## how do i plot a probabilitry function in 3 variabl...

How can i plot a probability function such as cos(x-y)*cos(y-z)*cos^3(x-2z)=0.6 where

x=0..5, y=0..x, z=0..y.

## How do I values to constants when using Invariants...

Dear Maple users,

I am progressing, but one last hitch, see below. A want the invariants of the PDE below. However, the final expression is too general to be useful. I would like to insert specific values for F1(R), F2(R), F3(R), and F4(R):

F3=F4=0; and F2=1, and F3(R)=aR, where a is a constant. R is one of my independent variables (the Reynolds number).

I would like to do this at the step where the Infinitiesimals are generated by

For example, the first entry would then be, infinies:=[ _xi[y](y, R, l, u) = y, ... ]. Then Invariants should give me much simplified expressions which I need.  How can i do this?

Thanks

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

## Opening and closing sections does not work properl...

Hi,

I am having trouble opening and closing sections in Maple 2018 (Mac OS version) recently. It used to work with just a single click to open, and another single click to close. Now sometimes it takes a single slick, sometimes two or more, and sometimes a richt-click and sometimes it doesn't work at all. This is becomming very frustrating, and I have no idea what caused the problem. The problem occurs with all my documents.

Thanks for help!

## Visualising solutions to sums of polynomials...

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 of differential equations related wi...

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?

## Permission denied : no read access...

Last month I still can read file

by

but

now it return error

and

I saw open file at c drive has many shell folders

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

## where is _LatexSmallFractionConstant documented?...

I am trying to find what the meaning of the values that _LatexSmallFractionConstant accepts and what they do.

For example

mu:=1/((4*t+1)^(8/5)*(t-1)^(7/5));
_LatexSmallFractionConstant:=34:
latex(simplify(mu))

{1 \left( 4\,t+1 \right) ^{-{\frac{8}{5}}} \left( t-1 \right) ^{-{
\frac{7}{5}}}}



Which renders wrong as follows

But when I set _LatexSmallFractionConstant to 35 instead of 34 this is what happens

restart;
mu:=1/((4*t+1)^(8/5)*(t-1)^(7/5));
_LatexSmallFractionConstant:=35:
latex(simplify(mu))

{\frac {1}{ \left( t-1 \right) ^{{\frac{7}{5}}}} \left( 4\,t+1
\right) ^{-{\frac{8}{5}}}}


which renders as a little better as

And when I set it to _LatexSmallFractionConstant:=100 it becomes good

However, no settings value will make latex render this fraction correctly

restart;
mu:=1/(x+y);
_LatexSmallFractionConstant:=2000000000:
latex(mu)

\left( x+y \right) ^{-1}


But if I set it to 35 again now it fails to handle fraction right

restart;
mu:=1/2;
_LatexSmallFractionConstant:=35:
latex(mu)

1/2


but changing to  either zero or 1 or 2 makes it generate the correct latex

restart;
mu:=1/2;
_LatexSmallFractionConstant:=0:  #1 and 2 also works. By anything larger it goes back to 1/2
latex(mu)

{\frac{1}{2}}  #but why extra {} ??


So it seems some values makes it work OK (35 for top example) but same value makes it not work well for another example.

It seems like random settings to me.

Where is all of this documented?  I can't find it in help. Which file to print to see what this option does?

Maple 2019.1  on windows.

 > restart; mu:=1/((4*t+1)^(8/5)*(t-1)^(7/5)); _LatexSmallFractionConstant:=34: latex(mu)

{1 \left( 4\,t+1 \right) ^{-{\frac{8}{5}}} \left( t-1 \right) ^{-{
\frac{7}{5}}}}

 > restart; mu:=1/((4*t+1)^(8/5)*(t-1)^(7/5)); _LatexSmallFractionConstant:=35: latex(mu)

{\frac {1}{ \left( t-1 \right) ^{{\frac{7}{5}}}} \left( 4\,t+1
\right) ^{-{\frac{8}{5}}}}

 > restart; mu:=1/((4*t+1)^(8/5)*(t-1)^(7/5)); _LatexSmallFractionConstant:=100: latex(mu)

{\frac {1}{ \left( 4\,t+1 \right) ^{8/5} \left( t-1 \right) ^{7/5}}}

 > restart; mu:=1/(x+y); _LatexSmallFractionConstant:=2000000000: latex(mu)

\left( x+y \right) ^{-1}

 > restart; mu:=1/2; _LatexSmallFractionConstant:=3: latex(mu)

1/2

 > restart; mu:=1/2; _LatexSmallFractionConstant:=0: latex(mu)

{\frac{1}{2}}

 >

## too many problems using algolib latex in Maple...

This is really a FYI more than a question, since I do not expect any more to be able to fix these since they are part of old Maple code called algolib, downloaded from  http://algo.inria.fr/libraries/

I was trying to see if the latex command included in the above will work better than Maple own latex command.  I downloaded the tar file from the above http://algo.inria.fr/libraries/17.0/algolib.tar    and extracted it.

At first I could not find where the latex command is, since it is not part of the .mla. After some struggle, I found I can get their latex command to work if I read the following 6 .mpl files (in this order) that show up after opening the above tar file

read "C:/MAPLE/algolib/mad/CommonLib.mpl";


Once I did the above, now I could do the command

MADLaTeX:-latex(sol);

#or

MADLaTeX:-latex(sol,'string')

And these work now. For example

MADLaTeX:-latex(1/2)

\frac{1}{2}

So I said, great, finally a Maple latex command that knows how to convert a fraction to latex the right way. Much better than Maple's latex command default output

latex(1/2)

1/2


But when I started testing it more, I found many problems. So I am posting these issues, since I do not know where to send them to, as this package is no longer being maintained. May be some Maple expert can figure how to fix them if there is an interest.  I looked at the code above, and too complicated for me to even figure where to look and how to fix these.

 > restart;
 > #EXAMPLE 1
 > V:=x->piecewise(0<=x and x<=a,0,infinity); ic:=f(x,0)=piecewise(0<=x and x<=a,A*x*(a-x),0); pde :=I*h*diff(f(x,t),t)=-h^2/(2*m)*diff(f(x,t),x$2) +V(x)*f(x,t); sol:=pdsolve([pde,ic],f(x,t)) assuming a>0; lprint(sol); f(x,t) = piecewise(0 <= x and x <= a,A*x*(a-x),0)+Sum(t^n*((U -> -I*(-1/2*h^2/m *diff(diff(U,x),x)+piecewise(0 <= x and x <= a,0,infinity)*U)/h)@@n)(piecewise( 0 <= x and x <= a,A*x*(a-x),0))/n!,n = 1 .. infinity)  > MADLaTeX:-latex(sol) Error, (in typetomath) 0 <= x and x <= a: invalid for math mode  > latex(sol) f \left( x,t \right) = \cases{Ax \left( a-x \right) &$0\leq x$\ and \$x\leq a$\cr 0&otherwise\cr} +\sum _{n=1}^{\infty }{\frac {{t}^{n} \left( U\mapsto {\frac {-i \cases{0&$0\leq x$\ and \$x\leq a$\cr \infty &otherwise\cr}U}{h}}^{ \left( n \right) } \right) \left( \cases{Ax \left( a-x \right) &$0\leq x$\ and \$x\leq a$\cr 0&otherwise\cr} \right) }{n!}}  > #EXAMPLE 2  > pde := diff(v(t, s), t) +s^2*(diff(v(t, s), s, s))/(2*sigma^2)+(r-q)*s*(diff(v(t, s), s))-r*v(t, s) = 0; ic:=v(T, s) = psi(s); sol:=pdsolve([pde,ic],v(t,s)); lprint(sol); v(t,s) = psi(s)+Sum((t-T)^n*((U -> -1/2*diff(diff(U,s),s)*s^2/sigma^2+s*(-r+q)* diff(U,s)+r*U)@@n)(psi(s))/n!,n = 1 .. infinity)  > MADLaTeX:-latex(sol) Error, (in symbol/string) only ANSI-C compliant symbols are handled  > latex(sol) v \left( t,s \right) =\psi \left( s \right) +\sum _{n=1}^{\infty }{ \frac { \left( t-T \right) ^{n} \left( U\mapsto rU^{ \left( n \right) } \right) \left( \psi \left( s \right) \right) }{n!}}  > #EXAMPLE 3  > interface(showassumed=0); pde := diff(u(x,t),t)=k*diff(u(x,t),x$2)- u(x,t)*x; ic  := u(x,0)=sin(x); bc  := u(0,t)=0,u(Pi,t)=0; sol:=pdsolve([pde,ic,bc],u(x,t)) assuming k>0; lprint(sol)

u(x,t) = casesplit/ans(Sum(-(AiryBi(-1/k^(1/3)*lambda[n])*AiryAi((-lambda[n]+
x)/k^(1/3))-AiryBi((-lambda[n]+x)/k^(1/3))*AiryAi(-1/k^(1/3)*lambda[n]))*(Int(
sin(x)*AiryBi((-lambda[n]+x)/k^(1/3)),x = 0 .. Pi)*AiryAi(-1/k^(1/3)*lambda[n])
-AiryBi(-1/k^(1/3)*lambda[n])*Int(sin(x)*AiryAi((-lambda[n]+x)/k^(1/3)),x = 0
.. Pi))*(-sinh(lambda[n]*t)+cosh(lambda[n]*t))/(Int(AiryBi((-lambda[n]+x)/k^(1/
3))^2,x = 0 .. Pi)*AiryAi(-1/k^(1/3)*lambda[n])^2-2*AiryBi(-1/k^(1/3)*lambda[n]
)*Int(AiryBi((-lambda[n]+x)/k^(1/3))*AiryAi((-lambda[n]+x)/k^(1/3)),x = 0 .. Pi
)*AiryAi(-1/k^(1/3)*lambda[n])+AiryBi(-1/k^(1/3)*lambda[n])^2*Int(AiryAi((-
lambda[n]+x)/k^(1/3))^2,x = 0 .. Pi)),n = 0 .. infinity),{And(AiryAi(1/k^(1/3)*
(-lambda[n]+Pi))*AiryBi(-1/k^(1/3)*lambda[n])-AiryBi(1/k^(1/3)*(-lambda[n]+Pi))
*AiryAi(-1/k^(1/3)*lambda[n]) = 0,-infinity <= lambda[n] and lambda[n] <=
infinity)})

Error, (in typetomath) -infinity <= lambda[n] and lambda[n] <= infinity: invalid for math mode

 > latex(sol)

u \left( x,t \right) =\mbox {{\tt casesplit/ans}} \left( \sum _{n=0
}^{\infty } \left( {(-\sinh \left( \lambda_{{n}}t \right) +\cosh
\left( \lambda_{{n}}t \right) ) \left( {{\rm Bi}\left({\frac {-
\lambda_{{n}}+x}{\sqrt [3]{k}}}\right)}{{\rm Ai}\left(-{\frac {\lambda
_{{n}}}{\sqrt [3]{k}}}\right)}-{{\rm Bi}\left(-{\frac {\lambda_{{n}}}{

\sqrt [3]{k}}}\right)}{{\rm Ai}\left({\frac {-\lambda_{{n}}+x}{\sqrt [
3]{k}}}\right)} \right)  \left( \int_{0}^{\pi}\!\sin \left( x \right)
{{\rm Bi}\left({\frac {-\lambda_{{n}}+x}{\sqrt [3]{k}}}\right)}
\,{\rm d}x{{\rm Ai}\left(-{\frac {\lambda_{{n}}}{\sqrt [3]{k}}}
\right)}-{{\rm Bi}\left(-{\frac {\lambda_{{n}}}{\sqrt [3]{k}}}\right)}
\int_{0}^{\pi}\!\sin \left( x \right) {{\rm Ai}\left({\frac {-\lambda_
{{n}}+x}{\sqrt [3]{k}}}\right)}\,{\rm d}x \right)  \left( \int_{0}^{
\pi}\! \left( {{\rm Bi}\left({\frac {-\lambda_{{n}}+x}{\sqrt [3]{k}}}
\right)} \right) ^{2}\,{\rm d}x \left( {{\rm Ai}\left(-{\frac {\lambda
_{{n}}}{\sqrt [3]{k}}}\right)} \right) ^{2}-2\,{{\rm Bi}\left(-{\frac
{\lambda_{{n}}}{\sqrt [3]{k}}}\right)}\int_{0}^{\pi}\!{{\rm Bi}\left({
\frac {-\lambda_{{n}}+x}{\sqrt [3]{k}}}\right)}{{\rm Ai}\left({\frac {
-\lambda_{{n}}+x}{\sqrt [3]{k}}}\right)}\,{\rm d}x{{\rm Ai}\left(-{
\frac {\lambda_{{n}}}{\sqrt [3]{k}}}\right)}+ \left( {{\rm Bi}\left(-{
\frac {\lambda_{{n}}}{\sqrt [3]{k}}}\right)} \right) ^{2}\int_{0}^{\pi
}\! \left( {{\rm Ai}\left({\frac {-\lambda_{{n}}+x}{\sqrt [3]{k}}}
\right)} \right) ^{2}\,{\rm d}x \right) ^{-1}} \right) , \left\{ {\it
And} \left( {{\rm Ai}\left({\frac {-\lambda_{{n}}+\pi}{\sqrt [3]{k}}}
\right)}{{\rm Bi}\left(-{\frac {\lambda_{{n}}}{\sqrt [3]{k}}}\right)}-
{{\rm Bi}\left({\frac {-\lambda_{{n}}+\pi}{\sqrt [3]{k}}}\right)}{
{\rm Ai}\left(-{\frac {\lambda_{{n}}}{\sqrt [3]{k}}}\right)}=0,-
\infty \leq \lambda_{{n}} \land \lambda_{{n}}\leq \infty  \right)
\right\}  \right)

 >
 >

## pdsolve 2D equations with unknown parameter...

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

## Cloud problem. ...

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

## Regular Expressions Checker...

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.

## Some Symbolical Operations (Edited and Expanded)...

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.

Best Regards...

## Maple error pls help!!!...

maple does not work at all

it displays this error

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

## A check on website functionality...

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