en>DrKiernan: subst:'ing, replaced: {{S}} → , added Empty section (1) tag using AWB

2012-10-30T17:42:11Z

subst:'ing, replaced: {{S}} → , added Empty section (1) tag using AWB

← Older revision		Revision as of 19:42, 30 October 2012
Line 1:		Line 1:
	~~Joey is what [http://Www.Google.de/search?q~~=~~people+simply people simply] call me but I never really preferred that identify. One particular~~ of the ~~points I like most is fishing~~ and ~~I will never ever quit undertaking it. [http://Search.About.com/?q=Software Software] package creating~~ is ~~how I help my family~~. ~~My family life in New Hampshire and~~ I ~~really don't plan on modifying it~~. ~~You can come across my site~~ right ~~here: http://www.sonriaporfavor.com/miedoDentista.asp?id~~=~~1<br><br>~~		{{quotebox\|quote=But the catalecticant of the biquadratic function of ''x'', ''y'' was first brought into notice as an invariant by Mr Boole; and the discriminant of the quadratic function of ''x'', ''y'' is identical with its catalecticant, as also with its Hessian. Meicatalecticizant would more completely express the meaning of that which, for the sake of brevity, I denominate the catalecticant.
			\|source={{harvtxt\|Sylvester\|1852}}, quoted by {{harv\|Miller\|2010}}\|align=right\|width=30%}}

	~~Feel free~~ to ~~visit my web site Salomon~~ ([http://~~www~~.~~sonriaporfavor~~.com/~~miedoDentista.asp~~?id=~~1 www~~.~~sonriaporfavor~~.com])		In mathematical [[invariant theory]], the '''catalecticant''' of a [[invariant of a binary form\|form]] of even degree is a polynomial in its coefficients that vanishes when the form is a sum of an unusually small number of powers of linear forms. It was introduced by {{harvtxt\|Sylvester\|1852}}; see {{harv\|Miller\|2010}}. The word [[catalectic]] refers to an incomplete line of verse, lacking a syllable at the end or ending with an incomplete foot.

			==Binary forms==

			The '''catalecticant''' of a [[invariant of a binary form\|binary form]] of degree 2''n'' is a polynomial in its coefficients that vanishes when the binary form is a sum of at most ''n'' powers of linear forms {{harvtxt\|Sturmfels\|1993}}.

			The catalecticant of a binary form can be given as the determinant of a '''catalecticant matrix''' {{harv\|Eisenbud\|1988}}, also called a '''[[Hankel matrix]]''', that is a [[square matrix]] with constant (positive sloping) skew-diagonals, such as

			:<math>\begin{bmatrix}
			a & b & c & d & e \\
			b & c & d & e & f \\
			c & d & e & f & g \\
			d & e & f & g & h \\
			e & f & g & h & i
			\end{bmatrix}.</math>

			==Catalecticants of quartic forms==

			The catalecticant of a quartic form is the resultant of its second partial derivatives. For binary quartics the catalecticant vanishes when the form is a sum of 2 4th powers. For a ternary quartic the catalecticant vanishes when the form is a sum of 5 4th powers. For quaternary quartics the catalecticant vanishes when the form is a sum of 9 4th powers. For quinary quartics the catalecticant vanishes when the form is a sum of 14 4th powers. {{harv\|Elliot\|1915\|loc=p.295}}

			==References==

			*{{Citation \| last1=Eisenbud \| first1=David \| author1-link=David Eisenbud \| title=Linear sections of determinantal varieties \| doi=10.2307/2374622 \| year=1988 \| journal=[[American Journal of Mathematics]] \| issn=0002-9327 \| volume=110 \| issue=3 \| pages=541–575 \| mr=944327}}
			*{{Citation \| last1=Elliott \| first1=Edwin Bailey \| title=An introduction to the algebra of quantics. \| origyear=1895 \| url=http://books.google.com/books?id=Az5tAAAAMAAJ \| publisher=Oxford. Clarendon Press \| edition=2nd \| jfm=26.0135.01 \| year=1913}}
			*{{Citation \| last1=Sturmfels \| first1=Bernd \| author1-link=Bernd Sturmfels \| title=Algorithms in invariant theory \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Texts and Monographs in Symbolic Computation \| isbn=978-3-211-82445-0 \| doi=10.1007/978-3-211-77417-5 \| year=1993 \| mr=1255980}}
			*{{Citation \| last1=Sylvester \| first1=J. J. \| author1-link=J. J. Sylvester \| title=On the principles of the calculus of forms \| year=1852 \| journal=Cambridge and Dublin Mathematical Journal \| pages=52–97}}

			==External links==
			*{{citation\|first=Jeff \|last=Miller\|year=2010\|url=http://jeff560.tripod.com/c.html \|title=Earliest Known Uses of Some of the Words of Mathematics (C)}}

			[[Category:Invariant theory]]

en>Statoman71: I did not find a Wikipedia page for Mr. Nori, removed link.

2012-07-28T18:14:12Z

I did not find a Wikipedia page for Mr. Nori, removed link.

New page

Joey is what [http://Www.Google.de/search?q=people+simply people simply] call me but I never really preferred that identify. One particular of the points I like most is fishing and I will never ever quit undertaking it. [http://Search.About.com/?q=Software Software] package creating is how I help my family. My family life in New Hampshire and I really don't plan on modifying it. You can come across my site right here: http://www.sonriaporfavor.com/miedoDentista.asp?id=1<br><br>

Feel free to visit my web site Salomon ([http://www.sonriaporfavor.com/miedoDentista.asp?id=1 www.sonriaporfavor.com])

Essentially finite vector bundle - Revision history

en>DrKiernan: subst:'ing, replaced: {{S}} → , added Empty section (1) tag using AWB

en>Statoman71: I did not find a Wikipedia page for Mr. Nori, removed link.