verify(2*cos(phi)^2-1, cos(2*phi), equal); returns FAIL even though is a trig identify. Any ideas why?
 

Maple currently can't integrate things like sin(x)^n or cos(x)^n. These have antiderivative in terms of  hypergeometric functions.

Is there a technical reason why Maple at version 18 still can't integrate these? Will it be able to in next version?

int(cos(x)^k, x) 
int(sin(x)^k, x) 

fyi, These are the antiderivatives

Same problem for tan(x)^n....  I am asking because Maple is able to solve many ODE's but some results contains unevaluated integrals such as the above. 

When making this call to dsolve

restart;
ode:=diff(y(x),x)=1:
stopat(dsolve);
dsolve(ode,y(x));

Then in the debugger, I see that dsolve signature is

dsolve := proc(ODEs::{anything} := NULL, 
                {atomizenames::truefalse := true, build::truefalse := false, type::name := 'none'})

When typing print(ODEs) inside the debugger, it gives "diff(y(x),x)=1" which is correct.

But where is the second argument I passed to dsolve in the above call, which is "y(x)" gone?  I also do print(_nparams) inside the debugger and Maple returns 1 and not 2.

I expected to see 2 since I passed in two arguments to dsolve.

dsolve actually works without passing y(x), as follows

dsolve(ode);

And it seems Maple figure inside what is the dependent variable.

But my question is, is the second argument being thrown away before calling dsolve? If not, why it does not show in the debugger?   Is there some other pre-processing being done between the time the user calls dsolve() and the time the debugger is called?

i have two ode equations, when try to solve, i face this error
Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system
any comment or help to solve this? ( or any simplifying comments to solve) . thnx in advance

 

Download zzv.mw

Here is a simple procedure that works fine if entered using 1D Maple input
> Q:=proc(x)
sin(x)
end proc;
but if you use 2D math input
> q:=proc(x)
sin(x);

  end proc;

Error, unterminated procedure
    Typesetting:-mambiguous(qAssignTypesetting:-mambiguous(

      procApplyFunction(x) sinApplyFunction(x),

      Typesetting:-merror("unterminated procedure")))
Error, unable to parse
    Typesetting:-mambiguous(  Typesetting:-mambiguous(end,

      Typesetting:-merror("unable to parse")) procsemi)

Ouch! But to confuse things further the following procedures may be entered using 2D math and work fine:
>H := proc (x) x^2*sin(x) end proc;
>K := proc (x) sin(x^2) end proc;
Doesn't make any sense to me. Perhaps 2D math is not ready for prime time?

 

So I have got the following integral:

around the square with corners 2, 2i, -2, -2i oriented counter-clockwise.

Do I need to tell Maple that z is complex? Do I need to manually parametrize z? Is Maple aware of Cauchy's theorem?

What is the quickest way of evaluating this sort of integrals.

ode_problem.mw Can someone please look at this? I am having a problem with the ordinary differential equations. 

Hello there,

I'm pretty new to MAPLE so this may probably an "easy" mistake, but I don't know what's the problem anyway...

I'd like to find a solution to a system of four equations with four unknowns:

fsolve({(T[1]-T[0])/(10000-T[1]+T[0]) = -2.000000000, (T[2]-T[0])/(20000-T[2]+T[0]) = 0, (T[3]-T[0])/(50000-T[3]+T[0]) = 50, .1*T[0]+.3*T[1]+.55*T[2]+0.5e-1*T[3]-5000 = 0}, {T[0], T[1], T[2], T[3]})

Problem: Instead of providing the single solutions, MAPLE is simply just rewriting the fsolve-statement and does not solve. There is no error-message.

Does anybody know, what the problem is here? Is there no solution after all?

How to let sqrt(5*x+5+y) become sqrt(5*(x+1)+y) automatically?

Hi!

I have a rather long Maple code and want it to be executed multiple times with a parameter changed each time.

Surely this can be done with the loop structure, but it seems the whole loop structure must be contained into one single execution group, which makes it to be a little inconvenient, since the code is too long.

So is there any alternative way to realize this utility?

Best regard and thanks!

I'm attempting to find the eigenvectors of a matrix without using the eigenvector function.

The matrix in question is a covariance matrix:

XCov:=Matrix([[4048/5, -817/5, -122/5], [-817/5, 921/10, -1999/10], [-122/5, -1999/10, 8341/10]]);

I've already found the eigenvalues by solving for lambda:

 det := Determinant(XCov-lambda*IdentityMatrix(3));
  lambda := solve(det=0.0, lambda);

(Yes I'm reusing the eigenvalue variable for the set of eigenvalues once they've been found😏)

Anyway, I've now set up the first eigenvector I want to find as:
e1 := Vector([e11,e12,e13]);

Now, the equation to find this first eigenvector is XCov . e1 = lambda[1] . e1
I first tried putting whats on the left in a variable called eigscale(what the vector is translated to by the matrix):

eigscale := Multiply(XCov,e1);
Which returns a vector:
eigscale = [(4048/5)*e11-(817/5)*e12-(122/5)*e13,
                  -(817/5)*e11+(921/10)*e12-(1999/10)*e13,
                  -(122/5)*e11-(1999/10)*e12+(8341/10)*e13]

Each component of this vector must equate to the corresponding component in the right vector:

lambda[1]*e1 = [7.943520930*e11, 7.943520930*e12, 7.943520930*e13]

At first I tried setting these vectors equal to each other and using a solve but of course it didnt like the equations being in a vector format. So I then seperated out each equation and gave the solve function a system of equations as it expects:

solve(eigscale[1] = lambda[1]*e1[1], eigscale[2] = lambda[1]*e1[2], eigscale[3] = lambda[1]*e1[3], [e11,e12,e13]);

But again, solve fails to solve them. The reason this time(I believe) is because it can't find an exact value for e11, e12 & e13.
When solving for an eigenvector we get
e11 = e11,
e12 = Ae11,
e13 = Be11 + Ce12

I was wondering if there was a way to do a partial solve to find the components in terms of each other?

Failing that, I'm aware I can do it manually through row operations but I believe that would require changing the format so that each equation is a component of a single vector:
eigsolve := Vector([eigscale[1] = lambda[1]*e1[1], eigscale[2] = lambda[1]*e1[2], eigscale[3] = lambda[1]*e1[3]]);

Since row operations cannot be performed on a equation of vectors (again, I believe).

Help appreciated!

Hello Everyone,

I have been working on a multi variable expression. I would like to have the intervals where the function is monotonically increasing. I am trying to study any available method for multivariable expressions.

I came across various papers and sites which are explicitly mentioned single variable equations. finding out the critical points and studying the sign of the first derivative. Same cannot be applied for the multi variable expression.

 https://www.math24.net/monotonic-functions/

above link explain for single variable functions. I would be grateful if someone could explain me a method or idea  which helps me out in solving for multivariable functions

Thanks a lot in advance

Hi,

I try to define the action of projectors of two discrete basis onto a general state. This works as expected when I define the projector by myself. However, when using the "Projector" command, I get a not fully simplified result; see below. It seems like there is a confusion with dot/tensor product.  Can somoeone help?

Best,

Henrik

Download projector_2d_space.mw

Two lines that look the same, produce different results. The first lines gives an error message, but the next line that looks the same, does not.

copying and pasting both lines in Notepad reveals the difference:

Determinant*(R1 . B+R2 . B+R3 . B+R4 . A)

Determinant(R1 . B+R2 . B+R3 . B+R4 . A)

It seems that there is a hidden character (the asterisk) in the first line that produces the error.

In the worksheet itself you cannot see the asterisk, but using the arrow keys you can notice that there is another character.

It's hard to debug your code if there are hidden characters.

Download weird.mw

If I have an expression like this

f:=ln((1-x)^2*(x+1)^2/((-I*x-I+sqrt(-x^2+1))^2*(I*x+I+sqrt(-x^2+1))^2))

maple has trouble to simplify the argument.

In particular is it possible to apply expand() only to the denominator?

This is meant in general, so if I have many terms with expressions like this (possibly of products with other functions in each term), I want this simplification to be done termwise for the arguments of the functions.

Expanding the fraction doesn't work as in frontend(expand, [f]).