4 years, 53 days

## Dot product of a free vector in cartesia...

Maple

When I create a rooted vector

```v1:=RootedVector(root=[1,Pi/4,0],[0,0,1],spherical[r,theta,phi])
```

and a free vector

`v2:=Vector([0,2,1],cartesian[x,y,z])`

and dot product them

`v1.v2`

it gives me 2.

But if I change v1 to

`v1:=RootedVector(root=[1,Pi/6,0],[0,0,1],spherical[r,theta,phi])`

the product of v1.v2 gives me an error

"..cannot combine two rooted vectors with different points of origin"

Can anyone explain me the problem?

Here is what I understand:

In spherical coordinates the unit vector e_r, e_th, e_ph are functions of theta and phi. So when I call root=[1,Pi/4,0] that means r=1, theta=Pi/4 and phi=0. This uniquely defines the unit vectors in spherical coordinates and r places the vector away in the e_r direction. The [0,0,1] then attaches a vector to the point r=1, theta=Pi/4 and phi=0  with only 1 unit along the e_ph direction.

What I don't understand is the concept of origin with the free vector and the rooted vector. How changing the theta from Pi/4 to Pi/6 makes the origin "different"?

Edit: This is part of the VectorCalculus pacakge.

## Solving inequality involving fatorials ...

Maple 2020

Hello,

I tried to solve an inequality involving factorials using solve, but I failed. The code is

```solve(1/(n+1)!<0.0001,n)
```

n should be 7.

Maple returns me "Warning, solutions may have been lost" message.

How can I solve an inequality like this using solve?

I worked around this with a for loop testing the value of the expression for every increasing value of n against the criteria. Is there a "magical" keyword that will help with solve?

## Assumptions in pdsolve...

Maple 2020

Hello,

How can I use assmptions in partial differential equations?

For example consider the following differential equation

```pde:=diff(u(x,t),t)+alpha*diff(u(x,t),x)=0
sol:=pdsolve(pde,build) assuming alpha=0
```

This gives me the same solution if alpha!=0

I also tried this

```assume(alpha=0)
pde:=diff(u(x,t),t)+alpha*diff(u(x,t),x)=0
sol=pdsolve(pde,build)
```

I again got the same result as if alpha!=0. Except this time there was a tilde on the right side of alpha (to my knowledge that means there are assumptions on alpha)

How do you apply assumptions in PDEs?

## Why integration of dirac delta with argu...

Maple 2020

Hello,

I am trying to calculate an integral involving dirac delta as given below

```int(Dirac(sin(x)),x=-3/2*Pi..3/2*Pi)
```

However, Maple returns the integral unevaluated as

How can I get it evaluated? the result should be 3 here.