## why plus zero different from not plus zero?...

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);

## Problem in integrating an expression...

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.

## Christoffel symbols for a metric with a vanishing ...

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.

## Problem with Physics:-Define...

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

with(Physics):
+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]));

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?

## Immediate evaluation and dealyed evaluation (Mathe...

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!

## Consistent statistical model...

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)

## Use output for function definition...

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

## dslove trigger time with rhs(SOL[1](last)...

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

 >
 >
 >
 >
 (1)
 >
 (2)
 >

## How many roots are there in this equation?...

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?

## replacing expression with function...

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.

 >
 >
 >
 (1)
 >
 >
 >
 (2)
 >
 >
 (3)
 >
 (4)
 >
 (5)
 >
 >
 (6)
 >
 >
 >
 >
 (7)
 >
 >
 >
 >
 >

## How can I solve an ODE numerically, when one of th...

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)= tt as well as other functions, intervals and initial condition only for the sake of illustration of the problem):

 >
 >
 >
 >
 >

Max

## is it possible to trim the surface along the inter...

Hello!
I'm a beginner in Maple. My question is: is it possible to trim the surface along the intersection line in Maple? There is a problem - inclined surfaces are constructed along the contour of the triangle, they intersect. Is it possible to get a pyramid along the intersection lines?
Thank you!trimming_surfaces.mwtrimming_surfaces.mw

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

 >
 >
 >
 >
 >
 >
 >
 >
 (1)

 >
 >
 >
 >
 >
 >
 >
 >
 >
 (2)
 >
 >
 >
 >
 >
 >
 >
 >
 (3)
 >

 >
 >
 >
 >

I really love this feature of course because it just allows you to learn so much about function properties via comparative learning processes, but I would also love to have the ability to:

1) Add elements to the list that is stored under known_functions: