MaplePrimes Questions

I want to calculate the arithmetic average of a class of 5 students for 3 different exams. I want to calculate a different average for each exam. I want to use i and j variables. exam grades will be random like 20*i. How can i do this program? Any can do this? Thank you 

I try this program but i get error

total:=0;

numb:=0;

for i from 1 to 3 do

for j from 1 to 5 do

N[i,j]:=20*i;

total:=total+N[i,j];

numb:=numb+i

end do;

end do;

evalf(total/numb);

 

The date, month, year  22/02/2022 is said a beautiful numbers. Because, the number 2202 symmetry to the number 2022. How can I find another beautiful numbers like that ?

I have two surfaces f=f(x,y) and g=g(x,y), is there any way to find the equation of intersection curve of them in maple?

contact.mw

hello i want to solve this pde equation numericaly with pdsolve:

diff(u(x, t), x, x) + diff(u(x, t), t, t)/0.5^2 - 2*diff(u(x, t), x, t)/0.5^2 = -0.0013*u(x, t) + 8.6510*u(x, t)^3

and enter this codes:

PDE := diff(u(x, t), x, x) + diff(u(x, t), t, t)/0.5^2 - 2*diff(u(x, t), x, t)/0.5^2 = -0.0013*u(x, t) + 8.6510*u(x, t)^3
IBC := {u(0, t) = 0.01, u(4, t) = 0, u(x, 0) = 0, D[1](u)(x, 0) = 0};
pds := pdsolve(PDE, IBC, numeric, t = time, rage = 0 .. 1);

but this error appear :

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[1](u))(x, 0)

and i don't know how ti fix it.

can someone help me?

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.
 

I start with this

restart

p := proc (i, j) options operator, arrow; sum('cat(A, _, i, j, k)', 'k' = 1 .. 3) end proc

proc (i, j) options operator, arrow; sum('cat(A, _, i, j, k)', 'k' = 1 .. 3) end proc

(1)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(2)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(3)

If I modify p (I make it twice its initial value), then this does not affect the value of q and r

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(4)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(5)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(6)

Why?
Even if I  unassign p, q and r, this does not work, either.

unassign('p', 'q', 'r')

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(7)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(8)

r := sum('q(i)', 'i' = 1 .. 3)

A_331+A_332+A_333+A_321+A_322+A_323+A_311+A_312+A_313+A_231+A_232+A_233+A_221+A_222+A_223+A_211+A_212+A_213+A_133+A_123+A_131+A_132+A_121+A_122+A_111+A_112+A_113

(9)

Only if I restart, then I can modify p and change the rest of values

restart

p := proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

proc (i, j) options operator, arrow; 2*(sum('cat(A, _, i, j, k)', 'k' = 1 .. 3)) end proc

(10)

q := proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

proc (i) options operator, arrow; sum('p(i, j)', 'j' = 1 .. 3) end proc

(11)

r := sum('q(i)', 'i' = 1 .. 3)

2*A_332+2*A_333+2*A_323+2*A_331+2*A_313+2*A_321+2*A_322+2*A_311+2*A_312+2*A_231+2*A_232+2*A_233+2*A_221+2*A_222+2*A_223+2*A_212+2*A_213+2*A_211+2*A_131+2*A_132+2*A_133+2*A_121+2*A_122+2*A_123+2*A_111+2*A_112+2*A_113

(12)

``

``


 

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((-`d&tau;` &t `d&tau;`/(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*(`d&tau;` &t dt) + Q*(dt &t `d&tau;`))

 

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 

hiiiiiiiiiii

i am working and modling on brushless motor for my project but when i run that i get this error and i can not fix that could you please help me. error is :

equation generation

(}),At offset 4370 in `:-2108.m`, unexpected DAG type: 0,125

every project  i run  has the same error 

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

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