I can calculate real number eigenvector with QR algorithm from rotation matrix

but this real number is just magnitude of complex number

what is the rotation matrix for calculating complex number?

what algorithm do maple use to calculate fraction eigenvector?

are complex decimal and complex fraction eigenvectors are two different algorithm?

Hello everyone!

how to solve system of 5 equations like as in attachment, but much more faster?

I tried to do this on my computer (CPU 8 Core 3,4 GHz, RAM DDR3 2x8 GB, SSD) but after 12 hour my computer doesn't respond.

What I can do if I don't have a supercomputer?

Forum.mw

with(LinearAlgebra):
A := Matrix([[1,2,3],[4,5,6],[7,8,9]]);
v, e := Eigenvectors(A):
evalf(e);
A := Matrix([[1,2,3+0*0.1],[4,5,6+0*0.1],[7,8,9+0*0.1]]);
v, e := Eigenvectors(A):
evalf(e);

Hi!

Hoped everything is fine. I want to integrate the following expression under the different conditions of discriments Delta. 

int(1/(a[3]*(u(eta)^3+d[2]*u(eta)^2+d[1]*u(eta)+d[0])), eta);

when Delta = 0;Delta > 0 and Delta < 0.

where discriments Delta = -27*(2*(d[2])^3/27+d[0]-d[1]*d[2]/3)^2-4*(d[1]-(d[2])^2/3)^3;

I am waiting your positive respone.

@acer @Carl Love @Kitonum @Preben Alsholm

Hello, I have a problem which might be very basic but I can't get over it.

I need to compute Christoffel symbols with the "Christoffel" command of the "Tensor" package. However, I noticed that whenever I give maple a metric with a vanishing diagonal element, I get the following error:

Error, (in DifferentialGeometry:-Tensor:-InverseMetric) expected 1st argument to be a metric tensor. Received: _DG([["tensor", M, [["cov_bas", "cov_bas"], []]], [`...`]])

For example, I tried with a very simple 2D case, giving coordinates (t,x) and a metric ds²=f(x)dtdx+h(x)dx²
for which I can compute by hand Christoffel symbols without any problem. The problem really seems to be about the missing diagonal element since if I add it, everything works fine.

By the way, I also noticed that if I apply the "InverseMetric" command I get exactly the same error, even though the matrix is invertible (except possibly at zeros of the functions f and h).

I will be grateful for any suggestion.

Consider the following expression (omega being the socalled minimal spin connection in the vierbein formalism of general relativity):

with(Physics):
with(Tetrads):
omegaDef := omega[mu,c,d] = 1/2*(
   +e_[~rho,c]*(d_[mu](e_[rho,d]) - d_[rho](e_[mu,d]))
   -e_[~rho,d]*(d_[mu](e_[rho,c]) - d_[rho](e_[mu,c]))
)
-1/2*e_[~a,mu]*e_[~rho,c]*e_[~sigma,d]*(d_[rho](e_[sigma,a]) - d_[sigma](e_[rho,a]));
Define(omegaDef):

The Define command raises "Error, (in Physics:-Define) numeric exception: division by zero" in Schwarschild spacetime (loaded with g_[sc]), but not, say, in Tolman spacetime (loaded with g_[tolman]). Furthermore, if either the first two terms, or the last term, are/is removed in omega, then no error is raised in Schwarzschild spacetime. What is going on?

I need to evaluate a variable inside the function definition in the moment it is defined and not every time it is called. Is there a way around?

a:=3;
f := x-> a*x;
f(t);

a:=4;
f(t);

I want the function "f" to be 3*x even if "a" is modified after the declaration. In Mathematica I am used to the so called immediate assignmet(=) and delayed assignment(:=) for which I cannot find an equivalent command in Maple. 

Any help is appreciated!

Hi

For the data presented below, assuming a linear model yields to observe the great amounts of standard errors.

Is there a way (an appropriate command) to find the best statistical model?

Y := `<,>`(.2, .2, .2, .2, .2, .3, .3, .3, .3, .3, .3, .35, .35, .35, .35, .35, .35);

X := `<,>`(2, 2.2, 2.4, 2.6, 2.8, 2, 2.2, 2.4, 2.6, 2.8, 3, 2, 2.2, 2.4, 2.6, 2.8, 3);

Z := `<,>`(15, 33.7, 62.8, 188, 394, 5.47, 5.82, 6.21, 8.3, 11.5, 24.1, .372, .485, .675, 1.11, 1.27, 1.35);

Statistics:-Fit(add(add(a[k, n-k]*x^k*y^(n-k), k = 0 .. n), n = 0 .. 2), `<|>`(X, Y), Z, [x, y], summarize = embed)

I want the output from a line to be used for the definition of a function, but it doesn't work. What am I missing?

x^2;
f := X -> eval(%, x=X);
f(t);

Thank you, Ale

I want to fetch the trigger time.
I use rhs function.
 

Download RHS_TEST.mw

I want to find all complex numbers such that 
abs(z)*(z-4-I)+2*I = (5-I)*z.
I tried solve(abs(z)*(z-4-I)+2*I = (5-I)*z, z)
and got the answer is z = -1.
This is a question in a test with multiple choice. The key of question is three numbers.

Is my commant wrong? Where is wrong?

If I have an expression which contains an unknown function f(t) e.g.

ex:=1+exp(f(t))*f(t+1)+f(t/2)

how do I replace it with some defined function F(t)?

Do I need to work with ::anything, i.e. something like

subs(f(t::anything)=F(t::anything),ex)

?

However this doesn't work.

Download Rindler_simulation_v2.mw

Dear Maple primes,

Could you, please, help me with numerical solution of an ODE?

The ODE looks like this

dz/dx = f₁(x,z) + f₂(z)

where f₁(x,z) is some simple function of x and z (that does not create any problem), but f₂(z) is given as

f₂(z) = int(f₃(t), t = z₁..z₂)

The problem appears, when the integral cannot be solved analytically.

Below is an example of the problem (here I chose the function f₃(t)= t^t as well as other functions, intervals and initial condition only for the sake of illustration of the problem):

Download z-for_primes_dsolve.mw

Thank you in advance!

Max