Re: [eigen] Does c++ use of "norm" bother anyone else? |

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*To*: eigen@xxxxxxxxxxxxxxxxxxx*Subject*: Re: [eigen] Does c++ use of "norm" bother anyone else?*From*: Markus Moll <markus.moll@xxxxxxxxxxxxxxxx>*Date*: Thu, 18 Jun 2009 14:15:01 +0200*Organization*: K.U. Leuven

Hi On Thursday 18 June 2009 13:40:34 Benoit Jacob wrote: > Indeed, std::complex norm() isn't a "norm" in this sense. But it still > is called "norm" in other mathematical contexts -- it's not just the > c++ people who were on crack, it's the whole mathematics tradition :) > > (Optional part: the other sense of "norm" -- skip if not interested: > let K/k be a Galois extension, let x in K, then the norm of x with > respect to this extension is the product of the sigma(x) for all sigma > in the Galois group of K/k. So for complex numbers, they are a Galois > extension of the real numbers, of degree 2, the Galois group Gal(C/R) > has 2 elements, the identity and complex conjugation, so the norm of a > complex number x is the product x * conj(x) which is what > std::complex calls norm(). More references: > http://en.wikipedia.org/wiki/Field_norm#Example > ) Oh, wow, I was totally unaware of this definition. (Although I still think it's better called "field norm" to avoid confusion). So I apologize to the C++ committee, they have actually done it right :-) > Actually I think that norm() isn't a method in std::complex, it's only > a global function in std:: , right ? Yes. > Then I think that it's safe to > implement std::norm also for Eigen::Complex, as it's documented there > what it does. That's the same problem as with std::vector, no? Eigen::Complex will be a template, so there's no way to specialize std::norm properly. Markus -- PGP key on www.esat.kuleuven.be/~mmoll/public_key.pgp Fingerprint is 90C4 B47D 1A00 5AC1 9147 3197 EDA7 1E0E 99E4 9EDB

**Follow-Ups**:**Re: [eigen] Does c++ use of "norm" bother anyone else?***From:*Markus Moll

**References**:**[eigen] Does c++ use of "norm" bother anyone else?***From:*Mark Borgerding

**Re: [eigen] Does c++ use of "norm" bother anyone else?***From:*Markus Moll

**Re: [eigen] Does c++ use of "norm" bother anyone else?***From:*Benoit Jacob

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