Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

The eval command doesn't work on random variables.

For instance:

X := RandomVariable(Normal(mu, sigma)):
Y := eval(X, mu=1);
Mean(Y); # returns mu

I once found a Maple command whose syntax is the same as eval's and acts as eval
Y := COMMAND(X, mu=1)
Mean(Y); # returns 1

Could someone remind me of its name?

Thanks in advance

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.

please guide me.

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

infinies := Infinitesimals(PDE)

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?





declare(u(y, R))

` u`(y, R)*`will now be displayed as`*u


declare(l(y, R))

` l`(y, R)*`will now be displayed as`*l


L := diff_table(l(y, R))

table( [(  ) = l(y, R) ] )



U := diff_table(u(y, R))

table( [(  ) = u(y, R) ] )


DepVars := ([l, u])(y, R)

[l(y, R), u(y, R)]


PDE := U[y, y]+2*l(y, R)^2*U[y]*U[y, y]+2*l(y, R)*L[y]*U[y]^2+1/R = 0

diff(diff(u(y, R), y), y)+2*l(y, R)^2*(diff(u(y, R), y))*(diff(diff(u(y, R), y), y))+2*l(y, R)*(diff(l(y, R), y))*(diff(u(y, R), y))^2+1/R = 0


infinies := Infinitesimals(PDE)

[_xi[y](y, R, l, u) = _F2(R)*y+_F3(R), _xi[R](y, R, l, u) = _F1(R), _eta[l](y, R, l, u) = (1/2)*l*(-R*_F2(R)+_F1(R))/R, _eta[u](y, R, l, u) = (2*R*_F2(R)-_F1(R))*u/R+_F4(R)]


InfinitesimalGenerator(infinies, DepVars, prolongation = 1)

proc (f) options operator, arrow; add(xi[x[j]]*(diff(f, x[j])), j = 1 .. 2)+add(eta[u[m]]*(diff(f, u[m]))+eta[u[m], [y]]*(diff(f, u[m][y]))+eta[u[m], [R]]*(diff(f, u[m][R])), m = 1 .. 2) end proc


Phi := Invariants(infinies, DepVars)

l*exp(-(1/2)*(Int((-R*_F2(R)+_F1(R))/(R*_F1(R)), R))), -(Int(_F3(R)*exp(-(Int(_F2(R)/_F1(R), R)))/_F1(R), R))+y*exp(-(Int(_F2(R)/_F1(R), R))), u*exp(Int((-2*R*_F2(R)+_F1(R))/(R*_F1(R)), R))-(Int(_F4(R)*exp(Int((-2*R*_F2(R)+_F1(R))/(R*_F1(R)), R))/_F1(R), R)), u[y]*exp(Int((-R*_F2(R)+_F1(R))/(R*_F1(R)), R)), l[y]*exp(-(1/2)*(Int((-3*R*_F2(R)+_F1(R))/(R*_F1(R)), R))), (1/2)*Intat(-exp((1/2)*(Int((2*(diff(_F1(_j), _j))*_j+_j*_F2(_j)-_F1(_j))/(_j*_F1(_j)), _j)))*(-2*(diff(_F2(_j), _j))*_j^2*l[y]*(y*exp(-(Int(_F2(R)/_F1(R), R)))-(Int(_F3(R)*exp(-(Int(_F2(R)/_F1(R), R)))/_F1(R), R))+Int(_F3(_j)*exp(-(Int(_F2(_j)/_F1(_j), _j)))/_F1(_j), _j))*exp(Int(_F2(_j)/_F1(_j), _j)+(1/2)*(Int((-3*_j*_F2(_j)+_F1(_j))/(_j*_F1(_j)), _j))-(1/2)*(Int((-3*R*_F2(R)+_F1(R))/(R*_F1(R)), R)))+l*(-(diff(_F2(_j), _j))*_j^2+(diff(_F1(_j), _j))*_j-_F1(_j))*exp((1/2)*(Int((-_j*_F2(_j)+_F1(_j))/(_j*_F1(_j)), _j))-(1/2)*(Int((-R*_F2(R)+_F1(R))/(R*_F1(R)), R)))-2*(diff(_F3(_j), _j))*l[y]*_j^2*exp((1/2)*(Int((-3*_j*_F2(_j)+_F1(_j))/(_j*_F1(_j)), _j))-(1/2)*(Int((-3*R*_F2(R)+_F1(R))/(R*_F1(R)), R))))/(_j^2*_F1(_j)), _j = R)+l[R]*exp((1/2)*(Int((2*(diff(_F1(R), R))*R+R*_F2(R)-_F1(R))/(R*_F1(R)), R))), u[R]*exp(Int(((diff(_F1(R), R))*R-2*R*_F2(R)+_F1(R))/(R*_F1(R)), R))+Intat(-exp(Int(((diff(_F1(_k), _k))*_k-2*_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k)-(Int((-_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k))-(Int((-2*_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k)))*(-(diff(_F2(_k), _k))*_k^2*u[y]*(y*exp(-(Int(_F2(R)/_F1(R), R)))-(Int(_F3(R)*exp(-(Int(_F2(R)/_F1(R), R)))/_F1(R), R))+Int(_F3(_k)*exp(-(Int(_F2(_k)/_F1(_k), _k)))/_F1(_k), _k))*exp(Int(_F2(_k)/_F1(_k), _k)+Int((-2*_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k)+Int((-R*_F2(R)+_F1(R))/(R*_F1(R)), R))+(diff(_F4(_k), _k))*exp(Int((-_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k)+Int((-2*_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k))*_k^2-_k^2*u[y]*(diff(_F3(_k), _k))*exp(Int((-2*_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k)+Int((-R*_F2(R)+_F1(R))/(R*_F1(R)), R))+exp(Int((-_k*_F2(_k)+_F1(_k))/(_k*_F1(_k)), _k))*(u*exp(Int((-2*R*_F2(R)+_F1(R))/(R*_F1(R)), R))-(Int(_F4(R)*exp(Int((-2*R*_F2(R)+_F1(R))/(R*_F1(R)), R))/_F1(R), R))+Int(_F4(_k)*exp(-(Int((2*_k*_F2(_k)-_F1(_k))/(_k*_F1(_k)), _k)))/_F1(_k), _k))*(2*(diff(_F2(_k), _k))*_k^2-(diff(_F1(_k), _k))*_k+_F1(_k)))/(_k^2*_F1(_k)), _k = R)


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!



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)

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);

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:


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

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


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


now it return error

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


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

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

For example


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

Which renders wrong as follows

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


{\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


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

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



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

_LatexSmallFractionConstant:=0:  #1 and 2 also works. By anything larger it goes back to 1/2

    {\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.




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



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



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



 \left( x+y \right) ^{-1}










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   

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    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";
read "C:/MAPLE/algolib/mad/DocumentGenerator.mpl";
read "C:/MAPLE/algolib/mad/MAD.mpl";
read "C:/MAPLE/algolib/mad/LaTeX.mpl";
read "C:/MAPLE/algolib/mad/HTMX.mpl";
read "C:/MAPLE/algolib/mad/DocumentGenerator.mpl";

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




And these work now. For example



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 



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.


read "C:/MAPLE/algolib/mad/CommonLib.mpl";
read "C:/MAPLE/algolib/mad/DocumentGenerator.mpl";
read "C:/MAPLE/algolib/mad/MAD.mpl";
read "C:/MAPLE/algolib/mad/LaTeX.mpl";
read "C:/MAPLE/algolib/mad/HTMX.mpl";
read "C:/MAPLE/algolib/mad/DocumentGenerator.mpl";


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;

V := proc (x) options operator, arrow; piecewise(0 <= x and x <= a, 0, infinity) end proc

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*(diff(f(x, t), x, x))/(2*m)+piecewise(0 <= x and x <= a, 0, infinity)*f(x, t)

f(x, t) = piecewise(0 <= x and x <= a, A*x*(a-x), 0)+Sum(t^n*((proc (U) options operator, arrow; -I*(-(1/2)*h^2*(diff(diff(U, x), x))/m+piecewise(0 <= x and x <= a, 0, infinity)*U)/h end proc)@@n)(piecewise(0 <= x and x <= a, A*x*(a-x), 0))/factorial(n), n = 1 .. infinity)

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)


Error, (in typetomath) 0 <= x and x <= a: invalid for math mode


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!}}


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);

diff(v(t, s), t)+(1/2)*s^2*(diff(diff(v(t, s), s), s))/sigma^2+(r-q)*s*(diff(v(t, s), s))-r*v(t, s) = 0

v(T, s) = psi(s)

v(t, s) = psi(s)+Sum((t-T)^n*((proc (U) options operator, arrow; -(1/2)*(diff(diff(U, s), s))*s^2/sigma^2+s*(-r+q)*(diff(U, s))+r*U end proc)@@n)(psi(s))/factorial(n), n = 1 .. infinity)

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)


Error, (in symbol/string) only ANSI-C compliant symbols are handled


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!}}


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;


diff(u(x, t), t) = k*(diff(diff(u(x, t), x), x))-u(x, t)*x

u(x, 0) = sin(x)

u(0, t) = 0, u(Pi, t) = 0

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

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


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


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)






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.




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. 



maple does not work at all

it displays this error

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

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? 



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