## how to get nonempty plot?...

I would like to plot h over the real interval from 0 to 2*Pi, but

produces an empty plot...  How can I plot successfully?

## Declare a multilinear operator as real valued...

I'm trying to define some multilinear forms to study differential geometry. What I need is only symbolic. My intention is symplify computations involving multilinear forms.

For example, to create an symbolic inner product "g" I used the command "define" like in this post:

http://www.mapleprimes.com/questions/203480-Define-And-Use-Abstract-Linear-Operator

So I tipped:

define(g, orderless, multilinear);

My doubt is: how can I declare that g(x,y) is always scalar?

With it I would simplify things like g(g(z,w)*x,y) = g(z,w)*g(x,y)

In my case, specifically, I type:

v:=(X,Y,Z)->g(Y,Z)*X-g(X,Z)*Y;

r:=(X,Y,Z,W)->g(v(X,Y,Z),W)-g(Y,T)*g(v(X,T,Z),W)+g(X,T)*g(v(Y,T,Z),W);

expand(r(X,Y,Z,W));

and the result is:

g(W,g(Y,Z)*X)-g(W,g(X,Z)*Y)-g(T,Y)*g(W,g(T,Z)*X)+g(T,Y)*g(W,g(X,Z)*T)+g(T,X)*g(W,g(T,Z)*Y)-g(T,X)*g(W,g(Y,Z)*T)

But I would enjoy that it were:

g(Y,Z)*g(W,X)-g(X,Z)*g(W,Y)-g(T,Z)*g(T,Y)*g(W,X)+g(X,Z)*g(T,Y)*g(W,T)+g(T,Z)*g(T,X)*g(W,Y)-g(Y,Z)*g(T,X)*g(W,T)

Is there a way to declare that g(x,y) is always scalar?

Thanks.

## Part Real of complex expression...

Hi, i try the part of Real of the complex expression:

restart;
w := A*exp(-alfa(1+I)*y)+B*exp((1+i)*y);
A exp(-alfa(1 + I) y) + B exp((1 + i) y)
u := Re(w);
Re(A exp(-alfa(1 + I) y) + B exp((1 + i) y))

But does not work.

Regards.

## Intersection of real intervals...

Let A and B two real closed intervals.
I define b(x) as B+x for any real x ; more precisely, if B=[B1, B2], b(x) = [B1+x, B2+x]

I want to build a function f(x) such that :

1. if  A and b(x) do not overlap then f(x) = 0
2. otherwise f(x) is some expression of the covering length

For example : if A=[0, 2] and B=[-2,-1], then

1. f(x) = 0 if  -1+x < 0 or -2+x > 2
2. otherwise f(x) = L   where L is the measure of the intersection of A and b(x)

I coded a few variants using piecewise or Heaviside functions.
In some sense I have already answered my own question ... but no one is neither elegant nor concise.

I wonder if there exist a Maple function that returns the measure of the intersection of two real intervals (when they overlap) and 0 otherwise ?

## How can I get result of real part?...

Hi all!

as shown below, how can get a result without 'R':

p_com(z,t):=Re(exp(I*omega*t-I*k*(lambda[r]+I*lambda[i])*z)) assuming omega::real,t::real,k::real,lambda[r]::real,lambda[i]::real,z::real

Thanks very much!

## Certain functions are partly plotted...

why the the software can't plot the function like x^(4/3)*sin(1/x) or x^(1/3)

it could only plot where x>0,but the value is does exist where x<0.

## Warning when solving equation...

Hi all,

I tried to find the real solution of the unlinear integral equation:

exp(-h^2/T)*(Int(exp(-x^2/T)*BesselI(0, h*x/T)*x, x = 0 .. 1))/T

but I got the warning and an complex solution:

solve(subs(T = 1, eq)-.99 = 0, h)

Warning, solutions may have been lost

-1.232350242*10^(-32)-1.130417828*I

Can anyone help me to find a real solution for this issue (if possible)...?

I would like to thank you in advance.

In the following problem though b and c are same (except the way denominator 2 is hanfled), command ' a-b ' readily answers zero, but a-c not so. Why? Only on condition of assumption real it gives zero!

 (1)

 (2)

 (3)

Why the answer is not given as zero?

What difference therms b and c make for Maple? Are they not same?

Ramakrishnan V

rukmini_ramki@hotmail.com

## Set of complexes ...

hi all

i have a set of complex numerics, so:

1- i want the numeric with least valence(potency) in imagin particle,

2- i want print the real particle of this numeric.

for example:

A:= .5464691235-.4473247264*I, -.4563184747+1.*10^(-14)*I, .5464691235+.4473247264*I

i want print: -.4563184747

plz help

## Obtaining only real numbers...

If for example I type :

It gives out this :

I want dsolve to know I'm using real numbers so it gives out something like :

I tried some assumptions and stuff like assume(a,real), but I didn't manage to figure it out.

If that matters, I'm using Maple 18 student.

EDIT : I know dsolve is not necessary for this particular example, but I want to know if it's possible with dsolve or maybe an other tool that can handle ODE.

## Real part of a matrix...

I have this matrix

and I want a matrix which components are de real parte of the components of A. I have tried this:

but it doesn't work.

What is wrong?

Thank you so much.

## Assume real matrix...

Hello,

I would like to assume a matrix to have only real components.

I have seen that the function assume has some features to assume properties for matrix. But, I didn't find the one that I want : "assume a matrix to have only real components".

This assumation should allow me to suppress this kind of choice in my code :

if A::{complexcons, undefined} then
evalf(1/A);
elif A::rtable and ArrayTools:-NumElems(A) = 1 then
Vector([evalf(1/A(1))]);
else
evalf(LinearAlgebra:-MatrixInverse(A));
end if;

Do you have some ideas ?

P.S: The matrix should be also a square matrix. So, the first code line will probably be : assume(a, 'SquareMatrix')

Thanks a lot for your help.

consider quadratic equation ax^2+bx+c =0 :
the coefficients vary between -1 and +1 . just like this :
-1<a<+1 , -1<b<+1 , -1<c<+1 ;
how can some one proove that this equation should have real answers ?! can anybody help ? thanks in advance.

## Can maple solve some tricky equation?...

Can I use Maple to solve equation like  for a,b,c?

a,b,c are real numbers and I need to solve it in real domain.