Unanswered Questions

This page lists MaplePrimes questions that have not yet received an answer

I am writing a maths books using maple now. It is fantastic to use maple for writing books in maths.
 

 

 

 in the polynomial x^3-3*x^2-33*x+35 This line is not copying in full line!!
Step 1: Find the sum of all the coefficients in the polynomial x^3-3*x^2-33*x+35 This line is copying in full!!
"= 1-3-33+35 = 0"
                                                 r x-1is a factor  ; 1 is a root of the polynomial.
In the next row, I copy pasted the lines above

 in the polynomial x^3-3*x^2-33*x+35 This line is not copying in full line!!

Step 1: Find the sum of all the coefficients in the polynomial x^3-3*x^2-33*x+35 This line is copying in full!!

"= 1-3-33+35 = 0"
                                                 r x-1is a factor  ; 1 is a root of the polynomial.
In the next row, I copy pasted the lines above

 

 

 

Can any one find the reason?

 

 

``


 

Download cannotCopyWhy.mw

I enclose a part of my document where in I made a particular line with text and maths formats combined.Then I made changes in the line. Now copy paste does work only for the later half (both text and maths formats). The corrected first part is not being copied.

How do I do the corrections properly so that copy paste is not a problem at laer stages.

Thanks for the answer.

Ramakrishnan V

My problem is related to recovering orbits from invariant polynomials, and their ideal of relations.

The invariant polynomials I obtained are:

u = x2 - x y + y2,
v = 2 x6 - 6 x5 y + 15 x4 y2 - 20 x3 y3 + 15 x2 y4 - 6 x y5 +  2 y6 ,
w = x6 - 4 x5 y + 10 x4 y2 - 10 x3 y3 + 5 x2 y4 - 2 x y5 + y6 .

Using the logic from the Cox et al. book I got that the algebraic relation (ideal of relations) between the invariants, which is:

11 u6 - 10 u3 v + 3 (v2 - v w + w2) = 0

Then, using Reduce[] (exact symbolic solver which uses cylindrical algebraic decomposition) from Mathematica I solved for x and y under the assumption x > y > 0, u > 0, v > 0 and w > 0, but I got rather a complex solution.


My question is whether there is a way to try getting something more straightforward than the solution given by Mathematica.
 

I tried to use Maple's solve function, but it immediately stops without any result of an error message.


My input for Reduce is:

Reduce[{x2 - x y + y2 == u, 2 x6 - 6 x5 y + 15 x4 y2 - 20 x3 y3 + 15 x2 y4 - 6 x y5 + 2 y6 == v,  x6 - 4 x5 y + 10 x4 y2 - 10 x3 y3 + 5 x2 y4 - 2 x y5 + y6 == w, 11 u6 - 10 u3 v + 3 (v2 - v w + w2) == 0, x > y > 0, u > 0, v > 0, w > 0}, {x, y}, Complexes]

 

and my input for solve:

 

solve({u = x^2 - x*y + y^2, v = 2*x^6 - 6*x^5*y + 15*x^4*y^2 - 20*x^3*y^3 + 15*x^2*y^4 - 6*x*y^5 + 2*y^6, w = x^6 - 4*x^5*y + 10*x^4*y^2 - 10*x^3*y^3 + 5*x^2*y^4 - 2*x*y^5 + y^6, 11*u^6 - 10*u^3*v + 3*v^2 - 3*v*w + 3*w^2 = 0, 0 < u, 0 < v, 0 < w, 0 < x, 0 < y, y < x}, {x, y})

 

Do you know what I am doing wrong, or what else could I try?

 

Hello Anybody can help me to write codes for PDE to solve by Galerkin finite element method or any other methods can be able to gain results? parameter omega is unknown and should be determined.

I attached a pdf file for more .

Thanks so much

fem2
 

"restart:  rho:=7850:  E:=0.193e12:  n:=1:  AD:=10:  upsilon:=0.291:   mu:=E/(2*(1+upsilon)):  l:=0:  lambda:=E*upsilon/((1+upsilon)*(1-2*upsilon)):  R:=2.5:  ii:=2:  J:=2:       m:=1:       `u__theta`(r,theta,phi):= ( V(r,theta))*cos(m*phi):  `u__r`(r,theta,phi):= ( U(r,theta))*cos(m*phi): `u__phi`(r,theta,phi):= ( W(r,theta))*sin(m*phi):  :        eq1:=(r (R+r cos(theta))^2 (mu+lambda) (((&PartialD;)^2)/(&PartialD;r&PartialD;theta) `u__theta`(r,theta,phi))+2 r^2 (mu+lambda/2) (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;r^2) `u__r`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((&PartialD;)^2)/(&PartialD;phi&PartialD;r) `u__phi`(r,theta,phi))+mu (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;theta^2) `u__r`(r,theta,phi))+(((&PartialD;)^2)/(&PartialD;phi^2) `u__r`(r,theta,phi)) mu r^2-3 (R+r cos(theta))^2 (mu+lambda/3) ((&PartialD;)/(&PartialD;theta) `u__theta`(r,theta,phi))+2 r (mu+lambda/2) (R+2 r cos(theta)) (R+r cos(theta)) ((&PartialD;)/(&PartialD;r) `u__r`(r,theta,phi))-r^2 sin(theta) (mu+lambda) (R+r cos(theta)) ((&PartialD;)/(&PartialD;r) `u__theta`(r,theta,phi))-3 r^2 cos(theta) (mu+lambda/3) ((&PartialD;)/(&PartialD;phi) `u__phi`(r,theta,phi))-r mu sin(theta) (R+r cos(theta)) ((&PartialD;)/(&PartialD;theta) `u__r`(r,theta,phi))-2 (mu+lambda/2) (2 (cos(theta))^2 r^2+2 cos(theta) R r+R^2) `u__r`(r,theta,phi)+r `u__theta`(r,theta,phi) sin(theta) (3 r (mu+lambda/3) cos(theta)+R mu))/(r^2 (R+r cos(theta))^2):  eq2:=(2 (mu+lambda/2) (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;theta^2) `u__theta`(r,theta,phi))+r (R+r cos(theta))^2 (mu+lambda) (((&PartialD;)^2)/(&PartialD;r&PartialD;theta) `u__r`(r,theta,phi))+r (mu+lambda) (R+r cos(theta)) (((&PartialD;)^2)/(&PartialD;phi&PartialD;theta) `u__phi`(r,theta,phi))+r^2 mu (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;r^2) `u__theta`(r,theta,phi))+(((&PartialD;)^2)/(&PartialD;phi^2) `u__theta`(r,theta,phi)) mu r^2+3 (R+r cos(theta)) ((4 r (mu+lambda/2) cos(theta))/3+R (mu+lambda/3)) ((&PartialD;)/(&PartialD;theta) `u__r`(r,theta,phi))-2 r (mu+lambda/2) sin(theta) (R+r cos(theta)) ((&PartialD;)/(&PartialD;theta) `u__theta`(r,theta,phi))+r mu (R+2 r cos(theta)) (R+r cos(theta)) ((&PartialD;)/(&PartialD;r) `u__theta`(r,theta,phi))+3 r^2 sin(theta) (mu+lambda/3) ((&PartialD;)/(&PartialD;phi) `u__phi`(r,theta,phi))+(-3 r R (mu+lambda/3) cos(theta)+(-lambda-2 mu) r^2-R^2 mu) `u__theta`(r,theta,phi)-2 r (mu+lambda/2) sin(theta) R `u__r`(r,theta,phi))/(r^2 (R+r cos(theta))^2):  eq3:=(r (mu+lambda) (R+r cos(theta)) (((&PartialD;)^2)/(&PartialD;phi&PartialD;theta) `u__theta`(r,theta,phi))+r^2 (mu+lambda) (R+r cos(theta)) (((&PartialD;)^2)/(&PartialD;phi&PartialD;r) `u__r`(r,theta,phi))+mu (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;theta^2) `u__phi`(r,theta,phi))+r (r mu (R+r cos(theta))^2 (((&PartialD;)^2)/(&PartialD;r^2) `u__phi`(r,theta,phi))+2 r (mu+lambda/2) (((&PartialD;)^2)/(&PartialD;phi^2) `u__phi`(r,theta,phi))+(4 r (mu+lambda/2) cos(theta)+R (mu+lambda)) ((&PartialD;)/(&PartialD;phi) `u__r`(r,theta,phi))+mu (R+2 r cos(theta)) (R+r cos(theta)) ((&PartialD;)/(&PartialD;r) `u__phi`(r,theta,phi))-mu sin(theta) (R+r cos(theta)) ((&PartialD;)/(&PartialD;theta) `u__phi`(r,theta,phi))-r (3 sin(theta) (mu+lambda/3) ((&PartialD;)/(&PartialD;phi) `u__theta`(r,theta,phi))+`u__phi`(r,theta,phi) mu)))/(r^2 (R+r cos(theta))^2):  "

EQ1 := collect(eq1, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ2 := collect(eq2, cos(m*phi))/cos(m*phi)+rho*omega^2; EQ3 := collect(eq3, sin(m*phi))/sin(m*phi)+rho*omega^2

(0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), theta))+0.2535718390e12*r^2*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), r))+0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(W(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), theta), theta))-0.7474825716e11*U(r, theta)*r^2-0.3283200960e12*(2.5+r*cos(theta))^2*(diff(V(r, theta), theta))+0.2535718390e12*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(U(r, theta), r))-0.1788235818e12*r^2*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), r))-0.3283200960e12*r^2*cos(theta)*W(r, theta)-0.7474825716e11*r*sin(theta)*(2.5+r*cos(theta))*(diff(U(r, theta), theta))-0.2535718390e12*(2.*cos(theta)^2*r^2+5.0*r*cos(theta)+6.25)*U(r, theta)+r*V(r, theta)*sin(theta)*(0.3283200960e12*r*cos(theta)+0.1868706429e12))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

 

(0.2535718390e12*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), theta), theta))+0.1788235818e12*r*(2.5+r*cos(theta))^2*(diff(diff(U(r, theta), r), theta))+0.1788235818e12*r*(2.5+r*cos(theta))*(diff(W(r, theta), theta))+0.7474825716e11*r^2*(2.5+r*cos(theta))^2*(diff(diff(V(r, theta), r), r))-0.7474825716e11*V(r, theta)*r^2+3.*(2.5+r*cos(theta))*(0.1690478927e12*r*cos(theta)+0.2736000800e12)*(diff(U(r, theta), theta))-0.2535718390e12*r*sin(theta)*(2.5+r*cos(theta))*(diff(V(r, theta), theta))+0.7474825716e11*r*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(V(r, theta), r))+0.3283200960e12*r^2*sin(theta)*W(r, theta)+(-0.8208002400e12*r*cos(theta)-0.2535718389e12*r^2-0.4671766072e12)*V(r, theta)-0.6339295976e12*r*sin(theta)*U(r, theta))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

 

(-0.1788235818e12*r*(2.5+r*cos(theta))*(diff(V(r, theta), theta))-0.1788235818e12*r^2*(2.5+r*cos(theta))*(diff(U(r, theta), r))+0.7474825716e11*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), theta), theta))+r*(0.7474825716e11*r*(2.5+r*cos(theta))^2*(diff(diff(W(r, theta), r), r))-0.2535718390e12*r*W(r, theta)-1.*(0.5071436780e12*r*cos(theta)+0.4470589545e12)*U(r, theta)+0.7474825716e11*(2.5+2.*r*cos(theta))*(2.5+r*cos(theta))*(diff(W(r, theta), r))-0.7474825716e11*sin(theta)*(2.5+r*cos(theta))*(diff(W(r, theta), theta))-1.*r*(-0.3283200960e12*sin(theta)*V(r, theta)+0.7474825716e11*W(r, theta))))/(r^2*(2.5+r*cos(theta))^2)+7850*omega^2

(1)

#BCs can be from following
``
U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0

U(0, theta) = 0, (D[1](U))(0, theta) = 0, U(1, theta) = 0, (D[1](U))(1, theta) = 0

(2)

NULL
V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0
NULL
W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0
``

V(0, theta) = 0, (D[1](V))(0, theta) = 0, V(1, theta) = 0, (D[1](V))(1, theta) = 0

 

W(0, theta) = 0, (D[1](W))(0, theta) = 0, W(1, theta) = 0, (D[1](W))(1, theta) = 0

(3)

``


 

Download fem2

buchanan2005.pdf

 

 

I'm working towards creating a way to visualise real polynomial ideals! (or at least the solutions of the polynomials in the ideals) this code creates a plot showing the solutions to all the polynomials in the ideal generated by P1 and P2 (these are specified in the code)

with(plots);
P1 := x^2+2*y^2-3;
solve(P1, y);
Plot1 := plot([%], x = -2 .. 2);

P2 := -2*x^2+2*x*y+3*y^2+x-4;
solve(%, y);
Plot2 := plot([%], x = -4 .. 2);

P2*a+P1;
solve(%, y);
seq(plot([%], x = -4 .. 2), a = 0 .. 10, .1);
display(%, Plot1, Plot2)




This is because when you multiply two polynomials their set of solution curves is just the union of the sets of curves associated with the previous polynomials.

For the next step I'd like to create a graph of the solutions associated with an ideal with three generators. To stop this from being excessively messy I'd like to do it with the RGB value of the colour of a curve is determined by  a and b where the formula for a generic polynomial that we are solving and graphing is given by:

P1+a*P2+b*P3;

where P3 is given by

P3 := x*y-3

I've tried various ways to use cury to make this work (my intuition is cury is the right function to use here)  but got no where. Any ideas how to procede?

Which sorting related with famous sequence

for example 

sorting differential equation in a list

then access the list with famous sequence as index such as using https://oeis.org/

after access with sequence as index, use choose function to get combinations then most result are isomorphism differential ideals?

is there methods about this sorting in Richard Stanley Combinatiric book? which page of it?

Last month I still can read file

by 

read “c://Users//hello//Documents//h.m”

but

now it return error

no read access c://Users//hello//Documents/

and 

in security I add the m file into readable 

I saw open file at c drive has many shell folders 

i just add m file

but still the same error

i unencrypted m file by window properties

still the same error

i save file into maple roaming directory under 12 folder , still the same error

i save into maple installation directory maple 12 , still the same error

possible to solve following equation with unknown parameter omega.

parameter constant.

I see before for one dimension ode this type equation was solved.

Now for 2d equation is possible?

can consider or I can send again.

Best

2d-2

 

Why am I not able to use my MaplePrimes login credentials to login into MapleCloud?

A few months ago i completely lost one of my linux operating systems in a single line of commands I entered into the terminal, and at some point I want to utilize the StringTools package with commands like  RegSubs and RegMatch to output the matching strings that match for the current command line content in a linux terminal, so I will know before I hit the enter key how stupid it was of me to do so *prior* to hitting the enter key.

 

The part I have no idea about is the piping of the keyboard input  for a terminal window to the maple session that will output the strings matching as previously described. I'm sorry if this question is not very clear I will try clarify more this afternoon. 

 

 

I have the following PDE

                         ...(1)

 

My Question: I have done manually following calculations. I want to verify the following operations are right, or not by MAPLE. Could you help me, please?

 

The METHOD:

Suppose that

                         ...(2)

In here,  is an Nx1 matrix, P, C are NxN matrices. (N is an integer and superscript T   denotes the transpose of the matrix.)  and P are given matrices. But the matrix C is ungiven I will find it in the final step. But my question doesn' t include all steps. I just wonder how to calculate the first two steps by Maple.

 

( If Maple doesn' t do matrix algebra, we can treat them as if , P, C were not matrix. I think the result won' t be changed. We will get again equation 9 by Maple.)

First Step

We will find the followings 

 

 in terms of the matrices  ,  P and C.

So, if we integrate Equation (2) with respect to x (from 0 to x), and  by using the following two assumptions

 

we have 

   ...(3)
 

substituting x=1  in Equation (3)

 ...(4)

if rewrite Eqn. (4), we have

...(5)

substituting Eqn. (5) to Eqn. (3), we have 

...(6)

integrating Equation (3) with respect to t,

we have 

...(7)

If we integrate Equation (2) from 0 to x with respect to t, we have

...(8)

Second Step We will substitute the terms to the pde ( Equation 1)

Substituting Eqn. (6), (7), (8) to Eqn. (1), we have finally

...(9)

I want to do the above calculations by Maple.  

Because I have more complex questions than above, I want to write a Maple code in order to avoid calculation errors.  

Final Step for curious: it's hard to explain the whole method here. Briefly, we will discretize equation 9 for some collocation points t and x. And after doing it, we will have a system of an algebraic equation. (N equation and N unknown ( C is Nx1 unknown vector to be find) )

And then we will substitute vector C to Eqn. 7

Code for Matrices , P^1, P^2,etc.

code.mw 

Best Regards...

maple does not work at all

it displays this error

Error, (in StringTools:-FormatMessage) unknown option MAPLE
 

Generally when I respond to questions on this site, I make sure that I tick the checkbox requesting that I get an email when updates are made to the thread.

I've just realised that I have been receiving no such updates for a week or so. Two possibilities

  1. Problem with Mapleprimes website, meaning that email updates aren't being generated/sent
  2. Problem with my ISP

Before I try investigating (2) above, I'd just like to know if anyone else has seen any issue which might be explained by (1) above

How to calculate potential function of Maxwell equations?

is there calculation examples of strong and weak force examples too?

which library can calculate intersection numbers of familes of potential function of Maxwell equations?

is there any examples?

Hi everybody:

I have the code in Maple that when run it I see this error, how can I solve this error? 

tnx...

 

hello everyone,

please I need our help to find the eigenvalues (m) of this equation (eq)

thank you 

eq.mw
 

``

restart

with(LinearAlgebra):

NULL

Digits := 5:

``

``

eq := exp(-m*xi)*(exp((1/4)*sqrt(-m)*r*(r-1))*(1+(7/20)*sqrt(m)*r+((49/800)*m-(1/4)*sqrt(m))*r^2)*r^I+exp((1/4)*sqrt(-m)*r*(r-1))*(1+(7/20)*sqrt(m)*r+((49/800)*m-(1/4)*sqrt(m))*r^2)*r^I*cos(theta)+r^I*sin(5*theta))

exp(-m*xi)*(exp((1/4)*(-m)^(1/2)*r*(r-1))*(1+(7/20)*m^(1/2)*r+((49/800)*m-(1/4)*m^(1/2))*r^2)*r^I+exp((1/4)*(-m)^(1/2)*r*(r-1))*(1+(7/20)*m^(1/2)*r+((49/800)*m-(1/4)*m^(1/2))*r^2)*r^I*cos(theta)+r^I*sin(5*theta))

(1)

``


 

Download eq.mw

 

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