cosmicstring

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14 years, 201 days

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These are answers submitted by cosmicstring

There are two unknowns: H(z) and z. There is no clue on how H(z) depends on z. You need either two equations for two unknowns or H(z) itself.

I haven't used the ATLAS package but the free (and extensively used) package grtensorii can do this easily.

http://grtensor.phy.queensu.ca/

It comes with a nice documentation.

I am not sure if integration by parts is applicable here but when you set (not in the Maple format, just for a sketch),

u=exp(btp*s*cos(2*Pi*x/a))

and

dv=exp(-(I*2)*Pi*n*x/a)*dx

Then v=0 for your assumptions. Thus, u*v-int(v,u) is zero.

 

But I need to repeat that I am not sure if this is applicable for your case...

From the 1st one,

y=4+x

Put it into the 2nd one:

x^2+4+x=3

x^2+x+1=0

This one is easy to solve for x. Then use y=4+x for the corresponding y value.

Thank your, it really works for a function but I couldn't manage it for a matrix as a whole.

Let us define a matrix:

M:=Matrix([[a1,a2],[a3,a4]]);

Now is there a shortcut to convert this matrix to

M:=Matrix([[a1(x,y),a2(x,y)],[a3(x,y),a4(x,y)]]);

Thank you but evalDG is not "enough" for many cases. (My mistake, the example was too trivial.)

evalDG(e[1] &wedge e[2] + e[2] &wedge e[1]);

or

evalDG(e[1] &wedge e[1]);

gives
                              0 dx ^ dy

but I need just zero.
 

I tried in many ways after your suggestions and understood that it is impossible to see a solution of the form,

f(u,v)=_C1*u*Heaviside(u)+_C2*v*Heaviside(v)+_C3*u^2*v*Heaviside(u)*Heaviside(v)

or something similar to this.

 

Thank you all!

Let us say that I have the following equation:

eqn:=diff(f(u,v),u,v)=0;

and I want to find the solution f(u,v)=u*Heaviside(u) or f(u,v)=v*Heaviside(v).

When I pdsolve this equation by

pdsolve(eqn);

it gives

f(u,v) = _F2(u)+_F1(v)

which is correct but not the solution that I am looking for. I have no idea about the form of the function I need, so I cannot use pdetest for trial and denial. Some HINT for pdsolve may solve the problem as Mr. Richard suggested but I could not find how to write it even for "HINT = any algebraic expression".

Mathematically, I want the solution of the form

f(u*Heaviside(u),v*Heaviside(v)), not f(u,v).

 

 

I could not open your worksheet but these lines may be useful:

 

M:=Matrix([[f(x,y,t),g(x,y,t)],[h(x,y,t),k(x,y,t)]]);

map(diff,M,x);

acer's answer was the key for me because I wanted to eliminate the whole x*Dirac(x)'s in the expression but I have stated my question in the wrong way as I have not thought such a simple answer. But my expression is too long and Joe's answer unlocked the other door for me.

Anyway, Maple is simplifying for more than two hours and I think I will not succeed having a small expression...

Thank you! This really works! Bu now I have a second question:

The function that I have to simplify is very long and it contains many of these u*Dirac(u) type components. So, can I tell Maple to first simplify those ones and then start simplifying the ordinary functions?

I also call the code in Maple by

read"C:/example/mycode.mws"

How should command change in Linux if the directory is home/user/example/mycode.mws ?

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