I'm using variable names that have subscripts, not as a table index but literal i.e. R__1 as a unique variable name.  It seems whenever I make assumptions on variables that have subscripts, when I use them the variables that have subscripts are printed twice:

Can anyone explain why this happens and how to get around it?

Thanks in advance.

alternatingseries.mw
I have a double about this alternating series.
According to maple this series converges:

evalf(sum((-1)^(n+1)*(ln(n)/n+1),n=1..infinity))
                          0.3401310963

However limit ln(n)/n + 1 does not equal to zero, it equals 1. Therefore the series should diverge.

Also while I am on the subject of series and limits, why is limit (-1)^n  as n goes to infinity a range between -1-I and 1 + I.

limit((-1)^(n), n=infinity)
                        -1 - I .. 1 + I

Hello, I am having a bit of difficulty simplifying some calculations in Maple 2019. In short, in order to verify that the tensors that I am trying to use are indeed inverses of each other, I am simply trying to multiply component wise, for example the tensor component e[2,~2] with the tensor component f[~2,2], since they are essentially inverses of each other, i.e. the matrix defining f is actually the inverse of the matrix e, i.e. f=e^(-1), should give back 1 as an answer. Nonetheless, when I attempt to take this simple multiplication Maple does not reduce it, but rather just gives multiplies the terms with no simplification. Is there anything I can do so that Maple may simplify its calculations? I have already tried the "eval" calling sequence but that didn't do the trick, and I fear that when escalating the calculations I will get a bunch of long expressions rather than concise solutions. Thank you for your help in advance,
 

Christoffel_symbols_of_de_Sitter_metric_research.mw

restart;
with(LinearAlgebra);
G := Matrix([[beta1^2, 0, -beta2^2, 0], [0, beta1*(b^2 - beta1^2), 0, beta2*(b^2 + beta2^2)], [beta1^2*cosh(beta1*l), beta1^2*sinh(beta1*l), -beta2^2*cos(beta2*l), -beta2^2*sin(beta2*l)], [beta1*sinh(beta1*l)*(b^2 - beta1^2), beta1*cosh(beta1*l)*(b^2 - beta1^2), -beta2*sin(beta2*l)*(b^2 - beta2^2), beta2*cos(beta2*l)*(b^2 + beta2^2)]]);
NULL;
NULL;
S := Determinant(G);
S := simplify(S);
S1 := S/(beta1^2*beta2^2);
F := Pi*d^2/4;
Q := F*d^2/8;
u := E/(2*(1 + v));
lambda := sqrt(w^2/c^2);
j := v*d*lambda/sqrt(8);
y1 := 1 - j^2 + sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
y2 := 1 - j^2 - sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
b := 2*(1 + v)*(8/(v^2*d^2) - w^2/c^2);
beta1 := sqrt(y1);
beta2 := sqrt(-y2);
S;
d := 24.8;
c := 5100;
v := 0.34;
l := 2000;
E := 2.1*10^5;
p := 7700;
S;
plot(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error

Error, (in plot) incorrect first argument (-HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I)*(HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I+(HFloat(2.918216722364015e-174)+HFloat(7.045198389075166e-174)*I)*(HFloat(1.2899139595562734e220)+HFloat(1.2899139595562734e220)*I+(HFloat(2.345679734289597e162)+HFloat(9.71612358926469e161)*I)*(.3015529528-0.1030372934e-6*w^2)^2)+(HFloat(2.739493386336394e-116)+HFloat(2.739493386336394e-116)*I)*(HFloat(1.5009648027561687e-231)-HFloat(2.757556062608314e294)*I+(-HFloat(5.478986772672788e-116)+HFloat(5.478986772672788e-116)*I)*(.3015529528-0.103 ... HFloat(2.739493386336394e-116)*I)*(.3015529528-0.1030372934e-6*w^2)^4)

w1 := fsolve(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error 

Error, (in fsolve) Digits cannot exceed 38654705646
 

Is it italic when copied and pasted?  Is it bold when copied from maple 8?  I just ahve not been able to work it out.

The only way that I can think of doing it is by multiplying by a tetrad.  Even then it does not work well see my worksheet:  The Dirac Equation in Robertson-Walker spacetime.

 Recently I often drew some graphs in Graph Theory  by Maple. I tried to use DrawGraph, but  I found that evey edge only meets straight line  style in this package.

For example: 

How do I draw some edges with curve syle in graph? like following:

Thanks!

Download funct_misrep.mw

Hi! 

I'm having a weird issue. :( 

DEplot command worked when I initially ran the executed it, but then when I executed the entire worksheet, it didn't plot. Instead I just get this output. 

This is the entire worksheet so far without the output. 

If someone could please help me, I would greatly appreciate it!!!!!

restart;
with(DEtools);

eq1 := diff(y(x), x) = 3*x*y(x);

dsolve(eq1, y(x));

ini1 := y(0) = 3;

dsolve({eq1, ini1}, y(x));

ini2 := y(1) = -3;

dsolve({eq1, ini2}, y(x));

eq2 := y(x)*diff(y(x), x) = -x;

dsolve(eq2, y(x));

dsolve({eq2, ini1}, y(x));

restart;
with(plots);

eq := diff(y(x), x) = 3*x*y(x);

ini := y(0) = 5;


dsolve({eq, ini}, y(x));




sol := rhs(%);

plot(sol, x = -2 .. 2, y = 0 .. 10);
DEplot(eq, y(x), x = -2 .. 2, y = 0 .. 10, [[ini]]);

Hi,

The VectorCalculus package offers a convenient way to compute multivariate integral over a non-square geometry. See help("VectorCalculus/int"). Here is an example taken from this help page:

with(VectorCalculus):

int( x*y, [x,y] = Triangle( <0,0>, <1,0>, <0,1> ) );

The question is: is there a way to draw the area “Triangle( <0,0>, <1,0>, <0,1> )” in order to quickly check that it matches the expected region of integration that one needs?

I am trying to plot the solution of the DE in the interval [0.3,4]

HI

I am using a simple piece of code to generate Lie derivatives, and I am interested in adapting it so that I can use it with vector Fields where that include RootOf expressions. 

LieDer_with_rootof.mw

The above includes an example where it works, and an example where RootOf appears in the vector field and it does not work. 

I seem to be getting false solutions with Maple 2019.2 from solve and cannot figure out why.

Example :

Thus the second reported solution is not a solution after all.

Any ideas are most welcome.

I was trying this in Maple to check Mathematica's result, and got this error. But googling and the link Maple gives lead to nothing.

Any one knows why Maple gives this error message here?

restart;

phi:=Pi;
A := <
          <0, 0, exp(I*k1) + m1, exp(I*k2) + m2>|
          <0, 0, exp(I*phi)*(exp(-I*k2) + m2), exp(-I*k1) + m1>|
          <exp(-I*k1) + m1, exp(-I*phi)*(m2 + exp(I*k2)), 0, 0>|
          <exp(-I*k2) + m2, exp(I*k1) + m1, 0, 0>
     >:
LinearAlgebra:-Eigenvectors(A)

Error, (in LinearAlgebra:-Eigenvectors) multiplicity mismatch

fyi, Mathemtica's result is

ClearAll[k1, m1, m2, k2];
Phi = Pi;
H = {{0, 0, Exp[I k1] + m1, Exp[I k2] + m2}, {0, 0, 
    Exp[I Phi] (Exp[-I k2] + m2), Exp[-I k1] + m1}, {Exp[-I k1] + m1, 
    Exp[-I Phi] (m2 + Exp[I k2]), 0, 0}, {Exp[-I k2] + m2, 
    Exp[I k1] + m1, 0, 0}};
Eigenvectors[H]

I tried tracing in Maple, but so far no useful result:

infolevel[all]:=5;
LinearAlgebra:-Eigenvectors(A)

.
.
.
simplify/size: [1/(2+m1^2+m2^2+2*m1*((1/2)*exp(I*k1)+(1/2)*exp(-I*k1))+2*m2*((1/2)*exp(I*k2)+(1/2)*exp(-I*k2)))^(1/2) exp(-I*k1) exp(-I*k2) exp(I*k1) exp(I*k2) _t[1] _t[2] m1 m2 k1 k2]
simplify/size: [exp(-I*k1) exp(-I*k2) exp(I*k1) exp(I*k2) m1 m2 _t[1] _t[2] k1 k2]
simplify/size: [1/(2+m1^2+m2^2+2*m1*cos(k1)+2*m2*cos(k2))^(1/2) exp(-I*k1) exp(-I*k2) cos(k1) cos(k2) _t[1] _t[2] m1 m2 k1 k2]
simplify/do: applying  commonpow  function to expression
simplify/do: applying  power  function to expression
simplify/do: applying simplify/size function to expression

Error, (in LinearAlgebra:-Eigenvectors) multiplicity mismatch

Maple 2019.2.1 on windows

Help me to solve this problem with pdsolve