Even and odd complement each other

how to find other sequence which complement each other?

such as 3 sequences divided integers or 5 sequences divided whole integers

is there monomials creation method such that solve result about coefficient and power are integers when right side columns are sequences?

i find even multiplication numbers are always solved into integers coefficient and power.

is there any more other sequences?

if I choose six multiplication table sequence, 

what is this complement of six multiplication table sequence?

How do i change keyboard shortcuts, E.g one of my keyboard keys are broken or have stopped working. How do i redirect my shortcut to another keyboard combination or another hotkey simply.

Hello, is it possible to have a document synchronized in the same way as Onenote? We're a group of engieneer students wanting to share documents, however the only way we can figure out a way to do it. Is uploading to maplecloud groups, sharing a "base" document, and everytime someone "updates" the document you save a new one. So it kind of defeats the purpose of making it a smart idea of collaborating on one document, am i missing something or is this really how oldschool it works?

I was wondering how Maple cope with piecewise functions during forward integration and if it's preferable to use dsolve events option in place of defining a piecewise discontinuos function.

As far as I understood dsolve/events halts the integration each time an event is triggered and subsequently restarts the integration using the pre-trigger outputs as new initial conditions. I suppose that by using a piecewise, if a discontinuity is detected, dsolve proceeds exactly in the same way halting and restarting the integration.

Here a toy example of a 2D rolling dice (idea of a rolling dice from the rolling cube by @one man :P ) in which the reaction forces of the floor can be seen as function of the compenetration dice/ground

Both the appraches (events and piecewise) give the same results

falling_dice.mw

Hi

In mathematics, the inverse problem for Lagrangian mechanics (Helmholtz inverse problem) is the problem of determining whether a given system of ordinary differential equations can arise as the Euler–Lagrange equations for some Lagrangian function. 

For more information read section IV.2. page 65 of the following reference:

http://www.unilim.fr/pages_perso/loic.bourdin/Documents/bourdin-thesis2013.pdf

________________________________________________________________________

I need some hints or procedures (if it is possible) for similar (but a little more complex) problem:

1- Assume that you have one ordinary differential equation, ode1(r) in polar coordinate system (i.e. (r, theta)). The ODE is taken to be independent from theta (It is not a PDE).

2- Assume that "Euler" is an operator that gives the Euler-Lagrange equation, I need a procedure to calculate ode2(r) such that

1/(2r)*Euler (ode2(r)) -Laplacian (1/(2r)*Euler(ode1(r)))=0

It is obvious that we need inverse of Euler operator (say IE) to calculate ode2(r).

ode2(r) =IE( 2r*Laplacian (1/(2r)*Euler(ode1(r))))

I calculate ode2(r) for some simpler cases via trial and error method.

s := proc (S) 
subs(w = w(r), w1 = diff(w(r), r), w2 = diff(w(r), r$2), S) 
end proc: 
Euler := proc (f) 
s(diff(f, w))-(diff(s(diff(f, w1)), r))+diff(s(diff(f, w2)), r$2) 
end proc:

Example:

ode1(r) = -r*(diff(w(r),r))^2:

ode2(r) = (diff(w(r),r))^2/r+r*(diff(w(r),r$2))^2:

-1/(2*r)*Euler(w1^2*r):

simplify(1/(2*r)*Euler(w1^2/r+r*w2^2)-VectorCalculus:-Laplacian(%,('polar')[r,theta]))

I will be grateful if you can hint me to write an appropriate procedure.

Thanks

A catenoid is the minimal surface between two 3D circles which are co-axial and parallel.

Is there a technique for finding the formula for the minimal surface if the circles are "stretched" into ellipses with proportional major and minor axes?

Download mapleprime2.mw

Please help me with the following worksheet containg a sample Equation. I need to equate the exponent and co-efficents of the cosine function

How I can solve these time delay  differential equations?

please see attatched files.

Best

Doc191.pdf

ny.mw

Download ny.mw

I have a complicated expression which includes RootOf( a quadratic ) but holds for all x what i'd like to do is turn it into a polynomial in x[1], x[2], x[3] so i can start looking at the monomial coefficients.

k[a1]*((x[1]+x[3])*k[d1]+C[T]*k[m])*(R[b]-x[1]-2*x[2])/((R[b]+R[m]-x[1]-2*x[2]-x[3])*k[a1]+k[m])-k[d1]*x[1]-k[a2]*x[1]*(R[b]-x[1]-2*x[2])+2*k[d2]*x[2] = (-R[b]*k[a2]+2*k[a2]*x[1]+2*k[a2]*x[2])*(k[a1]*kh[m]*((x[1]+x[3])*k[d1]+C[T]*k[m])*(R[b]+R[m]-Rh[m]-x[1]-2*x[2])/(k[m]*((R[b]+R[m]-x[1]-2*x[2]-x[3])*k[a1]*kh[m]/k[m]+kh[m]))-k[d1]*x[1]-kh[a2]*x[1]*(R[b]+R[m]-Rh[m]-x[1]-2*x[2])+2*kh[d2]*x[2])/(2*kh[a2]*RootOf(kh[a2]*_Z^2+(-R[b]*kh[a2]-R[m]*kh[a2]+Rh[m]*kh[a2]+2*kh[a2]*x[2])*_Z-2*k[a2]*x[1]*x[2]-k[a2]*x[1]^2+k[a2]*x[1]*R[b]+2*kh[d2]*x[2]-2*k[d2]*x[2])-R[b]*kh[a2]-R[m]*kh[a2]+Rh[m]*kh[a2]+2*kh[a2]*x[2])+(-2*kh[a2]*RootOf(kh[a2]*_Z^2+(-R[b]*kh[a2]-R[m]*kh[a2]+Rh[m]*kh[a2]+2*kh[a2]*x[2])*_Z-2*k[a2]*x[1]*x[2]-k[a2]*x[1]^2+k[a2]*x[1]*R[b]+2*kh[d2]*x[2]-2*k[d2]*x[2])+2*k[a2]*x[1]+2*k[d2]-2*kh[d2])*(kh[a2]*x[1]*(R[b]+R[m]-Rh[m]-x[1]-2*x[2])-2*kh[d2]*x[2])/(2*kh[a2]*RootOf(kh[a2]*_Z^2+(-R[b]*kh[a2]-R[m]*kh[a2]+Rh[m]*kh[a2]+2*kh[a2]*x[2])*_Z-2*k[a2]*x[1]*x[2]-k[a2]*x[1]^2+k[a2]*x[1]*R[b]+2*kh[d2]*x[2]-2*k[d2]*x[2])-R[b]*kh[a2]-R[m]*kh[a2]+Rh[m]*kh[a2]+2*kh[a2]*x[2])

If this were something like q(x)=p1(x)/sqrt(p2(x)) where p1 and p2 are polynomials and q is a quotient- this would be as simple as making sqrt(p2(x)) the subject and squaring both sides, and then movinbg everything onto one and multiplying out denominators. However RootOf is something I'm not used to manipulating.

Is there anyway of converting this expression to a polynomial using maple commands?

Hello people in mapleprimes,

I installed maple 2018 Japanese version.
And, with solve(x^2-1,x), its solution is expressed as _EXPSEQ(1, -1)

I know this expression is an internal represantation.
How can I have maple answer as 1, -1?

Thanks in advance.

Addition: my pc is mac osx 10.13.6.
 

After calculations the integral contains infinity. what it resembles? Is it correct  answer?  Please check the file maple
 

Download maple1.mw

1.mw maple1.pdf

Hi everybody, I have some programming difficulties on the maple, this is the algorithm and link article, hope everyone help me, please, thank you so much!!

Algorithm:

1: for Search every non-singular m × m matrix T with a few of XORs over F2. do

2: Find the minimum polynomial f(x) of T.

3: if f(x) = g(x)t(x) satisfying g(x) 6= 1, t(x) 6= 1 and g(x) is relatively prime with t(x). then

4: Find ri1(x), ri2 satisfying g(x)ri1 +t(x)ri2 = 1. Let pi1=g(x)ri1, pi2=t(x)ri2 = 1 . Sore pi1 and pi2.

5: end if

6: end for

7: for i from 1 to k. do

8: for Search a over F2[x]/(fi(x)). do

9: for Search b over F2[x]/(fi(x)). do

10: c = a + pi1(x), d = b + pi2.

11: if The circulant orthogonal matrix (a, b, c, d) is MDS. then

12: Store fi(x) and (a, b, c, d).

13: end if

14: end for

15: end for

16: end for

17: for Search every m × m non-singular matrix T with a few of XORs. do

18: for i from 1 to k. do

19: if fi(T) = 0. then

20: Substitute T into corresponding circulant orthogonal MDS matrix (a, b, c, d). Compute the sum of XORs of (a, b, c, d).

21: end if

22: end for

23: end for

Link: https://eprint.iacr.org/2017/371.pdf

Hi , 

I want to ask if there is any maple code of how to construct wavelet to solve fractional differential eqautions? Or any reference may be help me 

thanks 

Hello everyone! I have just started to using Maple 13. I want to solve complex eauation systems.

When I am working on Maple, If I write simple mathematical calculation and then press right click, the context menu open. However, I want to use solve command. Therefore I wrote an eauation after than press right click the context menu will not open. 

What is the reason of this problem? 

Hi folks,

I've just now installed Maple player, and I find it crashes immediately when I run it:

Exception in thread "Request id 1" java.lang.UnsupportedOperationException: PERPIXEL_TRANSLUCENT translucency is not supported
        at java.awt.Window.setBackground(Window.java:3842)
        at java.awt.Frame.setBackground(Frame.java:988)
        at com.maplesoft.worksheet.application.WmiSplashScreen.<init>(Unknown Source)
        at com.maplesoft.worksheet.player.WmiPlayerStartupStrategy.showSplash(Unknown Source)
        at com.maplesoft.worksheet.application.WmiGenericStartupStrategy.doStartup(Unknown Source)
        at com.maplesoft.worksheet.player.WmiPlayerStartupStrategy.doStartup(Unknown Source)
        at com.maplesoft.application.Maple.doStartup(Unknown Source)
        at com.maplesoft.application.Application.startup(Unknown Source)
        at com.maplesoft.application.ServerProtocol$StartApplicationHandler.processCommand(Unknown Source)
        at com.maplesoft.application.ServerProtocol.executeCommand(Unknown Source)
        at com.maplesoft.application.ServerProtocol.processNextStep(Unknown Source)
        at com.maplesoft.application.ExchangeProtocol.executeProtocol(Unknown Source)
        at com.maplesoft.application.ApplicationManager$Listener.run(Unknown Source)
        at java.lang.Thread.run(Thread.java:748)

The operating system is CentOS 7 (64 bit).   Any idea how I can fix this?

Thanks,

Bryan