## Feature #13208

### Vector.zero(n) and vector.zero?

**Description**

Found that I need this recently, and class `Matrix`

has these two function while `Vector`

not.

So I add two function based on `Matrix`

counterpart and also add test.

Usage

```
require 'matrix'
v = Vector.zero(3) # => Vector[0, 0, 0]
v.zero? # => true
w = Vector[1, 0, 0]
w.zero? # => false
```

**Files**

### Associated revisions

- lib/matrix.rb: Add Vector.zero and Vector#zero? Patch by Chia-sheng Chen [#13208]

- lib/matrix.rb: Add Vector.zero and Vector#zero? Patch by Chia-sheng Chen [#13208]

- lib/matrix.rb: Add Vector.zero and Vector#zero? Patch by Chia-sheng Chen [#13208]

### History

#### Updated by shevegen (Robert A. Heiler) over 2 years ago

I think the method is fine but of course that is just my own opinion,

the core team and matz will decide that.

One hopefully small request though:

- Do you think you could make the description for the method a bit more explicit? Right now the documentation to it states only:

"Return a zero vector."

Perhaps this is obvious to others but I am not entirely sure

what a zero vector per se is, although of course the example is

explicit enough to infer from it (I assume a zero vector is one that

contains only 0 as its members but from the documentation alone,

without the example, I am not sure everyone may be able to infer

this completely correctly so.)

#### Updated by marcandre (Marc-Andre Lafortune) over 2 years ago

**Assignee**set to*marcandre (Marc-Andre Lafortune)*

Looks good.

I think the short description is probably good enough. The example makes it clear if someone has doubts...

I'm travelling, will commit in a few days.

#### Updated by marcandre (Marc-Andre Lafortune) over 2 years ago

Thanks for the patch.

Committed.

PS: I allowed `Vector.zero(0)`

.

#### Updated by stomar (Marcus Stollsteimer) over 2 years ago

Just curious:

```
Vector.zero(0).zero? # => true or false?
```

Not sure what I would expect in this case.

#### Updated by duerst (Martin DÃ¼rst) over 2 years ago

stomar (Marcus Stollsteimer) wrote:

Just curious:

`Vector.zero(0).zero? # => true or false?`

Not sure what I would expect in this case.

Definitely `true`

. More generally,

```
Vector.zero(x).zero? # => true
```

for any value of `x`

.

Colloquially, all the values in the vector are zero, even if there aren't that many values there.

That also matches how Mathematics works.

It also works best that way in programming. The simplest implementation of `zero?`

is something like

```
class Vector
def zero?
all { |e| e.zero? }
end
end
```

which will automatically give the right result.

#### Updated by stomar (Marcus Stollsteimer) over 2 years ago

Granted, in the case of #zero? returning true might suggest itself, but is "nothing" really the same as "zero"...? If there was a method Vector.one with Vector.one(3) => Vector[1, 1, 1], should Vector.one(0).one? be true? (All the values in the vector are 1, even if there aren't that many values there...). In that case, for Vector[] both #one? and #zero? would be true at the same time...

Generally speaking: I'm a bit sceptical about allowing zero size for these creator methods and about allowing these properties for zero size vectors/matrices, and I'm not sure what mathematics says about it.

It's easier to demonstrate the possible problems using the Matrix class (which has more methods to play around). The current behavior is a bit strange and contradictory:

```
size = 0
z = Matrix.zero(size)
z.zero? && z.orthogonal? && z.unitary? # => true (a zero matrix that's also orthogonal!)
z.det # => 1 (should be 0 for *any* `size')
i = Matrix.identity(size)
i.zero? # => true (should be false for *any* `size')
# and of course:
i == z # true (!)
```

The question is whether the methods that generate those special matrices/vectors should allow size 0 (since the generated objects do not have all the expected properties), and/or whether the methods that query these properties should return a value or not (since the property might not be very meaningful).

#### Updated by marcandre (Marc-Andre Lafortune) over 2 years ago

Martin is exactly right. See https://en.wikipedia.org/wiki/Vacuous_truth