Maple evaluates

Int(ln(1+x)/(1+x^2),x=0..1);

as

1/2*I*dilog(1/2+1/2*I)-1/2*I*dilog(1/2-1/2*I)+1/4*Pi*ln(2)-Catalan

It would be nice if Maple could simplify this to 1/8*Pi*ln(2). If you evalf the integral and use "identify" then Maple does return 1/8*Pi*ln(2).

MMa directly returns 1/8*Pi*ln(2), which seems preferable.

Hello everyone.

I have a vector field in 2d-cartesian coordinates which I would like to convert to a "normal" function, that is f(x, y) where when you put x and y in, you get the magnitude of the vector at that point.

Example vector field:

This one is very hard to handle by hand which is why I want to use Maple for it.

I tried VectorCalculus[Norm] but it gave me this:

hello, I put in the code:

> with(plots), with(ColorTools), with(LinearAlgebra), with(RandomTools), with(ExcelTools);
> A := `<|>`(`<,>`(1, 2, 0, 2, 3, 4, 3, 4, 7, 9, 5, 3, 4, 6, 7, 8, 3), `<,>`(0, 4, 7, 2, 2, 2, 4, 5, 6.5, 7, 5, 3, 2, 5, 9, 0, 1), `<,>`(1, 5, 2, 0, 4, 1, 2, 3, 4.3, 7, 8, 5, 3, 2, 9, 6, 4)); J := convert(Import("testB1.xlsx", "Cartesian", "E2:G18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> B := matrix([[1], [.2], [.1], [.8], [.5], [.6], [.8], [.764], [.234], [0.4e-1], [.89], [.36], [.687], [.627], [.689], [.328], [.139]]); H := convert(Import("test.xlsx", "Cartesian", "D2:D18"), matrix);
Error, (in convert/matrix) expecting array, rtable or list
> C := [seq(Color([H[i, 1], 0, 0]), i = 1 .. RowDimension(A))];

 

And i get the error message everytime I try import m data list and I dont understand why. Any help would be appreciated. Thank you

 

Jennifer

restart;
eq:=diff(y(x),x) - y(x)^2 - x*y(x) - x + 1;
r:=dsolve(eq,y(x));
latex(r);

Gives an error "(in fprintf) string expected for string format". The problem seems when the math contains "erf"? Both examples below fail with result that contains this.

Maple 18, on windows 7.

Another example:

restart;
eq:=diff(y(x),x) + a*y(x)*(y(x)-x) - 1;
r:=dsolve(eq,y(x));
latex(r);

Another example, which seems to fail for different reason

restart;
eq:=diff(y(x),x) + a*x*y(x)^3+b*y(x)^2;
r:=dsolve(eq,y(x));
latex(r);

I've been using a maple package (written by another author) on earlier versions of Maple.  Recently I have been trying to rewrite it so it's a bit more Maple 16+ friendly (since I've read that Maple is not forward-compatible). However, I have been experiencing similar strange behavior in both the original and my current version: 

After saving the module to my personal library, I load with(MyPackage). Most functions work fine (all but a handful out of dozens).  However, some functions won't be recognized (e.g., Coproduct(...) will return itself Coproduct(...)).  

HOWEVER, when I execute the code in the module in its own Maple worksheet, all functions are recognized and work perfectly.  I look at the difference in the code between the functions that work upon loading the package (using with(MyPackage) command in a separate sheet) and those that don't, and there is no difference.

I'm assuming I'll just have to cut and paste the hundreds of lines of code for my package into each sheet I'd like to use it in, since I haven't been able to find others experience this problem in the knowledge base.  I'm hoping someone will be able to help out, however.

Hi,

Is it possible to solve linear matrix inequality in Maple?
For example, using Matlab and yalmip we can easily
solve Lyapunov equation
  
    A'P + P * A <0, P> 0

Is it possible to solve this equation in the Maple?


Regards,

 

Is it possible to solve piecewise differential equations directly instead of separating the pieces and solving them separately.

like for example if i have a two dimensional function f(t,x) whose dynamics is as follows:

dynamics:= piecewise((t,x) in D1, pde1, pde2); where D1 is some region in (t,x)-plane

now is it possible to solve this system with one pde call numerically?

pde(dynamics, boundary conditions, numeric); doesnot work

Hi,

With Maplets, it is possible to create popup windows to tell or ask the user something, but only when it is appropriate. That is, it is not there all the time. A particular usage would be to give the user a facilitating question when they have incorrect entries.

Is that possible in some way with Möbius apps also? Or does one have to always keep a blank TextArea available, just a blank space if invisible perhaps but using up space in the presentation nonetheless, to give the student the information?

Hi i have two questions about paths in graph package: 1. suppose we have: path1=[1,3,5,7,9] path2=[1,2,3,6,7,8,9] if we want to create a graph that it's edges are edges of path1 and edges of path2,how can we do this? edge set of our graph should be {[1,3],[3,5],[5,7],[7,9],[1,2],[2,3],[3,6],[6,7],[7,8],[8,9]} 2. suppose p is an arbitrary path on a given weighted graph G how can i calculate weight of p (that is sum of it's edges weights) in maple ? thanks very much for your help

Hi,

RTABLE(151446624,MATRIX([[tf[1,1] = 24110714285.0000/(1000000000000*s+1071534859*218^(1/2))], [tf[2,1] = .843883770817266e20*218^(1/2)/(2500000000000000000000000*s^2+4870187206000000000000*218^(1/2)*s+487482532797170793867)], [tf[1,2] = .841458646091250e19*218^(1/2)/(125000000000000000000000*s^2+350952468875000000000*218^(1/2)*s+50692506828944068713)], [tf[2,2] = 87390625000.0000/(5000000000000*s+3705223967*218^(1/2))]]),Vector[column])

 

How can I read the individual elements tf[1,1], tf[2,1], tf[2,1], tf[2,2] form this RTABLE?

Regards,

Can someone please help me to find first 5 coplex valued roots of the followind expression:

Frequency_Equation := -(2.220315292*10^21*I)*csgn(omega)*omega^4*sin(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.354665581*10^22*csgn(omega)*omega^3*sin(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.354665581*10^22*sinh(1.236117731*(omega^2)^(1/4))*csgn(omega)*omega^3*cos(1.236117731*(omega^2)^(1/4))-6.415296703*10^25*(omega^2)^(3/4)*cos(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))-2.177438228*10^22*cosh(1.236117731*(omega^2)^(1/4))*(omega^2)^(3/4)*omega^2*cos(1.236117731*(omega^2)^(1/4))-5.946035576*10^21*omega^2*(omega^2)^(3/4)-6.415296702*10^25*(omega^2)^(3/4)-(3.560760000*10^24*I)*sinh(1.236117731*(omega^2)^(1/4))*omega^3*cos(1.236117731*(omega^2)^(1/4))+(3.560760000*10^24*I)*cosh(1.236117731*(omega^2)^(1/4))*omega^3*sin(1.236117731*(omega^2)^(1/4))-(2.613877239*10^21*I)*cosh(1.236117731*(omega^2)^(1/4))*(omega^2)^(3/4)*omega^3*cos(1.236117731*(omega^2)^(1/4))-(6.049258752*10^24*I)*(omega^2)^(3/4)*omega-1.907153069*10^25*sinh(1.236117731*(omega^2)^(1/4))*omega^2*sin(1.236117731*(omega^2)^(1/4))*(omega^2)^(1/4)-(2.220315292*10^21*I)*sinh(1.236117731*(omega^2)^(1/4))*csgn(omega)*omega^4*cos(1.236117731*(omega^2)^(1/4))-(6.049258753*10^24*I)*(omega^2)^(3/4)*cos(1.236117731*(omega^2)^(1/4))*cosh(1.236117731*(omega^2)^(1/4))*omega-3.500000000*10^21*cosh(1.236117731*(omega^2)^(1/4))*omega^4*sin(1.236117731*(omega^2)^(1/4))+3.500000000*10^21*sinh(1.236117731*(omega^2)^(1/4))*omega^4*cos(1.236117731*(omega^2)^(1/4))-2.156220000*10^25*sinh(1.236117731*(omega^2)^(1/4))*omega^2*cos(1.236117731*(omega^2)^(1/4))+2.156220000*10^25*cosh(1.236117731*(omega^2)^(1/4))*omega^2*sin(1.236117731*(omega^2)^(1/4));

AOA. I want to plot the graph of the following function 

 

A new generalized complex representation of Euler gamma function in terms of Dirac delta function, which is

GAMMA(s) = 2*Pi*(sum((-1)^n*Dirac(s+n)/factorial(n), n = 0 .. infinity))

where*s = sigma+i*tau

for differenet values of parameters

 

i have 2 questions:

Question 1. suppose we have generated a random weighted graph with 100 vertices and 2300 edges and found shortest path frome node 1 to node 100 using function ShortestPath(G,1,100). this function returns a path like [1 3 8 2 9 100] but don't get us value of shortest path!

in other words if weights are costs of travelling on edges,we want to find minimum cost of travelling from node 1 to node 100.

how can i find value of shortest path (minimum weight/cost) ?

Question 2. i want to create a sub graph of G by removing the edge that has maximum weight on shortest path found in Question 1. how can i find such edge and how to create such sub graph?

thanks

The answer should be around 15.7, i.e., function h is maximized at around x=15.7, I don't know why my computer/maple is having a hard time with it.

f := proc (a, b, k) options operator, arrow; (sum(exp(-x)*x^m/(m!), m = a .. b))^k end proc;

h := f(0,0,82)*f(1,3,49)*f(4,6,47)*f(7,10,47)*f(11,15,57)*f(16,20,40)*f(21,25,38)*f(26,35,52)*(1-f(0,35,1))^91;

fsolve(diff(h,x),x);

 

thanks in advance!