## How to specify initial (Cauchy) data when given as...

I was trying to verify some solution to pde in textbook using Maple. The book gives the Cauchy data for this first order PDE in the form that Maple does not like when I used it as input. Here is an example

When I typed

pde:=u(x,y)*(x+y)*diff(u(x,y),x)+u(x,y)*(x-y)*diff(u(x,y),y)=x^2+y^2;
ic:=u(x,2*x)=0;
pdsolve([pde,ic],u(x,y))


Maple complained

Error, (in PDEtools:-Library:-NormalizeBoundaryConditions) unexpected
occurrence of the variables {x} in the 2nd operand of u(x, 2*x) in the given initial conditions


In Mathematica it accepts such form of Cauchy data:

pde=u[x,y]*(x+y)*D[u[x,y],x]+u[x,y]*(x-y)*D[u[x,y],y]==x^2+y^2;
ic=u[x,2*x]==0;
DSolve[{pde,ic},u[x,y],{x,y}]

(I have not verified the above answer is correct or not).

Am I doing something wrong in Maple?

Or is there a trick or option or method to allow Maple to accepts such initial conditions? The book I am looking at has many problems where Cauch data is given on such form (i.e. u=0 on specific curve or in 3D on some specific surface). Here is another example

Which I'd like write its initial conditions as u(x,1/x)=0 but can not.

I could ofcourse solve the pde without these initial conditions, and then post process the answer to find the constants of integration from the Cauchy data given. But it will be nice if Maple would accept the IC as is.

## Question and answer both removed...

Given my gender, my age, the region where I live, statistics say my life expectation is still 25.3 years, thus about 221650 hours.
Under these conditions, what does the loss of an hour to answer a question represent?
Practicaly nothing, particularly if the answer does present some interest for the OP who posted it.

But what if this same OP has removed his question once I answered it?

In this case it's a complete waste of time, without even complaining about the indelicacy that this PO has shown.

So, vv, why did you remove your last question once answered ?

As a reminder, it was a manual simplification (Maple did not succeed in doing so) of  expression

expr := 512*b^9 + (2303*a + 2304)*b^8 + (4616*a^2 + 9216*a + 4608)*b^7 + (5348*a^3 + 16128*a^2 + 16128*a + 5376)*b^6
+ (4088*a^4 + 16128*a^3 + 24192*a^2 + 16128*a + 4032)*b^5 + (1946*a^5 + 10080*a^4 + 20160*a^3 + 20160*a^2
+ 10080*a + 2016)*b^4 + (728*a^6 + 4032*a^5 + 10080*a^4 + 13440*a^3 + 10080*a^2 + 4032*a + 672)*b^3
+ (116*a^7 + 1008*a^6 + 3024*a^5 + 5040*a^4 + 5040*a^3 + 3024*a^2 + 1008*a + 144)*b^2
+ (26*a^8 + 144*a^7 + 504*a^6 + 1008*a^5 + 1260*a^4 + 1008*a^3 + 504*a^2 + 144*a + 18)*b + 9*a^8
+ 36*a^7 + 84*a^6 + 126*a^5 + 126*a^4 + 84*a^3 + 36*a^2 + 9*a + 1

in order to obtain (a+2*b+1)^9 - a*(a-b)^8

## Can this build and visualise as a tree?...

1,1,2,2,2,3,3,2,2,1,2,2,2,3,3,1,1

i would like to research the ordering mechanism of this kind of series Before sorting.

## use factor or using rule for simplify...

How I can simplify result? For factor or using rule.

Thanks

## A Number Theory Conjecture about Smoothness...

Hi Maple Experts and all,

There is a conjecture from a book written in 1986.

This conjecture states that

"Given any four consecutive integers greater than 11, there is at least one of them that is divisible by a prime greater than 11."

Is anyone willing to write Maple code to test this up to a reasonable numerical limit?

I imagine the ifactor() command and loops.  I'm not that good at coding.

Regards,

Matt

## can maple sim simulate a robot arm and hand catch ...

can maplesim simulate a robot arm and hand catch a throwing ball and picking objects?

can maplesim simulate a balancing a robot legs?

will these simulation require complex formula to draw the robots arm and hand and maintain the joints stick together during motions?

can maplesim output the specification to autodesk for 3D print parts?

i can not see the price in maple official site from Hong Kong area.

## How to track changes in a edited Maple Code?...

Dear there,

Is there a possibility for tracking changes like Microsoft Office in the saved a Maple worksheet after some editings?

I think that we all encounter the same case. I mean we don't remember generally all changes after editing our codes.

If there is no possibility for tracking changes,  what are your solutions or suggestions in order to prevent to forget?

## solving an equation...

Hi

how can i find x in terms of y(x)

y(x)=

## pdetest does not verify solution of pdsolve...

Is it considered a bug when pdetest does not give zero for a solution given by pdsolve?

restart;
pde := x*diff(w(x,y,z),x)+  a*z*diff(w(x,y,z),y)+b*y*diff(w(x,y,z),z)=c:
sol:=pdsolve(pde,w(x,y,z));
pdetest(sol,pde)


Gives

which is not zero.

This is the first time I've seen this happen.

Maple 2019.1 using Physics version 362

## How to write long expression...

If we have following expression

4*beta*c*lambda^2*mu^2+2*beta*c*lambda*mu^3+2*beta*c*lambda*mu^2*nu+beta*c*mu^3*nu-4*c*lambda^2*mu^2*sigma-2*c*lambda*mu^3*sigma-2*c*lambda*mu^2*nu*sigma-c*mu^3*nu*sigma+4*beta*lambda^3*sigma+4*beta*lambda^2*mu*sigma+2*beta*lambda^2*nu*sigma+2*beta*lambda*mu^2*sigma+2*beta*lambda*mu*nu*sigma+beta*mu^3*sigma+beta*mu^2*nu*sigma+4*lambda^2*mu^2*sigma+2*lambda*mu^3*sigma+2*lambda*mu^2*nu*sigma+mu^3*nu*sigma

If I use the command simplify(---,size), it gives

((2*c-2)*lambda-beta+nu*(-1+c))*mu^3+(2*(lambda*(-1+c)-(1/2)*beta))*(2*lambda+nu)*mu^2-2*beta*lambda*(2*lambda+nu)*mu-2*lambda^2*beta*(2*lambda+nu)

which can also be written if i did manually as

beta*mu^3+(2*lambda+nu)*(beta*mu^2+2*beta*lambda*mu+2*beta*lambda^2+(1-c)*(2*lambda+mu)*mu^2)

My question with all learned people is: in Maple, how i can get most simplified and short expression automaticall?

Thanking you in anticipation.

## how to use gamma in expression as symbol and not t...

I need to use gamma as a "free" symbol in pde that I pass to pdsolve, so that the latex comes out as \gamma OK in the solution.

in other words, the pde itself uses the symbol gamma (as it is written in the textbook and I want to keep it the same). This gamma is not the known constant gamma. Something similar to using alpha and beta or x and y.

But gamma in a known constant in Maple and I am worried this will affect some computation inside pdsolve if I use gamma  as known number in the PDE (even though I think it should not change the result of pdsolve as there are no other numbers in the PDE input, I just wanted to be safe).

I am not able to clear gamma

unassign(gamma)  gives error since it is protected.

Is  there a way around this? Should I use wrap the name with 'gamma'  or gamma for example?

Here is an example

pde := a*diff(w(x,y,z),x)+ b*diff(w(x,y,z),y)+c*diff(w(x,y,z),z)= alpha*x+beta*y+gamma*z+delta;

It is the gamma above I am worried about using in the input. What is the correct way to do this?

## Problem changing signature in Physics package...

Hello,

I am trying to work with the Physics package to calculate Christoffel symbols. I have just started using Maple today and am coming up against a few hurdles.

I want to change the signature of the metric from (+---) to (-+++). I am typing the following in math mode:

Setup( signature = '-+++')

However, this is returning the following error:

"Error, invalid sum/difference" with my command rewritten within a red box together with the last '+" within another red box. Can you please help me out with this?

Thank you.

## How do I tell maple that a variable is a function ...

I am completely new to maple and am stuck in the very beginning trying to use the Physics package to calculate Christoffel symbols. Suppose I have coordinates (t, x, sigma, theta). The metric g_ has coefficients that are functions of (t,x,sigma) i.e. the metric is like

g_ = a(t,x,sigma) dt^2 + b(t,x,sigma)dt dx + dx^2 + dsigma^2 + sigma^2 dtheta^2.

(Should I write dsigma^2 or (d sigma)^2?)

How do I tell maple to treat a, b as functions of (t,x,sigma)?

Thank you.

## Unable to save a worksheet once executed...

HI,

Yesterday I replied  denitsastaicova's question while providing an attached file.

Surprisingly, I wasn't able to save the worksheet after having executed it. The only way I found to save it was to copy-paste it's content in a new worksheet and save this latter without any execution.
Here is the file
events.mw

For info I'm working with  Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895
on Mac OS Mojave 10.14.3
If I open this file and execute it (and even if I execute only the commands from the initial restart to the three dsolve), I get this pop-up error message when trying to save it:

Does my worksheet contain some undesired character or is it a bug ?

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