how to transform this program using LinearAlgebra instead of linalg  ?

restart;
with(plots);
unprotect(gamma, D);
interface(rtablesize = 10): _EnvHorizontalName := 'x': _EnvVerticalName := 'y':
f := (x, y) -> 4*x^2 + 4*y*x + y^2 - 8*x + 16*y - 17: (for instance)
NULL;
Fg := proc(P::polynom, v::set, V::list, N::list) 
local C, M, i, j; 
C := coeffs(f(x, y), v, M); seq(`if`(member(op(i, [M]), N, 'j'), op(j, V) = op(i, [C]), NULL), i = 1 .. nops([M])); end proc:
Fg(f(x, y), {x, y}, [A, B, C, D, E, F], [x^2, y*x, y^2, x, y, 1]):
assign(%);
Delta := -4*A*C + B^2:
var := [x, y]:
with(linalg):
AA := matrix([seq([seq(diff(f(x, y), var[i], var[j])/2, j = 1 .. 2)], i = 1 .. 2)]):
vp := sort([eigenvals(AA)]):
print(`Valeur propres de AA ` = vp):
DD := jordan(AA, 'P11'):
print(`Matrice diagonale semblable à AA:   DD` = evalm(DD)):
G := map(normalize, GramSchmidt([col(P11, 1 .. 2)])):
PP := map(simplify, concat(op(G))):
print(`Matrice de passage orthogonale:   PP` = evalm(PP)):
print(`Directions principales de la conique:`):
print(`I1 ` = col(PP, 1), ` J ` = col(PP, 2)):
alpha := 1/2*arctan(B/(A - C)):
print('alpha' = evalf(%)):                 

M1 := matrix(1, 2, [X, Y]):
M2 := matrix(2, 1, [X, Y]):
multiply(M1, AA, M2):
N := matrix(1, 2, [D, E]):
multiply(M1, AA, M2) + multiply(N, M2):
multiply(M1, transpose(PP), AA, PP, M2) + multiply(N, PP, M2):

NULL;
The parabola in the new base is Y`^2 =X*(8*sqrt(5))/5 , <sqrt(5), -2*sqrt(5)>, <sqrt(5), 2*sqrt(5)>

I am trying to define a sum which is obtained from linked functions (which also contain the sum command). 

The problem is: if I modify the first function p and rerun the worksheet (except fot the restart command), then the changes do not affect the result. Does anyone know why? Thank you very much.
 

Download problem_with_sums.mw

I am working with the de Sitter metric which takes the form 

$$g=\tau^{-2}\left(-\left(\Lambda / 3-\tau^{2}\right)^{-1} d \tau^{2}+\left(\Lambda / 3-\tau^{2}\right) d t^{2}+g_{\mathbb{S}^{2}}\right)$$

or 

g := evalDG((-`dτ` &t `dτ`/(Lambda/3 - tau^2) + (Lambda/3 - tau^2)*(dt &t dt) + (dtheta &t dtheta) + sin(theta)^2*(dphi &t dphi))/tau^2)

in the co-ordinates $\{\tau, t, \theta, \phi\}.$

or 

DGsetup([tau, t, theta, phi], M1, verbose)

Define

F := evalDG(-Q*(`dτ` &t dt) + Q*(dt &t `dτ`))

Then I want to define the following function which takes a two tensor (metric) and returns a two tensor as well. 

Here \dot(g) is the input tensor, F is the two tensor defined above and the g is the de Sitter metric. 

I want to evaluate this expression of \dot{g} = d tau^2/tau^2 and other metrics. How can I do this in Maple?

Any help will be much appreciated.

With Maple, is there a way to quickly solve systems of equations where the solutions are the coordinates of a vector?
An example of an idea: A problem to solve:
There are points: M(1,0,0) and N(0,0-1); plane (Q): x-y-4=0. Determine the plane (P) containing M and N, making with (Q) a 45 degree angle.
Solution:
Assume: Equation of (P): Ax+By+Cz+D=0
We have:
Normal vector of (P): np(vector):=<A,B,C>
Normal vector of (Q): nq(vector):=<1,-1,0>
Direction vector of line NM: dNM(vector):=<1,0,1>
To determine: A, B, C, it is necessary to solve the system of equations:
cos(45 degrees)= np(vector).nq(vector)/abs(np(vector)) x abs(nq(vector))=1/Sqrt(2)
  dNM(vector).np(vector)=0....

Hi !

I want to solve several summations which at first glance seems very easy to me.

But I definitely hit a wall. I have Maple 2018 on Windows 10.

I'm not very familiar with the sumtools or Sumtools packages.

 I have attached a file that gives you an example summation and the

 solution I found and especially I show you the way that I obtained this solution.

  The big question is:

  Is there a way to transform this summation to arrive at my solution?

  Or . Can the result I obtained be demonstrated?

  Maple seems unable to solve this summation. Mathematica did no better.

  I know very well that this is more a question for mathematicians than for

Maple users. But when I look at the questions in Mapleprimes I see

although there are good mathematicians behind most of these questions.

Thank you in advance ! 

sum1.mw

Hi everyone...

How can I plot the below function: 

x^2+(y-x^(2/3))^2 = 1;

tnx...

Resistor grid of one ohm to make rubik cube of 3*4*5.
Resistance of red node to node is 

nx, ny, nz;

Ans := R3D;
Ans*Unit('ohm');
                            3, 4, 5

               1.211 Unit(&Omega;)

Tokoro.

grid cube electrical-engineering

R1 - R31 resistance is 17/11 ohm. (Top to bottom)

R1 - R2 resistance is 16273/25080 ohm. ( Each one element's node to node)

Can any one solve these Electric Circuit?

Tokoro.

Hi !

I just noticed a strange behavior of Maple with Greek letters. 
I have Maple 2017 and 2018 on Windows 10 .

Suppose you write a procedure that contains Greek letters.

If you run the procedure definition, the Greek letters are not displayed correctly. 
They will be displayed in words: alpha, beta, gamma,...
The procedure will still work.

Now close the file. Then open this file. Maple now shows you the procedure with the Greek letters correctly displayed.

I added a file as an example.
Maybe it's an annoying little problem known for a long time ? I don't know .
I have an old version of Maple V Release V (1997) which does not have this problem. 

Best regards !

alphabeta.mw

i want to find best equation with nonlinear fit or fit for my result
my first variable in column one with name h
 my second variable in column two with name d
 my result in the column 3

i just know that my ratio to b is exponential

Matrix(20, 3, [[70, 8, 8.468140006], [70, 10, 4.105515432], [70, 12, 2.36261199], [70, 14, 1.422093923], [70, 16, 0.9], [100, 8, 20.47249229], [100, 10, 9.618450629], [100, 12, 5.360869165], [100, 14, 3.399312905], [100, 16, 2.640399788], [130, 8, 35.90466304], [130, 10, 17.62958097], [130, 12, 9.828362586], [130, 14, 5.866863694], [130, 16, 3.799262645], [160, 8, 57.31814648], [160, 10, 34.49692774], [160, 12, 15.39340528], [160, 14, 9.991012951], [160, 16, 6.049343013]]);

how can i get best equation with ninlinearFit

thant you so much

i also show my result in below plot

I am using GenerateMatrix to construct a matrix out of a set of 6 equations with 6 variables.  The output of Generate Matrix is not sorted correctly.  Where am I going wrong? Is this a bug?

Download GenerateMatrix_Improper_Sorting.mw

Auto paste last entry

So maple uses % as the last expression entry.  My suggestion is to use Crtl+Space on the % command to re-display the last expression.  Yes one could easily use the mouse to select the last entry then Crtl+c and Crtl+v. 

Or maybe the command Crtl+Shift+L to auto paste last entry. 

**edit** actually I would prefer the Crtl+Shift+L option to auto paste the last entry.

** Appears to be a suggestion I made earlier https://www.mapleprimes.com/questions/148867-Is-There-A-Way-To-Recallrepeat-Previous

Hello

I want to declare 'd' as a constant.

Please tell me how to declare 'd' as a constant.

intersection de deux droites l1 et l2 telles que l1 sous forme parametrique est [57/5 + 20*t, -21/5 - 40*t, 20*t] et de la meme façon

 l2 [249/100 - 120*t, 471/100 - 80*t, 200*t]. t est le parametre  . maple donne pour l'intersection de l1 et l2 le point P de coordonnes

 [249/100, 471/100, 0] que je ne trouve pas .expliquez moi ce resultat et merci beaucoup.

I have a big matrix which is computed in a worksheet, now I have to use this matrix in another worksheet. Could you recommend some ways of healthy transferring of quantities between worksheets?