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Topic: Quotient object

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	Quotient - Wikipedia, the free encyclopedia
		In mathematics, a quotient is the end result of a division problem.
		In more abstract branches of mathematics, the word quotient is often used to describe sets, spaces, or algebraic structures whose elements are the equivalence classes of some equivalence relation on another set, space, or algebraic structure.
		Quotients also come up in certain tests, like the IQ test, which stands for intelligence quotient.
	en.wikipedia.org /wiki/Quotient (224 words)

	Derivative
		Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with repsect to time) of an object's position.
		Jerk is the derivative (with respect to time) of an object's acceleration.
		If the velocity of a car is given, as a function of time; then, the derivative of said function describes the acceleration of said car, as a function of time.
	www.ebroadcast.com.au /lookup/encyclopedia/de/Derivative.html (1600 words)

	PlanetMath: subobject
		Definitions of a subobject and a quotient object.
		Cross-references: arrows, equivalence classes, partitions, equivalence relation, commutative diagrams, morphisms, category, monomorphisms, objects
		Object id is 6399, canonical name is Subobject.
	planetmath.org /encyclopedia/QuotientObject.html (114 words)

	Derivative - Wikipedia, the free encyclopedia
		Arguably the most important application of calculus to physics is the concept of the "time derivative"—the rate of change over time—which is required for the precise definition of several important concepts.
		Velocity (instantaneous velocity; the concept of average velocity predates calculus) is the derivative (with respect to time) of an object's position.
		Acceleration is the derivative (with respect to time) of an object's velocity, that is, the second derivative (with respect to time) of an object's position.
	en.wikipedia.org /wiki/Derivative (2317 words)

	ATPM 9.03 - Roll Your Own: The Object of Programming
		Yet another advantage of object oriented programming is the concept of inheritance, where a new object can inherit all of the properties and handlers of an existing object, can modify them as needed, or even overwrite them completely.
		When a child object has a parent object, all of the properties, handlers, and any other code within the parent object are part of the child object.
		However, a general rule when creating objects is to build code only for what you need for each object and when you need to expand on that code, create a new object that inherits from the first.
	www.atpm.com /9.03/roll.shtml (5821 words)

	Comparable (Java 2 Platform SE v1.4.2)
		Objects that implement this interface can be used as keys in a sorted map or elements in a sorted set, without the need to specify a comparator.
		Returns a negative integer, zero, or a positive integer as this object is less than, equal to, or greater than the specified object.
		a negative integer, zero, or a positive integer as this object is less than, equal to, or greater than the specified object.
	java.sun.com /j2se/1.4.2/docs/api/java/lang/Comparable.html (503 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-10-23)
		consists of all regular (strict, normal, etc.) epimorphisms, then the corresponding quotient objects are called regular (strict, normal, etc).
		For example, in the category of topological spaces quotient spaces correspond to regular quotient objects.
		The concept of a quotient object of an object in a category is dual to that of a subobject.
	eom.springer.de /Q/q076900.htm (148 words)

	Common Lisp Extensions - Numbers
		except that it rounds the argument or quotient of the arguments to the nearest integer.
		In the case of a tie (the argument or quotient is exactly halfway between two integers), it rounds to the even integer.
		may also be an integer in which case the new object is seeded from that integer; each different integer seed will result in a completely different sequence of random numbers.
	www.csupomona.edu /reference/gnu/emacs-19.30/cl_8.html (1049 words)

	[No title]
		Therefore the objects in mod D coincide, up to isomorphism, with the objects in* * mod C. Moreover, the maps in mod D are obtained via a calculus of fractions from the m* *aps in mod C; see [11, I.2.5].
		We conclude that F is not a cohomological quotient funct* *or.
		Moreover, The* orem 4.4 implies that F is a cohomological quotient* functor.
	www.math.purdue.edu /research/atopology/KrauseH/quotient.txt (17394 words)

	Wikinfo \| Derivative (Site not responding. Last check: 2007-10-23)
		Arguably the most important application of calculus, to physics, is the concept of the "time derivative" -- the rate of change over time -- which is required for the precise definition of several important concepts.
		For example, if an object's position p(t) = -16t2 + 16t + 32; then, the object's velocity is p'(t) = -32t + 16; the object's acceleration is p''(t) = -32; and the object's jerk is p'''(t) = 0.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Derivative (1691 words)

	Reduction of nonlinear dynamic cintrol systems. (Site not responding. Last check: 2007-10-23)
		If two objects S1 and S2 are defined on the sets M1 and M2, respectively, then a morphism f of the object S1 into the object S2 is a mapping f from M1 to M2 that preserves the structure of a given kind (i.e., preserves the corresponding relationships between the elements of the sets).
		The concept of a subobject results from our desire to construct correctly the restriction of an object S1 defined on a set M to a subset N of M. It is generally not possible to restrict an object S1 to an arbitrary set.
		An object S2 defined on a subset N is called a subobject if the canonical injection of N to M is a morphism.
	www.ccas.ru /Pavlovsky/Edecomp1.htm (1150 words)

	RsaXli::ExtDiv
		The ExtDiv member function divides the numerical value encapsulated by the presenting RsaXli object by the numerical value of the rOth object and places the quotient in the rQuo object and the remainder in the rRem object.
		The identification of the most significant quotient digit is done just as it is done in long division by hand: the number of significant digits of the divisor is subtracted from the number of significant digits of the dividend to produce the (maximum) number of significant digits in the quotient.
		The quotient digit is reliably underestimated by dividing the key digit of the current dividend by the quantity 1 plus the most-significant digit of the divisor.
	www.grc.nasa.gov /WWW/price000/rsa/htm/rsaxli_extdiv.html (646 words)

	Metadata for Data Warehousing using Extended Relational Models
		It is suitable as a concept of an object oriented meta model for OLAP-data, since it inherently uses the concept of object identifiers, a typology of different object types, such as: associations, characteristics, and kernel object types; and a meta model description on the relationships between the different types.
		The use of quotient and nested relations in object oriented databases is relatively easy possible by defining the appropriate class-hierarchies for these relations together with their well defined operators.
		Especially for MOLAP databases the complex objects of quotient relations and nested relations are highly suitable for performing roll-up and drill-down on the fly.
	www.ifs.tuwien.ac.at /ifs/research/pub_html/man_ieeemd99/man_ieeemd99.html (3791 words)

	CoCoA 3.5 Help (Site not responding. Last check: 2007-10-23)
		If the object E is tagged with the string S, then when the user enters the command 'Describe E', CoCoA first looks for a user-defined function with name 'Describe_S' and executes it; if not found, the output depends on the type of Untagged(E).
		Variables containing objects such as integers which are not dependent on a particular ring are not labeled.
		This object represents the submodule, generated by V_1,...,V_n, of the free module of rank r which is the direct sum of R(P_1),...,R(P_r).
	sun.uni-regensburg.de /cocoa-3.5/cocoa-3.5.html (7916 words)

	[No title]
		Thus all objects are cofibrant, f and f0 are cofibrations, Z = Y=X and Z0= Y 0=* X0, g and g0 are quotient* maps, and h and h0are connecting maps ffi.
		Thus* , in each case, the first map is a cofibration, the second map is a quotient* map, and the third map is a connecting map as in (5.4).
		Since maps in C between fibrant and cofibrant objects are homotopy classes of maps, the left square is homotopy commutative.
	www.math.purdue.edu /research/atopology/May/AddJan01.txt (6188 words)

	glyf: worse was "better", but now "superior" - better now stuponfucious and we don't know what it was
		Given the explicit task of upgrading a few simple objects (of the style present in the code from which the New Jersey example is taken) to a new and better representation, the Right Thing wins hands down.
		It makes you think about what other objects need to be included in the representation in order for the evalled object to be considered "equivalent" to the original.
		Someone changes something in a new release of Quotient and the object is now different than it was before and the persistence becomes broken.
	glyf.livejournal.com /6877.html (2704 words)

	IIIc
		The objects, on the other hand are 'complicated' in the sense of the many levels of abstraction and the great time and effort needed to 'construct' them in the mind of the student.
		She finally employs a proceptual argument in order to indicate the flexibility in shifting from the process to the object aspects of a concept as a sign of mathematical maturity: this flexibility is a requirement for successful handling of tasks like finding the inverse of a compound element.
		Normality is also confused with commutativity and the students' ignoring the condition of normality for the existence of the quotient group influences heavily their attempts to construct the cosets.
	www.uea.ac.uk /~m011/thesis/chapter1/3civ.htm (3220 words)

	[Inquiry] Re: Examples! Examples! Examples!
		Lattice of Objects Inducing a Diversity of Sign Partitions But for the present I ought to say what I intend by this: Infinite diversity poses an obstacle to nominal thinking.
		Well, one way to reduce the problem is to ignore the problematic domain of objects in toto, whether intentional or clear and present, and one way to get away with it is suggested by the very k-ptyches that we have staring at all this while.
		Well, then, we would have a form-preserving copy of the object domain quite well in hand with the quotient object of the sign domain and the object domain should be a "world well wiled" out of mind.
	stderr.org /pipermail/inquiry/2003-July/000618.html (321 words)

	The Fundamental Existent
		That is, the amount of space traversed by an object divided by the amount of space traversed by my clock (Imagine a slider control – like on the front of a stereo.) gives a measure of a relative change in position.
		There are no length restrictions on the reference objects (they could be shovels or boots), only that if they are in the same frame that their measurement be unity and that they be identical in composition.
		(notice that with respect to this spinning object the rest of the objects are rotating in the opposite direction and it is not rotating with respect to it self).
	www.martinelli.org /fundamental (4437 words)

	Title
		// Postcondition: the binary_number object is initialized HexNumber.assign("00"); if((X.size()) > 0){ Input = X; } else{ Input = "0"; } zeroBinary(); DecimalNumber = 0; Converted = 0; Valid = 1; zeroBinary(); Valid_digits.insert('0'); Valid_digits.insert('1'); initializeBinary(X); validateNumber(); } string binary_number::binary(void) { // Returns the binary number as a string.
		// It resets the binary_number object (in case there are // multiple calls to this method, the object must be reset // each time), validates the input then initializes the // binary number vector.
		If either objects are not valid, an error // code -1 is returned.
	cc.ysu.edu /~cahughes/binary_number.html (448 words)

	Class crw.math.Complex
		Returns the complex quotient of the first (complex) argument divided by the second (complex) argument.
		Returns the complex quotient of the first (complex) argument divided by the second (double) argument.
		Multiplies a complex number with this object and this object is replaced by the product.
	jas.eng.buffalo.edu /semiconductor/apiWIE/crw.math.Complex.html (1422 words)

	Arithmetic Operations
		A predefined method returns the quotient of two complex numbers.
		Returns the floor of the quotient of two numbers.
		Returns the ceiling of the quotient of two numbers.
	www.cs.indiana.edu /~jsobel/dylan-manual/drm-100.html (647 words)

	Categories and Functors (Site not responding. Last check: 2007-10-23)
		It is easy to check that two objects in same equivalence class are naturally isomorphic.
		The dual notion to subobject is quotient object.
		It is easily verified that direct sum and direct product of a finite family of objects are isomorphic (if they exist).
	www.imsc.res.in /~sgautam/main/node2.html (550 words)

	[No title]
		This primitive builds an object to control Mosaic (typicaly to be used by some helper applications).
		When Mosaic is not running, the object tries to launch it (the first command generally fails, because of the start up time of Mosaic, and the home URL).
		OBJECT should be an external object, HEADER should have the form: (SEL: VARIABLE...
	koala.ilog.fr /abaird/oscheme/doc/kernel-help.html (6500 words)

	<stdlib.h> (Site not responding. Last check: 2007-10-23)
		is a null pointer and if multibyte characters have a state-dependent encoding in the current locale, the function stores the initial conversion state in its internal static-duration object and returns nonzero; otherwise, it returns zero.
		The function can use a conversion state stored in a static-duration object to determine how to interpret the multibyte character string.
		is a null pointer and if multibyte characters have a state-dependent encoding in the current locale, the function stores the initial conversion state in its static-duration object and returns nonzero; otherwise, it returns zero.
	www-cse.ucsd.edu /users/kube/stdc/stdlib.html (1928 words)

	Object Math in ECMAScript 262
		A global, non-instantiable object which holds certain math-related functions and values.
		A reference to the constructor class for the current object instance.
		Determines if the calling object prototype is in the inheritance chain for the supplied argument.
	phrogz.net /objjob/object.asp?id=315 (164 words)

	define-foreign-function (Site not responding. Last check: 2007-10-23)
		The result of the foreign call is written into this object and the foreign pointer is returned as the primary value from the Lisp function.
		This allows the caller to maintain control over the lifetime of this object (in C this would typically be stored in a local variable).
		In this foreign function definition the main result is the quotient and the second return value is the remainder:
	www.lispworks.com /documentation/lw445/FLI/html/fli-75.htm (793 words)

	Quotient Image Page
		conditions on a collection of objects all having the same shape but differ in their surface texture (albedo) can be characterized analytically.
		of the same objects yield novel images of the object under new illuminations.
		This signature image is actually the quotient between the novel image b and a linear combination of 3 model images.
	www.eng.tau.ac.il /~tammy/qimage.html (425 words)

	Class mpfun.MPComplex (Site not responding. Last check: 2007-10-23)
		A MPComplex object consists of two MP objects.
		Returns the value of the object as DComplex This may involves truncation or rounding.
		This routine divides the MP complex numbers A and B to yield the MPC quotient c.
	www.cs.unc.edu /~sc/research/HARPOON/mpjava/doc/mpfun.MPComplex.html (1639 words)

	Class BigInt
		BigInts support the Classical Algorithms of addition, subtraction, multiplication and division giving a quotient and remainder.
		For example, when adding zero to a thousand digit number, it is more efficient to return the thousand digit number than to make a copy.
		an array of two BigInts, with the quotient at index 0, and the remainder at index 1.
	www.swiss.ai.mit.edu /~adams/BigInt/BigInt.html (546 words)

	[No title]
		The print function creates these objects in a fake /// first printing pass, and then it uses these objects during a real second /// printing pass to determine whether the object needs to be tagged, /// printed normally, or printed by reference to the objects circular ID to /// avoid infinite recursive printing.
		The assumption is that there is no harm in turning // it off for some object, and because it is odd to request no pretty // printing, the calling code probably has good reason to turn it off.
		The object passed in and all head /// pointers are handled naturally via calls to print.
	www.cs.cmu.edu /afs/cs.cmu.edu/project/gwydion-7/rgs/runtime/print/print.dylan (4961 words)

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