Talk:Canonical form

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example

I don't know whether the order of terms in a polynomials is a good example, since it would be more logical to write it in ascending order.

Btw almost all links on this page point to things about which the canonical page says (or said ;) that they are not canonical... also in view of the length of the present article, I think it might be merged into normal form. — MFH: Talk 18:52, 27 May 2005 (UTC)[reply]

Yes, I think normal form is a better general concept. Charles Matthews 18:59, 27 May 2005 (UTC)[reply]

Use in computer linguistics

The term "canonical form" is also used to designate the normal form of dictionary entries. For single words this is the lemma form (e.g. infinitive for verbs and nominal singular for nouns if these forms exist).

For multiword terms, usually there is a head word in lemma form, but the other words may be inflected.

Example: "grüner Tee" is a canonical forms, the head word is "Tee", and it is different from the series of lemmata "grün Tee".

I totally agree!!. —Preceding unsigned comment added by Demonic224 (talk • contribs) 16:12, 30 September 2008 (UTC)[reply]

merge with canonical form (boolean algebra)

This page is so short, it should be merged with the boolean algebra page. Also, i find it very odd that the page "maxterm" redirects here.... I'm going to change that redirect. Fresheneesz 07:24, 6 February 2006 (UTC)[reply]

Scope of this article / classification theorems

OK, some of the examples I included, while fitting the general pattern, probably wouldn't be called "canonical forms", but rather "classification theorem" (e.g. the types of Hilbert spaces), "structure theorem" or "representation theorem"...

But I still think it would be nice to have a big list of all these things somewhere... Ideas how to organize this?

Functor salad 12:03, 20 September 2007 (UTC)[reply]

Rationalizing the denominator

...is an instance of a canonical form. Where should it be within this article. Michael Hardy (talk) 03:49, 15 September 2009 (UTC)[reply]

Difference between canonical and normal form

Actually there seems to be a difference between normal and canonical forms: if two objects have different canonical forms then they are different, while the same is not true for normal forms (equality of normal or canonical forms implies the objects are identical, no difference here).

See e.g. [1] which talks about _the_ canonical form for univariate polynomials and several normal forms for multivariate polynomials: "_a_ (not the) normal form".

Does anyone know if this distinction is established throughout mathematics? Should the normal and canonical form articles be split again? — Preceding unsigned comment added by Jszymon (talk • contribs) 10:42, 31 August 2011 (UTC)[reply]

As far as I know, this distinction has been introduced by computer algebraists and is well established in this area. For a reference, you may look in Davenport, James H.; Siret, Yvon; Tournier, Èvelyne (1988). Computer algebra: systems and algorithms for algebraic computation.. In WP, this distinction is described in Computer algebra#Equality.

I do not think useful to split this article into "normal form" and "canonical form", because the first concept may not be understood without reference to the second one. On the other hand, some edit would be needed to make the terminology of this article compatible with that of computer algebra. This not easy because normal and canonical forms rely, in computer algebra, on mathematical equality, while in this article they rely on belonging to the same equivalence class, i.e. on equality of equivalence classes. For example, the Jordan normal form (or Hermite normal form or Smith normal form) of a matrix is, in the computer algebra terminology, the canonical form of an equivalence class of matrices. D.Lazard (talk) 11:09, 1 January 2013 (UTC)[reply]

Canonical form of a positive integer

"The canonical form of a positive integer in decimal representation is a finite sequence of digits that does not begin with zero"

Objection: according to the aforementioned definition of a canonical form, it is a unique representation. Yet, one can represent the positive integer 2, for instance, in decimal representation as 2.0 or 1.999....