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	PlanetMath: division algorithm for integers
		The division algorithm is not an algorithm at all but rather a theorem.
		There are similar forms of the division algorithm that apply to other rings (for example, polynomials).
		This is version 3 of division algorithm for integers, born on 2001-11-16, modified 2002-02-14.
	planetmath.org /encyclopedia/DivisionAlgorithm.html (111 words)

	Division algorithm - Wikipedia, the free encyclopedia
		The division algorithm is a theorem in mathematics which precisely expresses the outcome of the usual process of division of integers.
		The name is something of a misnomer, as it is a theorem, not an algorithm, i.e.
		a well-defined procedure for achieving a specific task — although the division algorithm can be used to find the greatest common divisor of two integers.
	en.wikipedia.org /wiki/Division_algorithm (687 words)

	Long division - Wikipedia, the free encyclopedia
		In arithmetic, long division is a procedure for calculating the division of one integer, called the dividend, by another integer called the divisor, to produce a result called the quotient.
		Long division of integers can easilly be extended to include non-integer dividends, as long as they are rational.
		A generalized version of this method called polynomial long division is also used for dividing polynomials (sometimes using a shorthand version called synthetic division).
	en.wikipedia.org /wiki/Long_division (562 words)

	Long Division Algorithm
		It is a division of one number by another in the long way that "brings down" each digit of the dividend.
		In the long division procedure, the dividend must equal the sum of the remainder and all the numbers that have been subtracted.
		That is, the q we have found in the long division is indeed the one and only value possible, namely the quotient of a when divided by d.
	www.mathpath.org /Algor/algor.long.div.htm (481 words)

	PlanetMath: division
		Division is the operation which assigns to every two numbers (or more generally, elements of a field)
		For positive numbers the quotient may be obtained by performing the division algorithm with
		This is version 19 of division, born on 2004-09-06, modified 2006-03-26.
	planetmath.org /encyclopedia/Division.html (200 words)

	division algorthm for microcontrollers
		If a remainder is left at the end of the division, the process can continue (step 5 to 8) to generate a fixed point fraction.
		The numerator in the approximation, Fm, is a polynomial in inverse powers of two, with binary coefficients, that are "generated" by the algorithm.
		The first point is, that if we use the binary algorithm, which is very fast and easy to implement on a binary computer, we will find a result that is not a decimal (in the sense that a decimal fraction has a power of 10 in the denominator, not a power of 2).
	www.emesystems.com /division.htm (1269 words)

	Math 413 Lecture 2 - Divisibility & Euclidean Algorithm (Site not responding. Last check: 2007-09-08)
		This is useful both because the Euclidean algorithm is the primary computational tool in number theory and because the existence of a Euclidean algorithm has strong consequences for the structure of the ring.
		The division algorithm for this ring is often implemented by a means called synthetic division.
		Divisions are often counted as multiplications, as they can often be accomplished in a similar time and additions and other operations are ignored, as they are generally negligible when compared to a multiplication.
	www.math.umbc.edu /~campbell/Math413Spr01/Lectures/lecture2.html (455 words)

	Long Division (Site not responding. Last check: 2007-09-08)
		For one thing, all the algorithms of arithmetic are preparatory for algebra, since there are (again, not by accident, but by virtue of the construction of the decimal system) strong analogies between arithmetic of ordinary numbers and arithmetic of polynomials.
		The standard arithmetic algorithms, and the long division algorithm in particular, did not appear at all, or were drastically abridged, in all of the elementary school curricula on the government's list.
		The long division algorithm is the essential tool in establishing that any rational number has a repeating block of digits in its decimal representation.
	math.stanford.edu /ftp/milgram/long-division/longdivsiondone.htm (6312 words)

	C Board - Division Algorithm
		Could you do division by subtraction for the integer portion and then do a final "normal" division for the non integer portion.
		Otherwise, I the divide and conquer guess and check algorithm, though its use is actually within a method taught to me in primary school.
		One very interesting thing I discovered while experimenting with division that I didn't realize before (but is basic division) is that the sum of the quotient of the integer part and the decimal part over the same denominator yields the same answer.
	cboard.cprogramming.com /printthread.php?t=58595 (2111 words)

	Binary Division Algorithm
		Of all the elemental operations, division is the most complicated and can consume the most resources (in either silicon, to implement the algorithm in hardware, or in time, to implement the algorithm in software).
		The division function that is included here is of the former variety - a basic binary integer division function.
		Like the long division we learned in grade school, a binary division algorithm works from the high order digits to the low order digits and generates a quotient (division result) with each step.
	www.bearcave.com /software/divide.htm (755 words)

	LEON Hardware Division Algorithm
		This algorithm corresponds to a recurrence where each iteration produces one redundant digit of the result.
		In the SRT algorithm, the quotient is computed as with the pencil and paper procedure.
		If the division block is busy then it indicates the same to the control machine and the control machine then keeps issuing the signal till the request is operated.
	klabs.org /DEI/Arithmetic/division/leon_division/leon_division.htm (417 words)

	Division Algorithm
		Clearly the algorithm is a generalized form of the high school division algorithm.
		, the algorithm proceeds as in the one-variable case.
		Note that the generalized division algorithm does not have several of the same nice properties as the one variable case:
	www.geocities.com /CapeCanaveral/Hall/3131/divisionalg.html (544 words)

	Multiplication Algorithm
		The closely related division algorithm can find a specified eigenvalue and the corresponding eigenvector is three or four times n^3 multiplications, typically.
		Deflation in the case of the multiplication algorithm for a matrix corresponds to the division by the found factor in the Horner's method for a polynomial.
		The closely-related division algorithm consists of applying the foregoing multiplication-algorithm to B = 1 / (y I - A).
	www.rism.com /LinAlg/multiplication_algorithm.htm (3162 words)

	MathSteps: Grade 4: Division: What Is It?
		Since division and multiplication are inverse operations, students can use models similar to the models used in multiplication, to divide.
		Since multiplication is a form of repeated addition, division is a form of repeated subtraction.
		When beginning the long division algorithm, realize that you are asking questions such as "what number times 6 is less than or equal to 300?" Remember that the 3 is in the hundreds place.
	www.eduplace.com /math/mathsteps/4/d (485 words)

	Division algorithm - TheBestLinks.com - Algorithm, Absolute value, Equivalence relation, Integer, ... (Site not responding. Last check: 2007-09-08)
		Division algorithm - TheBestLinks.com - Algorithm, Absolute value, Equivalence relation, Integer,...
		Division algorithm, Algorithm, Absolute value, Equivalence relation, Integer...
		Specifically, the division algorithm states that given two integers a and d, with d ≠ 0, there exists unique integers q and r such that a = qd + r and 0 ≤ r <
	www.thebestlinks.com /Division_algorithm.html (728 words)

	A Deterministic, Relevance-Weighted, Time-Division Algorithm for Television Channel Switching
		The round-robin algorithm, in turn, allows no tuning of the algorithm for relevance except on an ad-hoc basis during the viewing of a particularly relevant segment.
		It is meant to show simply that an efficient algorithm based on integer operations can allow the viewer to adjust his or her evaluation of channels' relevance while keeping basic constraints of channel switching in place.
		Relevance-weighted switching algorithms may prove useful not only in adding value to viewer experiences with television programs, but in providing models for other decisions that users have to make throughout their day in allocating time to information, tasks, and personal interactions.
	www.praxagora.com /andyo/professional/channel_switching.html (2210 words)

	ipedia.com: Natural number Article (Site not responding. Last check: 2007-09-08)
		Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory.
		This, the Division algorithm, is key to several other properties (divisibility), algorithms (such as the Euclidean algorithm), and ideas in number theory.
		Two generalizations of natural numbers arise from the two uses: ordinal numbers are used to describe the position of an element in a ordered sequence and cardinal numbers are used to specify the size of a given set.
	www.ipedia.com /natural_number.html (1440 words)

	The Prime Glossary: Euclidean algorithm (Site not responding. Last check: 2007-09-08)
		If r is the remainder when a is divided by b (see the division algorithm), then gcd (a,b)=gcd(b,r).
		This ancient algorithm was stated by Euclid in his Elements over 2000 years ago, and is still one of the most efficient ways to find the greatest common divisor of two integers.
		One of the uses of the Euclidean algorithm is to solve the diophantine equation ax+by = c.
	primes.utm.edu /glossary/page.php?sort=EuclideanAlgorithm (206 words)

	Square root (Site not responding. Last check: 2007-09-08)
		A commonly used algorithm for approximating √ x is known as the "Babylonian method" is based on Newton's method.
		This algorithm works equally well in the p-adic numbers but cannot be used to identify square roots with p-adic square roots; it easy for example to construct a sequence rational numbers by this method which converges +3 in the reals but to -3 the 2-adics.
		The algorithm is in fact much to perform in base 2 as in step only the two digits 0 and have to be tested.
	www.freeglossary.com /SquareRoot (1713 words)

	Factorization Techniques
		Although the algorithm can be sped up by keeping track of certain variables, this particular algorithm is not suitable for factoring large numbers.
		The problem with both trial division and Fermat's algorithm is that they do not only find factors, but if left running long enough, they prove primality.
		Together, the Pollard Rho and p-1 algorithms are intermediate tests between the trial division and Fermat's algorithm and the big guns such as the Quadratic sieve.
	members.tripod.com /irish_ronan/rsa/factorization.html (595 words)

	Strength in Numbers
		By adjusting the ratio of m and c and carefully selecting the checksum algorithm, we can increase the number of bits that must be in error for any one valid packet to be inadvertently changed into another valid packet during transmission or storage and, hence, the likelihood of successful transmission.
		So, whereas the implementation of a checksum algorithm based on addition is straightforward, the implementation of a binary division algorithm with an m+c-bit numerator and a c+1-bit denominator is nowhere close.
		Ignoring special types of errors that are always detected by a particular checksum algorithm, the percentage of detectable errors is limited strictly by the width of a checksum.
	www.netrino.com /Connecting/1999-12 (2420 words)

	Long Division Algorithm (Site not responding. Last check: 2007-09-08)
		When I was in 4th grade the teacher made us work endless examples of the long-division algorithm.
		With the advent of calculators I fear the use of this algorithm is fast becoming a lost art.
		So that future generations may understand how we suffered, this form will run a cgi-script that solves, in complete detail, any desired long-division problem.
	barnyard.syr.edu /longdiv.html (132 words)

	OPENCORES.ORG
		They consider that both algorithms may be used in sequential calculation scheme, when one digit of the result is achieved during one clock.
		Restoring algorithm is seemed to be sequential in nature because during remainder restoring there is positive feedback (A=A — B + B at the same cycle).
		Thus, non-restoring algorithm was chosen as basic for one-clock division algorithm.
	www.opencores.org /projects.cgi/web/single_clock_divider (202 words)

	Extended Euclidean Algorithm
		You repeatedly divide the divisor by the remainder until the remainder is 0.
		Before presenting this extended Euclidean algorithm, we shall look at a special application that is the most common usage of the algorithm.
		We will give a form of the algorithm which only solves this special case, although the general algorithm is not much more difficult.
	www-math.cudenver.edu /~wcherowi/courses/m5410/exeucalg.html (718 words)

	[No title]
		Balanced tree in divide-and-conquer algorithm has logarithmic height, so its size is only logarithmically larger than the original numbers.
		Recursive algorithm to compute a mod b1, a mod b2,..., a mod bk.
		Algorithm produces all small prime factors of each integer.
	cr.yp.to /2002-501/inclass.html (864 words)

	New Division Algorithm for Hardware (Site not responding. Last check: 2007-09-08)
		This algorithm allows at least 2 dividend bits to be retired per full-precision addition (or subtraction), but is much simpler than traditional Radix-4 SRT algorithms.
		It appears at this time that the best implementation of the new algorithm may be with the partial remainder kept in regular binary format, but this is not at all clear, since both the redundant and non-redundant hardware can be tuned to obtain better performance.
		Kantabutra's new division algorithm appears to be easier to implement correctly than traditional radix-4 SRT algorithms, due to the lack of a lookup table.
	www.isu.edu /~kantviti/div.html (335 words)

	Fair Division: The Fair Division Calculator
		The idea for the algorithm was sparked by Forest Simmons, and further developed by Elisha Peterson and myself.
		The algorithm halts when a final division is reached (although you do not have to wait until that happens if you and your friends are satisfied with something sooner!).
		The divisions are measured in units out of 100 (or out of the total rent), but keep in mind that there are other factors which may influence your decision--- such as whether you prefer
	www.math.hmc.edu /~su/fairdivision/fdc-1 (672 words)

	Division algorithm (Site not responding. Last check: 2007-09-08)
		Algorithm for the numerical integration of systems of ordinary differential equations arising in chemical problems.
		Contains the Diamonds division, the Minerals, Oil and Gas division, the Investment and Economic Analysis division, the Industrial Initiatives division, the NWT Film Commission and the Tourism and Parks division.
		An algorithm for obtaining an exact solution for the three dimensional location of a mobile given the locations of four fixed stations (like a GPS satellite or a base station in a cell) and the signal time of arrival (TOA) from the mobile to each station.
	www.omniknow.com /common/wiki.php?in=en&term=Division_algorithm (1865 words)

	CZ1101, Lecture Notes, Week 8 (Site not responding. Last check: 2007-09-08)
		Booth's algorithm is a multiplication algorithm which worked for two's complement numbers.
		In Booth's algorithm, if the multiplicand and multiplier are n-bit two's complement numbers, the result is considered as 2n-bit two's complement value.
		For division, there is no algorithm similar to Booth's algorithm for signed integers.
	www.cse.mrt.ac.lk /~sumith/cei/ref/BoothAlgorithm02.htm (1215 words)

	3. Division & Euclid's Algorithm (Math 413, Number Theory) (Site not responding. Last check: 2007-09-08)
		The largest number which divides two numbers n and m is called the greatest common divisor of n and m, and denoted gcd(n, m).
		If you think carefully about the Euclidean algorithm you will see that at each step both numbers are formed by adding some multiples of the original numbers.
		Given this norm all of the algorithms push through to the case of polynomials.
	www.math.umbc.edu /~campbell/Math413Fall98/3-Euclid.html (268 words)

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