cases. Maybe this is something that maple can do natively?

thanks!

Example of problematic file:  Model050913.mw

Maple 2020 (either 32- or 64-bit), Maple 2019, and Maple 2017 cannot open a .mw file that I created in 2006.  These Maple versions display this .mw file from 2006 as a garbled mess and cannot work with the garbled mess.  In contrast, Maple 18 opens this file from 2006 without problems.  Did the .mw file format change some time after Maple 18?  Interestingly, Maple 2020 can open a .mw version of the problematic 2006 file that I save with Maple 18.  Can Maple 2020 be updated so that Maple 2020 can open old .mw files (e.g., 2006 and earlier)?  Is the inability of Maple 2020 to open files from 2006 and earlier a bug in Maple 2020?  I can workaround this problem by using Maple 18.  But correcting a bug in Maple 2020 that garbles old .mw files would be helpful.

Hello everyone,

I am trying to represent a set of data using the errorplot command as follows

plotlims50 := ErrorPlot(xcoords = vectorl, sigmasl50, yerrors = [0.1e-1, 0.4e-1, 0.1e-1, 0.3e-1, 0.3e-1, 0.6e-1, 0.6e-1, 0.1e-1, 0.4e-1, 0.6e-1, 0.5e-1, 0.3e-1, 0.2e-1, 0.2e-1], color = "green")

I guess it's okey, but I would like to have that kind of small lines at the end of the bar and perpendicular to it (like in the image below). Is it possible?

Thank you so much in advance

im solving 2 ODe with boundary conditions.. i got this error Error, (in dsolve/numeric/bvp/convertsys) too few boundary conditions: expected 10, got 8
 

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  ?
 

Hi,

I'm working on a procedure involving conic equations such as follows... 

Conic:=a*x^2+2*h*x*y+b*y^2+2*f*x+2*g*y+c;

and I have a file filled with values in order of the variables I want them assigned to.

e.g 2,-6,3,0,0

I'm only looking for the specific command I need for maple to link the two.

Any help would be greatly apreciated.

from help, it says 

The expression assuming property calling sequence evaluates the expression under the assumption property on all names in expression.

Then why 

restart;
expr := Sum((-1)^n - 1, n = 1 .. infinity):
simplify(op(1,expr)) assuming n::even;

does not simplify expr to zero, while

restart;
expr := Sum((-1)^n - 1, n = 1 .. infinity):
assume(n::even):
simplify(op(1,expr))

does simplify expr to zero.

I would have expected both to give zero. 

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.

I am trying to customize the Venn Diagram generated by the VennDiagram command in the Statistics package. I would like to be able to shade just any of the regions. For example, if only two sets (A and B) are being displayed, I would like to be able to shade just A, just B, both A and B, or both A and/or B. Also, is it possible to have a rectangle surrounding the circles which represents the universal set? Could the circles be labeled with the letter "A" or "B" to be able to identify each set?

venn.mw

Here is a strange one...

1> /Library/Frameworks/Maple.framework/Versions/2019/bin/maple ; exit;
    |\^/|     Maple 2019 (APPLE UNIVERSAL OSX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2019
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> version();
 User Interface: 1435526
         Kernel: 1435526
        Library: 1435526
                                    1435526

> DE := (28*x + 44)*u(x) + (336*x^2 +
> 726*x - 12)*diff(u(x), x) + (144*x^3 + 396*x^2 - 9*x)*diff(u(x), x, x);
                               2               /d      \
DE := (28 x + 44) u(x) + (336 x  + 726 x - 12) |-- u(x)|
                                               \dx     /

                               / 2      \
             3        2        |d       |
     + (144 x  + 396 x  - 9 x) |--- u(x)|
                               |  2     |
                               \dx      /

> dsolve({DE,u(0)=2},u(x));
memory used=21.5MB, alloc=44.3MB, time=0.37
memory used=53.3MB, alloc=84.3MB, time=0.94
Error, (in dsolve) when calling 'property/ConvertRelation'. Received: 'numeric
exception: division by zero'

Presumably, the solution should be

u0:=2*HeunG((11 - 5*sqrt(5))/(11 + 5*sqrt(5)), 352/(9*(11 + 5*sqrt(5))^3*(-11 + 5*sqrt(5))^2), 1/6, 7/6, 4/3, 1/2, -8*x/(11 + 5*sqrt(5)));

(I get that by replacing coefficient 44 in DE with variable e44, solve, then substitute back e44 = 44.)

But maybe the problem is that this solution turns out to be an algebraic function:

u1:=2^(7/6)/(1 - 22*x + sqrt(-16*x^2 - 44*x + 1))^(1/6);

Dear friends, please I would like to ask for your help with an odd problem I have using the remove command. 

I have an array 

A:=Array([1,4,1,7]);

and I need to remove its first element A[1]. 

A:= remove[flatten](x -> x = A[1], A);

Instead of getting the result  A:= [4 1 7] I get  A:=[4 7], and I can't understand why. 

Could you please help me with a solution to the problem? Many thanks for the help.  

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