id stringlengths 14 20 | title stringlengths 4 181 | text stringlengths 1 43k | source stringclasses 1
value |
|---|---|---|---|
wiki_25_chunk_31 | Algebraic geometry | Nowadays, the projective space Pn of dimension n is usually defined as the set of the lines passing through a point, considered as the origin, in the affine space of dimension , or equivalently to the set of the vector lines in a vector space of dimension . When a coordinate system has been chosen in the space of dimen... | wikipedia |
wiki_25_chunk_32 | Algebraic geometry | A polynomial in variables vanishes at all points of a line passing through the origin if and only if it is homogeneous. In this case, one says that the polynomial vanishes at the corresponding point of Pn. This allows us to define a projective algebraic set in Pn as the set , where a finite set of homogeneous polynomi... | wikipedia |
wiki_25_chunk_33 | Algebraic geometry | The only regular functions which may be defined properly on a projective variety are the constant functions. Thus this notion is not used in projective situations. On the other hand, the field of the rational functions or function field is a useful notion, which, similarly to the affine case, is defined as the set of ... | wikipedia |
wiki_25_chunk_34 | Algebraic geometry | The fact that the field of the real numbers is an ordered field cannot be ignored in such a study. For example, the curve of equation is a circle if , but does not have any real point if . It follows that real algebraic geometry is not only the study of the real algebraic varieties, but has been generalized to the stu... | wikipedia |
wiki_25_chunk_35 | Algebraic geometry | One of the challenging problems of real algebraic geometry is the unsolved Hilbert's sixteenth problem: Decide which respective positions are possible for the ovals of a nonsingular plane curve of degree 8. | wikipedia |
wiki_25_chunk_36 | Algebraic geometry | Computational algebraic geometry
One may date the origin of computational algebraic geometry to meeting EUROSAM'79 (International Symposium on Symbolic and Algebraic Manipulation) held at Marseille, France, in June 1979. At this meeting,
Dennis S. Arnon showed that George E. Collins's Cylindrical algebraic decomposit... | wikipedia |
wiki_25_chunk_37 | Algebraic geometry | Since then, most results in this area are related to one or several of these items either by using or improving one of these algorithms, or by finding algorithms whose complexity is simply exponential in the number of the variables. A body of mathematical theory complementary to symbolic methods called numerical algebr... | wikipedia |
wiki_25_chunk_38 | Algebraic geometry | A Gröbner basis is a system of generators of a polynomial ideal whose computation allows the deduction of many properties of the affine algebraic variety defined by the ideal. | wikipedia |
wiki_25_chunk_39 | Algebraic geometry | Given an ideal I defining an algebraic set V:
V is empty (over an algebraically closed extension of the basis field), if and only if the Gröbner basis for any monomial ordering is reduced to {1}.
By means of the Hilbert series one may compute the dimension and the degree of V from any Gröbner basis of I for a monomia... | wikipedia |
wiki_25_chunk_40 | Algebraic geometry | Gröbner basis computations do not allow one to compute directly the primary decomposition of I nor the prime ideals defining the irreducible components of V, but most algorithms for this involve Gröbner basis computation. The algorithms which are not based on Gröbner bases use regular chains but may need Gröbner bases ... | wikipedia |
wiki_25_chunk_41 | Algebraic geometry | Gröbner bases are deemed to be difficult to compute. In fact they may contain, in the worst case, polynomials whose degree is doubly exponential in the number of variables and a number of polynomials which is also doubly exponential. However, this is only a worst case complexity, and the complexity bound of Lazard's al... | wikipedia |
wiki_25_chunk_42 | Algebraic geometry | Cylindrical algebraic decomposition (CAD)
CAD is an algorithm which was introduced in 1973 by G. Collins to implement with an acceptable complexity the Tarski–Seidenberg theorem on quantifier elimination over the real numbers. | wikipedia |
wiki_25_chunk_43 | Algebraic geometry | This theorem concerns the formulas of the first-order logic whose atomic formulas are polynomial equalities or inequalities between polynomials with real coefficients. These formulas are thus the formulas which may be constructed from the atomic formulas by the logical operators and (∧), or (∨), not (¬), for all (∀) an... | wikipedia |
wiki_25_chunk_44 | Algebraic geometry | The complexity of CAD is doubly exponential in the number of variables. This means that CAD allows, in theory, to solve every problem of real algebraic geometry which may be expressed by such a formula, that is almost every problem concerning explicitly given varieties and semi-algebraic sets. While Gröbner basis compu... | wikipedia |
wiki_25_chunk_45 | Algebraic geometry | Since 1973, most of the research on this subject is devoted either to improving CAD or finding alternative algorithms in special cases of general interest. As an example of the state of art, there are efficient algorithms to find at least a point in every connected component of a semi-algebraic set, and thus to test if... | wikipedia |
wiki_25_chunk_46 | Algebraic geometry | Asymptotic complexity vs. practical efficiency
The basic general algorithms of computational geometry have a double exponential worst case complexity. More precisely, if d is the maximal degree of the input polynomials and n the number of variables, their complexity is at most for some constant c, and, for some input... | wikipedia |
wiki_25_chunk_47 | Algebraic geometry | Among these algorithms which solve a sub problem of the problems solved by Gröbner bases, one may cite testing if an affine variety is empty and solving nonhomogeneous polynomial systems which have a finite number of solutions. Such algorithms are rarely implemented because, on most entries Faugère's F4 and F5 algorith... | wikipedia |
wiki_25_chunk_48 | Algebraic geometry | The main algorithms of real algebraic geometry which solve a problem solved by CAD are related to the topology of semi-algebraic sets. One may cite counting the number of connected components, testing if two points are in the same components or computing a Whitney stratification of a real algebraic set. They have a com... | wikipedia |
wiki_25_chunk_49 | Algebraic geometry | Abstract modern viewpoint
The modern approaches to algebraic geometry redefine and effectively extend the range of basic objects in various levels of generality to schemes, formal schemes, ind-schemes, algebraic spaces, algebraic stacks and so on. The need for this arises already from the useful ideas within theory of... | wikipedia |
wiki_25_chunk_50 | Algebraic geometry | Most remarkably, in the late 1950s, algebraic varieties were subsumed into Alexander Grothendieck's concept of a scheme. Their local objects are affine schemes or prime spectra which are locally ringed spaces which form a category which is antiequivalent to the category of commutative unital rings, extending the dualit... | wikipedia |
wiki_25_chunk_51 | Algebraic geometry | Sometimes other algebraic sites replace the category of affine schemes. For example, Nikolai Durov has introduced commutative algebraic monads as a generalization of local objects in a generalized algebraic geometry. Versions of a tropical geometry, of an absolute geometry over a field of one element and an algebraic a... | wikipedia |
wiki_25_chunk_52 | Algebraic geometry | The language of schemes, stacks and generalizations has proved to be a valuable way of dealing with geometric concepts and became cornerstones of modern algebraic geometry. | wikipedia |
wiki_25_chunk_53 | Algebraic geometry | Algebraic stacks can be further generalized and for many practical questions like deformation theory and intersection theory, this is often the most natural approach. One can extend the Grothendieck site of affine schemes to a higher categorical site of derived affine schemes, by replacing the commutative rings with an... | wikipedia |
wiki_25_chunk_54 | Algebraic geometry | History | wikipedia |
wiki_25_chunk_55 | Algebraic geometry | Before the 16th century
Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC. The Delian problem, for instance, was to construct a length x so that the cube of side x contained the same volume as the rectangular box a2b for given sides a and b. Menaechmus (circ... | wikipedia |
wiki_25_chunk_56 | Algebraic geometry | Renaissance | wikipedia |
wiki_25_chunk_57 | Algebraic geometry | Such techniques of applying geometrical constructions to algebraic problems were also adopted by a number of Renaissance mathematicians such as Gerolamo Cardano and Niccolò Fontana "Tartaglia" on their studies of the cubic equation. The geometrical approach to construction problems, rather than the algebraic one, was f... | wikipedia |
wiki_25_chunk_58 | Algebraic geometry | During the same period, Blaise Pascal and Gérard Desargues approached geometry from a different perspective, developing the synthetic notions of projective geometry. Pascal and Desargues also studied curves, but from the purely geometrical point of view: the analog of the Greek ruler and compass construction. Ultimatel... | wikipedia |
wiki_25_chunk_59 | Algebraic geometry | 19th and early 20th century
It took the simultaneous 19th century developments of non-Euclidean geometry and Abelian integrals in order to bring the old algebraic ideas back into the geometrical fold. The first of these new developments was seized up by Edmond Laguerre and Arthur Cayley, who attempted to ascertain the ... | wikipedia |
wiki_25_chunk_60 | Algebraic geometry | The second early 19th century development, that of Abelian integrals, would lead Bernhard Riemann to the development of Riemann surfaces. | wikipedia |
wiki_25_chunk_61 | Algebraic geometry | In the same period began the algebraization of the algebraic geometry through commutative algebra. The prominent results in this direction are Hilbert's basis theorem and Hilbert's Nullstellensatz, which are the basis of the connexion between algebraic geometry and commutative algebra, and Macaulay's multivariate resul... | wikipedia |
wiki_25_chunk_62 | Algebraic geometry | 20th century
B. L. van der Waerden, Oscar Zariski and André Weil developed a foundation for algebraic geometry based on contemporary commutative algebra, including valuation theory and the theory of ideals. One of the goals was to give a rigorous framework for proving the results of Italian school of algebraic geometry... | wikipedia |
wiki_25_chunk_63 | Algebraic geometry | In the 1950s and 1960s, Jean-Pierre Serre and Alexander Grothendieck recast the foundations making use of sheaf theory. Later, from about 1960, and largely led by Grothendieck, the idea of schemes was worked out, in conjunction with a very refined apparatus of homological techniques. After a decade of rapid development... | wikipedia |
wiki_25_chunk_64 | Algebraic geometry | An important class of varieties, not easily understood directly from their defining equations, are the abelian varieties, which are the projective varieties whose points form an abelian group. The prototypical examples are the elliptic curves, which have a rich theory. They were instrumental in the proof of Fermat's La... | wikipedia |
wiki_25_chunk_65 | Algebraic geometry | In parallel with the abstract trend of the algebraic geometry, which is concerned with general statements about varieties, methods for effective computation with concretely-given varieties have also been developed, which lead to the new area of computational algebraic geometry. One of the founding methods of this area ... | wikipedia |
wiki_25_chunk_66 | Algebraic geometry | Analytic geometry
An analytic variety is defined locally as the set of common solutions of several equations involving analytic functions. It is analogous to the included concept of real or complex algebraic variety. Any complex manifold is an analytic variety. Since analytic varieties may have singular points, not all... | wikipedia |
wiki_25_chunk_67 | Algebraic geometry | Applications
Algebraic geometry now finds applications in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling. There are also connections to string theory, game theory, graph matchings, solitons and integer programming. See also Algebraic statistics
Differential geometry... | wikipedia |
wiki_25_chunk_68 | Algebraic geometry | Textbooks and references for schemes External links Foundations of Algebraic Geometry by Ravi Vakil, 808 pp.
Algebraic geometry entry on PlanetMath
English translation of the van der Waerden textbook
The Stacks Project, an open source textbook and reference work on algebraic stacks and algebraic geometry Fields o... | wikipedia |
wiki_26_chunk_0 | Array data structure | In computer science, an array data structure, or simply an array, is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is stored such that the position of each element can be computed from its index tuple by a mathematical formula... | wikipedia |
wiki_26_chunk_1 | Array data structure | For example, an array of 10 32-bit (4-byte) integer variables, with indices 0 through 9, may be stored as 10 words at memory addresses 2000, 2004, 2008, ..., 2036, (in hexadecimal: 0x7D0, 0x7D4, 0x7D8, ..., 0x7F4) so that the element with index i has the address 2000 + (i × 4). The memory address of the first element o... | wikipedia |
wiki_26_chunk_2 | Array data structure | Because the mathematical concept of a matrix can be represented as a two-dimensional grid, two-dimensional arrays are also sometimes called matrices. In some cases the term "vector" is used in computing to refer to an array, although tuples rather than vectors are the more mathematically correct equivalent. Tables are ... | wikipedia |
wiki_26_chunk_3 | Array data structure | Arrays are among the oldest and most important data structures, and are used by almost every program. They are also used to implement many other data structures, such as lists and strings. They effectively exploit the addressing logic of computers. In most modern computers and many external storage devices, the memory ... | wikipedia |
wiki_26_chunk_4 | Array data structure | Arrays are useful mostly because the element indices can be computed at run time. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are required to have the same size and should use the same dat... | wikipedia |
wiki_26_chunk_5 | Array data structure | The term array is often used to mean array data type, a kind of data type provided by most high-level programming languages that consists of a collection of values or variables that can be selected by one or more indices computed at run-time. Array types are often implemented by array structures; however, in some langu... | wikipedia |
wiki_26_chunk_6 | Array data structure | The term is also used, especially in the description of algorithms, to mean associative array or "abstract array", a theoretical computer science model (an abstract data type or ADT) intended to capture the essential properties of arrays. | wikipedia |
wiki_26_chunk_7 | Array data structure | History
The first digital computers used machine-language programming to set up and access array structures for data tables, vector and matrix computations, and for many other purposes. John von Neumann wrote the first array-sorting program (merge sort) in 1945, during the building of the first stored-program computer.... | wikipedia |
wiki_26_chunk_8 | Array data structure | Assembly languages generally have no special support for arrays, other than what the machine itself provides. The earliest high-level programming languages, including FORTRAN (1957), Lisp (1958), COBOL (1960), and ALGOL 60 (1960), had support for multi-dimensional arrays, and so has C (1972). In C++ (1983), class templ... | wikipedia |
wiki_26_chunk_9 | Array data structure | Applications
Arrays are used to implement mathematical vectors and matrices, as well as other kinds of rectangular tables. Many databases, small and large, consist of (or include) one-dimensional arrays whose elements are records. | wikipedia |
wiki_26_chunk_10 | Array data structure | Arrays are used to implement other data structures, such as lists, heaps, hash tables, deques, queues, stacks, strings, and VLists. Array-based implementations of other data structures are frequently simple and space-efficient (implicit data structures), requiring little space overhead, but may have poor space complexi... | wikipedia |
wiki_26_chunk_11 | Array data structure | One or more large arrays are sometimes used to emulate in-program dynamic memory allocation, particularly memory pool allocation. Historically, this has sometimes been the only way to allocate "dynamic memory" portably. | wikipedia |
wiki_26_chunk_12 | Array data structure | Arrays can be used to determine partial or complete control flow in programs, as a compact alternative to (otherwise repetitive) multiple IF statements. They are known in this context as control tables and are used in conjunction with a purpose built interpreter whose control flow is altered according to values contain... | wikipedia |
wiki_26_chunk_13 | Array data structure | Element identifier and addressing formulas
When data objects are stored in an array, individual objects are selected by an index that is usually a non-negative scalar integer. Indexes are also called subscripts. An index maps the array value to a stored object. There are three ways in which the elements of an array can... | wikipedia |
wiki_26_chunk_14 | Array data structure | 0 (zero-based indexing) The first element of the array is indexed by subscript of 0.
1 (one-based indexing) The first element of the array is indexed by subscript of 1.
n (n-based indexing) The base index of an array can be freely chosen. Usually programming languages allowing n-based indexing also allow negative ind... | wikipedia |
wiki_26_chunk_15 | Array data structure | Using zero based indexing is the design choice of many influential programming languages, including C, Java and Lisp. This leads to simpler implementation where the subscript refers to an offset from the starting position of an array, so the first element has an offset of zero. | wikipedia |
wiki_26_chunk_16 | Array data structure | Arrays can have multiple dimensions, thus it is not uncommon to access an array using multiple indices. For example, a two-dimensional array A with three rows and four columns might provide access to the element at the 2nd row and 4th column by the expression A[1][3] in the case of a zero-based indexing system. Thus tw... | wikipedia |
wiki_26_chunk_17 | Array data structure | In standard arrays, each index is restricted to a certain range of consecutive integers (or consecutive values of some enumerated type), and the address of an element is computed by a "linear" formula on the indices. One-dimensional arrays
A one-dimensional array (or single dimension array) is a type of linear array. A... | wikipedia |
wiki_26_chunk_18 | Array data structure | As an example consider the C declaration int anArrayName[10]; which declares a one-dimensional array of ten integers. Here, the array can store ten elements of type int . This array has indices starting from zero through nine. For example, the expressions anArrayName[0] and anArrayName[9] are the first and last element... | wikipedia |
wiki_26_chunk_19 | Array data structure | If the valid element indices begin at 0, the constant B is simply the address of the first element of the array. For this reason, the C programming language specifies that array indices always begin at 0; and many programmers will call that element "zeroth" rather than "first". | wikipedia |
wiki_26_chunk_20 | Array data structure | However, one can choose the index of the first element by an appropriate choice of the base address B. For example, if the array has five elements, indexed 1 through 5, and the base address B is replaced by , then the indices of those same elements will be 31 to 35. If the numbering does not start at 0, the constant B ... | wikipedia |
wiki_26_chunk_21 | Array data structure | Multidimensional arrays
For a multidimensional array, the element with indices i,j would have address B + c · i + d · j, where the coefficients c and d are the row and column address increments, respectively. More generally, in a k-dimensional array, the address of an element with indices i1, i2, ..., ik is
B + c1 · i... | wikipedia |
wiki_26_chunk_22 | Array data structure | This means that array a has 2 rows and 3 columns, and the array is of integer type. Here we can store 6 elements they will be stored linearly but starting from first row linear then continuing with second row. The above array will be stored as a11, a12, a13, a21, a22, a23. This formula requires only k multiplications a... | wikipedia |
wiki_26_chunk_23 | Array data structure | The coefficients ck must be chosen so that every valid index tuple maps to the address of a distinct element. | wikipedia |
wiki_26_chunk_24 | Array data structure | If the minimum legal value for every index is 0, then B is the address of the element whose indices are all zero. As in the one-dimensional case, the element indices may be changed by changing the base address B. Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then ... | wikipedia |
wiki_26_chunk_25 | Array data structure | Dope vectors
The addressing formula is completely defined by the dimension d, the base address B, and the increments c1, c2, ..., ck. It is often useful to pack these parameters into a record called the array's descriptor or stride vector or dope vector. The size of each element, and the minimum and maximum values allo... | wikipedia |
wiki_26_chunk_26 | Array data structure | Compact layouts Often the coefficients are chosen so that the elements occupy a contiguous area of memory. However, that is not necessary. Even if arrays are always created with contiguous elements, some array slicing operations may create non-contiguous sub-arrays from them. There are two systematic compact layouts fo... | wikipedia |
wiki_26_chunk_27 | Array data structure | In the row-major order layout (adopted by C for statically declared arrays), the elements in each row are stored in consecutive positions and all of the elements of a row have a lower address than any of the elements of a consecutive row:
{| class="wikitable"
|-
| 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9
|} | wikipedia |
wiki_26_chunk_28 | Array data structure | In column-major order (traditionally used by Fortran), the elements in each column are consecutive in memory and all of the elements of a column have a lower address than any of the elements of a consecutive column:
{| class="wikitable"
|-
| 1 || 4 || 7 || 2 || 5 || 8 || 3 || 6 || 9
|} | wikipedia |
wiki_26_chunk_29 | Array data structure | For arrays with three or more indices, "row major order" puts in consecutive positions any two elements whose index tuples differ only by one in the last index. "Column major order" is analogous with respect to the first index. | wikipedia |
wiki_26_chunk_30 | Array data structure | In systems which use processor cache or virtual memory, scanning an array is much faster if successive elements are stored in consecutive positions in memory, rather than sparsely scattered. Many algorithms that use multidimensional arrays will scan them in a predictable order. A programmer (or a sophisticated compiler... | wikipedia |
wiki_26_chunk_31 | Array data structure | Static arrays have a size that is fixed when they are created and consequently do not allow elements to be inserted or removed. However, by allocating a new array and copying the contents of the old array to it, it is possible to effectively implement a dynamic version of an array; see dynamic array. If this operation ... | wikipedia |
wiki_26_chunk_32 | Array data structure | Some array data structures do not reallocate storage, but do store a count of the number of elements of the array in use, called the count or size. This effectively makes the array a dynamic array with a fixed maximum size or capacity; Pascal strings are examples of this. Non-linear formulas
More complicated (non-linea... | wikipedia |
wiki_26_chunk_33 | Array data structure | Efficiency
Both store and select take (deterministic worst case) constant time. Arrays take linear (O(n)) space in the number of elements n that they hold. | wikipedia |
wiki_26_chunk_34 | Array data structure | In an array with element size k and on a machine with a cache line size of B bytes, iterating through an array of n elements requires the minimum of ceiling(nk/B) cache misses, because its elements occupy contiguous memory locations. This is roughly a factor of B/k better than the number of cache misses needed to acces... | wikipedia |
wiki_26_chunk_35 | Array data structure | Memory-wise, arrays are compact data structures with no per-element overhead. There may be a per-array overhead (e.g., to store index bounds) but this is language-dependent. It can also happen that elements stored in an array require less memory than the same elements stored in individual variables, because several arr... | wikipedia |
wiki_26_chunk_36 | Array data structure | Array accesses with statically predictable access patterns are a major source of data parallelism. Comparison with other data structures Dynamic arrays or growable arrays are similar to arrays but add the ability to insert and delete elements; adding and deleting at the end is particularly efficient. However, they rese... | wikipedia |
wiki_26_chunk_37 | Array data structure | Associative arrays provide a mechanism for array-like functionality without huge storage overheads when the index values are sparse. For example, an array that contains values only at indexes 1 and 2 billion may benefit from using such a structure. Specialized associative arrays with integer keys include Patricia tries... | wikipedia |
wiki_26_chunk_38 | Array data structure | Linked lists allow constant time removal and insertion in the middle but take linear time for indexed access. Their memory use is typically worse than arrays, but is still linear. | wikipedia |
wiki_26_chunk_39 | Array data structure | An Iliffe vector is an alternative to a multidimensional array structure. It uses a one-dimensional array of references to arrays of one dimension less. For two dimensions, in particular, this alternative structure would be a vector of pointers to vectors, one for each row(pointer on c or c++). Thus an element in row i... | wikipedia |
wiki_26_chunk_40 | Array data structure | Dimension
The dimension of an array is the number of indices needed to select an element. Thus, if the array is seen as a function on a set of possible index combinations, it is the dimension of the space of which its domain is a discrete subset. Thus a one-dimensional array is a list of data, a two-dimensional array i... | wikipedia |
wiki_26_chunk_41 | Array data structure | This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array. For example, an array with 5 rows and 4 columns is two-dimensional, but such matrices form a 20-dimensional space. Similarly, a three-dimensional vector can be represented by a on... | wikipedia |
wiki_27_chunk_0 | Automatic number announcement circuit | An automatic number announcement circuit (ANAC) is a component of a central office of a telephone company that provides a service to installation and service technicians to determine the telephone number of a line. The facility has a telephone number that may be called to listen to an automatic announcement that includ... | wikipedia |
wiki_27_chunk_1 | Automatic number announcement circuit | Operation
A technician calls the local telephone number of the automatic number announcement service. This call is connected to equipment at a local central office that uses a voice synthesizer or digital samples to announce the telephone number of the line calling in. The main purpose of this system is to allow telep... | wikipedia |
wiki_27_chunk_2 | Automatic number announcement circuit | Automatic number announcement systems are based on automatic number identification, and meant for phone company technicians, the ANAC system works with unlisted numbers, numbers with caller ID blocking, and numbers with no outgoing calls allowed. Installers of multi-line business services where outgoing calls from all ... | wikipedia |
wiki_27_chunk_3 | Automatic number announcement circuit | Some ANACs are very regional or local in scope, while others are state-/province- or area-code-wide: there appears to be no consistent national system for them. Most are provider-specific. Every telephone company, whether large or small, determines its own ANAC for each individual central office, which tends to perpetu... | wikipedia |
wiki_27_chunk_4 | Automatic number announcement circuit | 958 local test exchanges
Under the North American Numbering Plan, almost all North American area codes reserve telephone numbers beginning with 958 and 959 for internal local and long-distance testing (respectively), sometimes called plant testing. (One exception is Winnipeg, which reserves 959 only.) Numbers within t... | wikipedia |
wiki_27_chunk_5 | Automatic number announcement circuit | In some area codes, multiple additional prefixes had been reserved for test purposes, in addition to the standard 958 and 959. Many area codes reserved 999; 320 was also formerly reserved in Bell Canada territory. As widespread inefficiencies in numbering (such as the assignment of entire blocks of 10000 numbers to eve... | wikipedia |
wiki_27_chunk_6 | Automatic number announcement circuit | Some carriers have been known to disable payphone calls to 958 or 959 test lines, such as Bell Canada's system-wide ANAC line at (area code) 958-2580. Conversely, a standard line on which voice service has been unsubscribed (such as an ADSL dry loop) may still accept calls to the 958 test exchange but not allow calls t... | wikipedia |
wiki_27_chunk_7 | Automatic number announcement circuit | Tollfree numbers
Some large telephone companies have toll-free numbers set up. In most cases, these numbers remain undisclosed to prevent abuse, but MCI maintains this widely published, toll-free ANAC: 1-800-437-7950. This is distinct from technical support and other lines which use ANI so that a computer can automatic... | wikipedia |
wiki_27_chunk_8 | Automatic number announcement circuit | Formerly, some companies changed their ANAC number every month for secrecy; this is still the case with a few numbers. In one example of this concern, most payphones in the United States are assigned a telephone number and can ring if the number is called. The phone can then be used to make and receive calls by anyone,... | wikipedia |
wiki_27_chunk_9 | Automatic number announcement circuit | Late in the 20th century, after caller ID and pre-paid cell phone service became commonplace and with these services being more easily exploited for criminal purposes, especially in the case of burner phones, this type of abuse of payphones faded from concern. In Canada, this behaviour has always been more difficult. A... | wikipedia |
wiki_27_chunk_10 | Automatic number announcement circuit | There are some private national toll-free numbers that use ANI and then have a computer read back the number that is calling, but these are not intended for use in identifying the customer's own phone number. They are used in order for the agent in the call center to confirm the phone the customer is calling from, so t... | wikipedia |
wiki_27_chunk_11 | Automatic number announcement circuit | One such toll-free service is one owned by MCI - 1-800-444-4444. This number (US only) is easy to remember and, when called, will read back the number after a very short message. A suspended (out of service) line or an incoming only line would not be able to reach any toll-free numbers. ANAC numbers | wikipedia |
wiki_27_chunk_12 | Automatic number announcement circuit | These numbers appear on various lists circulated on-line, many from the 1980s and 1990s. Most were published years ago by Phrack, 2600 Magazine, the alt.2600 Usenet newsgroup (as part of the FAQ) or phone phreaks and are now hopelessly outdated. The information is not reliable, as numbers change often. Many of the list... | wikipedia |
wiki_27_chunk_13 | Automatic number announcement circuit | United States
The North American Numbering Plan reserves 958-XXXX and 1-NPA-959-XXXX for local and long-distance test numbers in almost all USA and Canadian area codes. | wikipedia |
wiki_27_chunk_14 | Automatic number announcement circuit | Frequently, a prefix outside the 958 or 959 range (such as 200, 997, 998, 999) was also listed as a test exchange, only to be reclaimed and issued as a block of standard numbers at a later date. NANPA's utilised codes report will indicate 'UA' (unassignable) for valid test prefixes; if a formerly 'UA' code newly appear... | wikipedia |
wiki_27_chunk_15 | Automatic number announcement circuit | 958, 959 test prefixes The standard location for test numbers in most NANP area codes, although specific local numbers vary. 1-NPA-959 traditionally contained long-distance test numbers, but this convention is often ignored; AT&T's 959-1122 and GTE (Verizon)'s 959-1114 are local. Some area codes will flag additional co... | wikipedia |
wiki_27_chunk_16 | Automatic number announcement circuit | A few commonly-used 958 or 959 numbers for major incumbent landline carriers:
958, as a three-digit number in many former NYNEX/Bell Atlantic areas, now Verizon or FairPoint (207 Maine, 212 New York, 215 Pennsylvania, 315 New York, 413 Massachusetts, 508 Massachusetts, 516 New York, 603 New Hampshire, 609 New Jersey, ... | wikipedia |
wiki_27_chunk_17 | Automatic number announcement circuit | Numbers otherwise vary arbitrarily by locality:
216: 959-9892 Akron/Canton/Cleveland/Lorain/Youngstown, Ohio
301: 958-9968 Hagerstown/Rockville, Maryland
309: 959-1114 Central Illinois (Frontier, Ex-Verizon)
309: 959-9833 Quad City Illinois Area (AT&T)
412: 959-1114 Pittsburgh Pennsylvania (Verizon)
503: 958 Port... | wikipedia |
wiki_27_chunk_18 | Automatic number announcement circuit | Other regionally nonassignable (UA) test prefixes These are, over time, being phased out. As each reservation consumes a block of 10000 numbers, the prefixes are increasingly being recovered for use as regular exchange codes and the test numbers moved (usually) to 958-XXXX. If the number is active for test, the prefix ... | wikipedia |
wiki_27_chunk_19 | Automatic number announcement circuit | Vertical service codes, carrier-specific Most vertical service codes are activated with #, * or a leading 11- and are internal to an individual landline or wireless carrier. This block mostly contains codes to activate or deactivate features such as call forwarding, but rarely a test number may appear in this set.
515... | wikipedia |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.