143.117.68.31: /* Application */

2013-11-11T10:45:09Z

Application

← Older revision		Revision as of 12:45, 11 November 2013
Line 1:		Line 1:
	~~The writer~~ is ~~called Irwin Wunder but it'~~s ~~not~~ the ~~most masucline name out there~~. ~~To gather badges~~ is ~~what her family members~~ and ~~her enjoy~~. ~~For many years he~~'~~s been residing in North Dakota~~ and ~~his family members enjoys~~ it~~. She~~ is ~~a librarian but she~~'~~s usually needed her personal company.~~<br><br>~~Take a look at my website -~~ [~~http~~://~~Www~~.~~Smithandkenworld~~.~~com~~/~~activity~~-~~posted~~-by-~~2455/ Www.Smithandkenworld.com~~]		In mathematics, the method of '''equating the coefficients''' is a way of solving a functional equation of two [[polynomial]]s for a number of unknown parameters. It relies on the fact that two polynomials are identical precisely when all corresponding coefficients are equal. The method is used to bring formulas into a desired form.

			==Example==
			Suppose we want to apply [[partial fraction decomposition]] to the expression:

			:<math>\frac{1}{x(x-1)(x-2)},\,</math>

			that is, we want to bring it into the form:

			:<math>\frac{A}{x}+\frac{B}{x-1}+\frac{C}{x-2},\,</math>

			in which the unknown parameters are ''A'', ''B'' and ''C''.
			Multiplying these formulas by ''x''(''x'' − 1)(''x'' − 2) turns both into polynomials, which we equate:

			:<math>A(x-1)(x-2) + Bx(x-2) + Cx(x-1) = 1,\,</math>

			or, after expansion and collecting terms with equal powers of ''x'':

			:<math>(A+B+C)x^2 - (3A+2B+C)x + 2A = 1.\,</math>

			At this point it is essential to realize that the polynomial 1 is in fact equal to the polynomial 0''x''<sup>2</sup> + 0''x'' + 1, having zero coefficients for the positive powers of ''x''. Equating the corresponding coefficients now results in this [[system of linear equations]]:

			:<math>A+B+C = 0,\,</math>
			:<math>3A+2B+C = 0,\,</math>
			:<math>2A = 1.\,</math>

			Solving it results in:

			:<math>A = \frac{1}{2},\, B = -1,\, C = \frac{1}{2}.\,</math>

			==References==
			*{{cite book \|title=Encyclopedia of Mathematics \|first=James \|last=Tanton \|page=162 \|publisher=Facts on File \|year=2005 \|isbn=0-8160-5124-0}}

			{{DEFAULTSORT:Equating Coefficients}}
			[[Category:Elementary algebra]]
			[[Category:Equations]]

en>Thehelpfulbot: r2.6.5) (Robot: Adding es:Criptografía con umbral

2012-05-23T08:03:31Z

r2.6.5) (Robot: Adding es:Criptografía con umbral

New page

The writer is called Irwin Wunder but it's not the most masucline name out there. To gather badges is what her family members and her enjoy. For many years he's been residing in North Dakota and his family members enjoys it. She is a librarian but she's usually needed her personal company.<br><br>Take a look at my website - [http://Www.Smithandkenworld.com/activity-posted-by-2455/ Www.Smithandkenworld.com]

Threshold cryptosystem - Revision history

143.117.68.31: /* Application */

en>Thehelpfulbot: r2.6.5) (Robot: Adding es:Criptografía con umbral