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	Function Fields
		The function field of the curve is the corresponding field of fractions.
		This is a vector subspace of the function field of a curve.
		Since function fields are realised by completely separate code, one cannot automatically expect rational functions written in terms of the generators of the coordinate ring of the curve to be elements of the function field.
	www.umich.edu /~gpcc/scs/magma/text1031.htm (1849 words)

	Function Fields
		The function field of the curve is the corresponding field of fractions in the affine case and the homogeneous degree 0 part of this in projective cases.
		As with schemes generally, a function field is attached to projective curves and the same object represents the function field of all of its affine patchs.
		Return the function f in the function field of a scheme as a function in projective coordinates (as an element in the field of fractions of the coordinate ring of the projective scheme having function field the parent of f).
	www.math.lsu.edu /magma/text1176.htm (2592 words)

	Algebraic Function Fields
		A "random" element of the global function field F. The size of the coefficients of the element are determined by m.
		The k(x)-basis 1, alpha,..., alpha^(n - 1) of the function field F/k(x).
		The Zeta function of the constant field extension of degree m of the global function field F/k.
	www.math.niu.edu /help/math/magmahelp/text707.html (3140 words)

	Fields \| Palm OS® Programmer's API Reference
		Applications should call this function on field objects that edit data records in place before the field is unlocked, or at any other time when a compact field is desirable; for example, before writing to the storage heap.
		Fields allocate memory for the text string as needed, so it is not an error to call this function while the field is still displayed.
		If the field points to a database record, you want the memory associated with the text handle to persist; however, this memory and all other memory associated with the field is freed when the field itself is freed, which happens when the form is closed.
	www.palmos.com /dev/support/docs/palmos/Field.html (6054 words)

	Springer Online Reference Works
		In the first case the algebraic function is a rational, in the second case it is an elliptic, while in the third case it is a general function.
		is identical with the field of meromorphic functions on the Riemann surface of the algebraic function.
		Each algebraic function field in one variable is the field of fractions of a Dedekind ring, so that many results and concepts of the theory of divisibility in algebraic number fields can be applied to function fields [12].
	eom.springer.de /A/a011490.htm (1619 words)

	PlanetMath: function field
		, is the field of all rational functions
		rational function field, geometric extension, genus of a function field, degree of a prime
		This is version 4 of function field, born on 2005-11-10, modified 2005-11-10.
	planetmath.org /encyclopedia/RationalFunctionField2.html (172 words)

	CHKPCK: Validating a Packed Field
		The function prevents a data exception from occurring when a request reads a field that is expected to contain a valid packed number but does not.
		If the value it examines is a valid packed number, the function returns the value; if the value is not packed, the function returns an error code.
		Is the name of the field that contains the result, or the format of the output value enclosed in single quotation marks.
	www.bgsu.edu /its/admin/focus/mf_functions/numeric5.htm (371 words)

	Algebraic Function Fields [HB 57]
		The functionality of extensions of algebraic function fields has been extended to almost match that of ordinary algebraic function fields.
		The functionality of the orders of algebraic function fields has been extended to almost match the functionality of the orders of algebraic number fields.
		All functions for algebraic function fields can be called on extensions of function fields with the exception of those involving series rings, galois groups and subfields.
	www.math.wayne.edu /answers/magma2.10/htmlhelp/rel/node31.htm (533 words)

	Adding New Field Types
		All field types must have a field validation function associated with it unless (1) it is a string-type field and you will store the string exactly as it appears in the field and (2) you will do no range checking for a field of this type.
		If data entered in a field of this field type is stored as a pointer (this includes such fields as dates and times), you must write your own range set function.
		Function prototype or extern declarations for any added functions should be placed in a header file.
	www.vtsoft.com /VVHTMLHelp/VVUsersGd/htm/addingnewfieldtypes.htm (1483 words)

	Divisors
		Given a function field F/k and a divisor D belonging to F/k, return a vector space V and a k-linear mapping h: V longrightarrow F such that V is isomorphic to the Riemann-Roch space (L)(D) subset F under h.
		Return the complementary divisor D^# of D. The function field F/k of D must be a finite extension of a rational function field k(x).
		A bound B such that the places of degree (over the exact constant field) less than or equal to B, taken together with the places of a divisor of degree one, generate the whole divisor class group of any global function field of genus g over the exact constant field of q elements.
	www.math.niu.edu /help/math/magmahelp/text710.html (2569 words)

	5 The Time Dependent Spin Polarization in Zero Field (Site not responding. Last check: 2007-10-03)
		The origin of these fields can be nuclear dipoles, electron orbital or spin moments, and generally the fields may be dynamic (either because of dynamics of the magnetic system or because of muon motion).
		This extra enhancement in zero field, from terms in the interaction which in ZF cause the muon and nuclear moments to flip-flop, does not occur in the case of magnetically ordered moments, because the energy required to flip the ordered moment is non-zero (it is given by an exchange energy, which is generally quite large).
		The quenching field thus depends sensitively on the particular dynamics involved, but is generally much larger than the field esimated from the zero field relaxation function (assuming it is of static origin).
	musr.physics.ubc.ca /theses/MacFarlane/node38.html (1905 words)

	class FieldArchetype (Site not responding. Last check: 2007-10-03)
		This field element has no knowledge of the field properties being used on it which means the field object must supply these operations.
		This function assumes the output field element x has already been constructed, but that it is not necessarily already initialized.
		This function assumes the output field element x has already been constructed, but that it is not already initialized.
	www.eecis.udel.edu /~linbox/html/FieldArchetype.html (1033 words)

	A Function-Based Data Model for Visualization
		The base space is analogous to the independent variables of a function while fiber space is analogous to the dependent variables of a function, and fiber bundle section is analogous to a function (field).
		Operations imply a process of transformation between different functions of this class, whether it is solved as a set of partial differential equations that define flow of heat or generating pixels as a rendering of some geometry.
		Hence, access to the categorical data is packaged as a new function to provide the equivalent of traditional field as well as calculation of a derived one for sample points where the material is not homogenous.
	www.research.ibm.com /people/l/lloydt/dm/function/dm_fn.htm (4765 words)

	functions :: Functions (MATLAB Function Reference)
		The value of each field is the path and name of the file that defines the method.
		field of the return structure contains the names of the nested function and the function in which it is nested in the format.
		field containing the variables that are in context at the time you call this function by its handle:
	www.mathworks.com /access/helpdesk/help/techdoc/ref/functions.html (386 words)

	PHP: mysql_fetch_field - Manual
		This function can be used to obtain information about fields in the provided query result.
		If the field offset is not specified, the next field that was not yet retrieved by this function is retrieved.
		Be sure to note that $max_length is the length of the longest value for that field in the returned dataset, NOT the maximum length of data that column is designed to hold.
	www.php.net /manual/en/function.mysql-fetch-field.php (676 words)

	Class Field Theory
		In the number field case, all abelian extensions can be parameterized using more general class groups, in the case of global function fields, the same will be achieved using the divisor class group and extensions of it.
		Note that in contrast to the number field case, the ray class group of a function field is infinite.
		Since this function uses the class group of the function field in an essential way, it may be necessary for large examples to precompute the class group.
	www.math.lsu.edu /magma/text715.htm (2760 words)

	Calling a Function
		A function is called with the function name, arguments, and, for external functions, an output field.
		For functions that require this, it is specified in the detailed information for that function.
		Creates a virtual field that may be used in a request as though it is a real data source field.
	www.bgsu.edu /its/admin/focus/mf_functions/usefunc2.htm (318 words)

	Correlation function (quantum field theory) - Wikipedia, the free encyclopedia
		In quantum field theory, correlation functions generalize the concept of correlation functions in statistics.
		Depending on n (the number of inserted operators), the correlation functions are called one-point function (tadpole), two-point function, and so on.
		Sometimes, the phrase Green's function is used not only for two-point functions, but for any correlators.
	en.wikipedia.org /wiki/Correlation_function_(quantum_field_theory) (161 words)

	PHP: mysql_field_name - Manual
		if you are trying to get all the field names from your table, but don't feel like doing all that typing.
		This is useful if you have a result set that joins several tables dynamicaly and you are never sure what all the fields will be when you come to display them.
		I suggest you place this within a loop through your result rows and include a field flag check around the echo to only show certain data types like this.
	www.php.net /manual/en/function.mysql-field-name.php (467 words)

	Appendix E - Import Field Parameters and Function Fields (Site not responding. Last check: 2007-10-03)
		These parameters may be required by a function field, or they may be added by the user to change the way the import process handles a record.
		Placing a value in square brackets (‘[ ]’) after the field name indicates that the value inside the square brackets should be used for the value.
		By placing these fields at the bottom of the import setup, no additional fields are necessary in the import file.
	www.comtronic.com /debtmaster/dmwhelp/16_appen/appendix/import_f.htm (2429 words)

	FUNCTION FIELD ARITHMETIC
		This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems.
		While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons.
		It certainly will be useful to graduate students wishing to pursue research in the area of function fields, and at the same time it can be used as a reference book.
	www.worldscibooks.com /books/mathematics/5535.html (354 words)

	Modify Field Dialog: Function, Entry/Exit System, or Alert Inputs
		Note: Some functions may require some input values to be integers, such as when a number of bars is being specified as a period.
		Note: If this is a field defined for an entire group, optimization cannot be turned off for this field once it has been used.
		The Modify Field Dialog has many different property pages that will be displayed as is appropriate for the type of field being modified.
	www.tradingsolutions.com /webhelp/dialogs/hidd_field_func_inputs.html (961 words)

	Modify Field Dialog: Function, Entry/Exit System, or Alert Definition
		To select a function definition, entry/exit system, alert, or trading solution to use for a field, select a group from the group list, then select an entry from that group.
		This function definition has a problem which is causing it to not resolve properly.
		This is typically due to the function requiring an external product to be installed or due to the function requiring a licensing step to be completed before being used.
	www.tradingsolutions.com /webhelp/dialogs/hidd_field_function.html (861 words)

	Python: module field
		The underlying functions of aryOperation and aryFunction field
		Returns a Field object whose data is the result of the binary
		Field object that is a copy of all the metadata and only the meta-
	geosci.uchicago.edu /csc/modelutil/doc/field.html (3779 words)

	Function Field (Site not responding. Last check: 2007-10-03)
		The torsion or division polynomials are the polynomials or functions defining the subschemes of n-torsion points on the elliptic curve.
		The affine equation order of the function field is the natural home of the torsion polynomials.
		A point worth noting is that even if the roots of the division polynomial lie in the field, the corresponding points may not, instead lying in a quadratic extension.
	www.umich.edu /~gpcc/scs/magma/text1061.htm (442 words)

	VaMMIS Recipient Enrollment Menu, Function (Site not responding. Last check: 2007-10-03)
		The Function field allows the selection of a function.
		Only available when the Select field is Case and Enrollee.
		This is a required field unless you are initiating a name search.
	www.vcu.edu /vissta/medialab/vammis/em_function.htm (89 words)

	Introduction to VisAD - Functions
		is the subclass of Function for functions represented by finite sets of samples of function values (for example, a satellite image samples a continuous radiance function at a finite set of pixel locations).
		While mathematically this is a continuous function, in reality, a vertical profile of temperature like this is usually sampled as discrete points along the vertical extent, so would be implemented using a Field or one of it's subclasses.
		The resample method is invoked implicitly for many visualization and mathematical operations on Functions and can be invoked by applications for image remapping and a variety of similar Function operations.
	www.unidata.ucar.edu /staff/donm/visad/functions.html (534 words)

	VisAD: Interface Function
		Function is the interface for approximate implmentations of mathematical function.
		Resample range values of this Function to domain samples in set; return a Field (i.e., a finite sampling of a Function).
		Data object corresponding to the function value at that domain, using the sampling_mode and error_modes specified.
	www.ssec.wisc.edu /~dglo/visad/visad/Function.html (1020 words)

	Transient Field Problems
		Thus, the generalized exact virtual or weighting function field for the transient field problems can be approximately represented as:
		It is now important to note that since W(t) is a generalized approximated virtual or weighting function field, one cannot disregard the choice of
		as was the case with the generalized exact virtual or weighting function field.
	www.menet.umn.edu /~xiangmin/wf/node22.html (259 words)

	PHP mysql_field_flags() Function
		The mysql_field_flags() function returns the flags of a field in a recordset.
		This function gets field data from the mysql_query() function and returns a string on success, or FALSE on failure or when there are no more rows.
		The data pointer is the result from the mysql_query() function
	www.w3schools.com /php/func_mysql_field_flags.asp (411 words)

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