Really simple maths question! If I convert 2 to -2, what is that called?

AARRRGH

Hello

I am looking for the word for this operation. I don't think it is negation...

The additive inverse of a geometric point is simply the SOMETHING of the y value. For example, the additive inverse of (27, 2) is (27, -2).

Does anyone know what the SOMETHING should be?

I've tried googling, but no joy.

Thanks!

RubenJ

Maybe inflection?

Fremen

I wouldn't be surprised if it's called reflection.
Specifically, reflection about the Y axis.

keane2097

I believe it's called "the multiplication by minus one"

LeixlipRed

Again, I'm pretty sure this has to do with points on an elliptic curve. Is it AAARGH? It's not reflection in that case

AARRRGH

Yep, points on an elliptic curve! But they're normal enough, (x, y)...

I will investigate inflection and reflection. Thanks.

Grudaire

AARRRGH wrote: »

The additive inverse of a geometric point is simply the SOMETHING of the y value. For example, the additive inverse of (27, 2) is (27, -2).

But 2 isn't a geometric point, it is a number, by definition the additive inverse of a number v is -v here and what I was told in college

However you're talking about translating it into -2 I think? Can you explain a bit better?

LeixlipRed

He's talking about additive inverse of a point in E(F_p) i.e. -(x,y)=(x,-y)

AARRRGH

Could "negation" or "inverse" be used?

LeixlipRed

Negation is a logic term. The points are additive inverses of each other but I'm not sure exactly what you're trying to say. If you could give us more information

Fremen

Adjoint, maybe?

carbsy

Mirror?

AARRRGH

Thanks everyone. I just rewrote what I was trying to say and to be something like "where the sign of the y value changes to a minus"...

Cheers!

LeixlipRed

AARRRGH wrote: »

"where the sign of the y value changes to a minus"...

Cheers!

:eek:

Be gone to a physical science forum you evil doer :P

thebaldsoprano

Assuming the values of x are never negative this would indeed be a reflection. If x does take on negative values I'm not quite sure what it would be. More about reflections can be found here:

http://mathworld.wolfram.com/Reflection.html

You'd want to be a little careful using terms like 'additive inverse' here and make sure to define it first, since it seems to be a little different to the usual meaning.

More about the additive inverse can be found here:

http://mathworld.wolfram.com/AdditiveInverse.html

Interestingly, the way you define additive inverse would leave no additive identity.

Using something like "where the sign of the y value changes to a minus"... should be okay, since it's reasonably unambiguous, but something like "upon multiplication of the y value by minus one" might look a bit sharper

LeixlipRed

The additive identity here is a point on an eliptic curve at infinity (theta as its normally denoted). This is not normal geometry in the R2 plane he's talking about.

Flashweaver

What's a hypotenuse?

LeixlipRed

It's a strange type of monkey only found on the equator. Why you ask?

thebaldsoprano

LeixlipRed wrote: »

The additive identity here is a point on an eliptic curve at infinity (theta as its normally denoted). This is not normal geometry in the R2 plane he's talking about.

Hhmm, that complicates things a little. I was assuming based on the initial post, as were probably most people reading this, that we are dealing with Euclidean geometry in R2. What exactly is the geometry we're dealing with here?

I can't see for the life of me how such an additive identity would work, short of having a somewhat odd addition operation. If you could point me to an article describing it that'd be much appreciated.

Cheers!

LeixlipRed

The problem is that the original poster is doing a masters in elliptic curve cryptography from the computer science/engineering side of things and isn't too up on the maths of it all. This article on wikipedia should explain it all

thebaldsoprano

Jeepers, elliptic curve cryptography wouldn't be one of my stronger points, but by the looks of things it uses Affine geometry. That does complicate things a bit alright.

Thanks.

LeixlipRed

Yeh it's a but messy alright. I'm handing in a project on a slightly related matter on Wednesday. Struggling to get it done in time. Probably shouldn't be messing around on here I suppose

MathsManiac

Although "negation" is indeed a term in logic, its use in the sense described here (multiplication by -1) is also pretty standard.

For example, it appears on the disambiguation page for "negation" on wikipedia.