janhardo

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11 years, 41 days

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These are replies submitted by janhardo

@ecterrab 

Thanks

Interesting to know more how the PDE can be possibly solved
I did one PDE:  u[x,y]  = - u[x] by hand following: a long calculation to arrive at the general analytical solution equation.
 

This could be a big question 

https://mathworld.wolfram.com/SingularMatrix.html 

@janhardo 


 

  restart;
  with(plots):
  with(ArrayTools):
  doPlot:= proc( A )
           local rooster, p1;
            rooster:= plot3d
                       ( 0, 0..op([2, 1, 2], A),
                         0..op([2, 2, 2], A),
                         grid= [op([2, 1, 2],
                         A)+1,
                         op([2, 2, 2],
                         A)+1], style=wireframe,
                         color= COLOR(RGB, .15$3),
                         thickness= 0
                       );
            p1:=spacecurve({[[0,0,0], [0,0,0.5]],[[1,0,0], [1,  0,0.5]],               [[0,1,0], [0,1,0.5]], [[1,1,0], [1,1,0.5]]}, color=black):
            display
                 (  rooster, p1, [ seq
                     ( seq
                       ( plot3d
                         ( A[i,j],
                           x=i-1..i,
                           y=j-1..j,
                           shading=zhue,
                           style=surface,
                           axes=normal,
                           view=[ 0..op([2, 1, 2], A),
                                  0..op([2, 2, 2], A),
                                  min(0, A[..,2] )..max(A[..,2])
                                ]
                         ),
                         i=1..Size(A,1)# 1..5
                       ),
                       j=1..Size(A,2)
                     )
                   ],
                   scaling=constrained,
                   size=[1000, 1000]
                 );
          end proc:
  T1:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ]
             ]
           );
   T2:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ],
              [ 1.5,  1  ],
               [ 1.75, 2  ],
               [ 2,    2.5]
             ]
           ):
  T3:=Array( [ [ 0.5, -1, 3, 4  ],
               [ 1,    2, 4, 6  ],
               [ 1.5,  1, -4, 4 ],
               [ 1.75, 2, 5, 2  ],
               [ 2,    2.5, 2, 2]
            ]
          ):
  doPlot(T1);
  doPlot(T2):
  doPlot(T3):

Matrix(2, 2, {(1, 1) = .5, (1, 2) = -1, (2, 1) = 1, (2, 2) = 2})

 

 

with(plots):

 

p1:=polygonplot3d([[1,1,5],[2,1,5],[2,3,5],[1,3,5]]):

p2:=polygonplot3d([[2,3,2],[3,3,2],[3,4,2],[2,4,2]]):

p3:=spacecurve([[0,0,0],[3,0,0],[3,4,0],[0,4,0],[0,0,0]],color=black):

display({p1,p2,p3},axes=normal,orientation=[-16,78]);

 

p4:=spacecurve({[[1,1,0],[1,1,5]],[[2,1,0],[2,1,5]],[[2,3,0],[2,3,5]],[[1,3,0],[1,3,5]],[[2,3,0],[2,3,2]],[[3,3,0],[3,3,2]],[[3,4,0],[3,4,2]],[[2,4,0],[2,4,2]]},color=black):

display({p1,p2,p3,p4},axes=normal,orientation=[-16,78]);

 

 

 

 

New proc for this existing procedure doPlot

- planes are now made with polygonplot3d .. or use exising plane with borderlines 
-vertical line segments


How to do this ?
Input doPlot is a
T1:=Array( [ [ 0.5, -1  ],
               [ 1,    2  ]
By input this array for example a plane 0.5  has for z = 0.5
For every plane you get 8 points , and must generate this for plotting vertical lines between the points.

 

 

 

 


 

Download arrplot3-1_laatste_tom_leslie1.mw

@vv 
He is from Holland  André Heck .. me too. 
For some books: aging is no problem and agree with you.

I bought recently : introduction to Maple from André Heck ,the first edition and brandnew for  8 USD
Got the impression that this book is dated : Maple V release 2 ?

I am interesed in this bookversion, but is it somewhere to find used? 

 

@Carl Love 

Seems that the package is not freely  without copyright issues, so removed links to the package.
5 LAMP commands not working in Maple:  
Drawlines,Drawplanes, Backsolve,Matsolve, Inverse
As i undertstand the coding from this package is not the best one at the moment ( 20 years back)
Is there another free Maple package for maple programming training purposes?
 

 

@Carl Love 

What the command for instance Drawlines ( )  excactly does, it is not explained in the section: commands in this module( see worksheet link)
The book text gives more explanation for the  command Drawlines: plot the lines without first having to solve each equation for y

No plotting and there is a error message

Interesting to know this code works?    
 

 

@acer 

What is wrong with this code ?

"As I recall, the accompanying code was not a great example of Maple programming, even when less outdated"

Then i could learn from this

@Carl Love 

Thanks

In folder lampmod all course mws
Also there is no help for the commands from LAMP ?
The LAMP commands are found under: Mathematics...Linear Algebra...Lamp Library...

 

@Carl Love 

Note: i removed the link

This second new  file for LAMP- where you asked for-  is a easier one to use then th e first one 

@vv 

Thanks
Works great for 2 D 
For 3 D solids (conics etc)  classification maple has no existing procedure ? 

@Kitonum 

Thanks

There was a procedure in Maple what is taken for classification conics 2D 

@acer 

Thanks

Outdated yes, and programmed by students at that time
Can't be much for value for me then, for studying example programming?

Seems that 5 LAMP commands not working in Maple 
-Drawlines,Drawplanes, Backsolve,Matsolve, Inverse
Lamp book is detailled in basic linear algebra and its well done
Probabably there are some unique commands made specially for Lamp .

Take the first lesson:

You can also use the special command Drawlines (not working correct)  to plot the lines without first having to solve each equation for y: (Geometric Perspectives On Linear Equations chapter).
 

Or take The Drawplanes command (not working correct)(Geometric Perspectives On Linear Equations chapter) can also display the planes in another way that is sometimes easier to see: instead of planes it shows circles with intersectionline(s)

 All basic math

c1m1_v3.mws

@Carl Love 

Thanks!

I noticed already the linear algebra  has two versions in Maple,interesting.
Seems to be working now Lamp!

 

@Carl Love 

Thanks

A answer is : `Lamp environment loaded.`

and with(lamp); gives error

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received Matrix(3, 13, {(1, 1) = 6, (1, 2) = 10, (1, 3) = 10, (1, 4) = 4, (1, 5) = 4, (1, 6) = 8, (1, 7) = 8, (1, 8) = 3, (1, 9) = 5, (1, 10) = 9, (1, 11) = 11, (1, 12) = 6, (1, 13) = 6, (2, 1) = 3, (2, 2) = 3, (2, 3) = 2, (2, 4) = 2, (2, 5) = 3, (2, 6) = 3, (2, 7) = 8, (2, 8) = 8, (2, 9) = 13, (2, 10) = 13, (2, 11) = 8, (2, 12) = 8, (2, 13) = 3, (3, 1) = 1, (3, 2) = 1, (3, 3) = 1, (3, 4) = 1, (3, 5) = 1, (3, 6) = 1, (3, 7) = 1, (3, 8) = 1, (3, 9) = 1, (3, 10) = 1, (3, 11) = 1, (3, 12) = 1, (3, 13) = 1})
Its a package for linear algebra what is bought for study purposes, but get never far with it
Now at the moment i am learning about  quadric surfaces and some linear algebra is needed

Also the programming of the lamp commands could be helpful for learning programming ?

 

@janhardo 

But i see that quadric surfaces are handled in some linear algebra books. 
The simplest equation for  surfaces are in standard positions.
Like with the conics in 2D, the surfaces can be rotated out of standard position too.

The example in Maple can be a good start to study this further.
Ok , what's a Hessian determinant content (3x 3)for a solid 3D compared with the Hessian for 2D?  

The surfaces are interesting, because they are solutions of a partial diff equation? 
This type of equation ( Pdiff) i never studied before,
Do have here a second hand book bought in a bundle when i started to study math : partial differential equations: analytical solution techniques by J.Kevorkian.
But i don't have enough needed base math knowledge when i read the preface.

 

Introduction to Partial
Differential Equations:
A Computational
Approach
Aslak Tveito
Ragnar Winther
Springer

-------------------------------

found some studymaterial..  

You are embarking on a journey in a jungle called Partial Differential Equations.
Like any other jungle, it is a wonderful place with interesting sights
all around, but there are also certain dangerous spots. On your journey,
you will need some guidelines and tools, which we will start developing in
this introductory chapter.

 

 

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