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Probabilistic algorithm for computing discrete logarithms
In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. Dedicated to the discrete
Index_calculus_algorithm
Algorithm in computational number theory
algorithm, see the index calculus algorithm. The algorithm is well known by two names. The first is "Pollard's kangaroo algorithm". This name is a reference
Pollard's_kangaroo_algorithm
Baby-step giant-step Index calculus algorithm Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Euclidean algorithm: computes the greatest
List_of_algorithms
Problem of inverting exponentiation in groups
sieve Index calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm for logarithms Pollard's kangaroo algorithm (aka Pollard's
Discrete_logarithm
Algorithm to solve the discrete logarithm problem
to the sieving step in other sieving algorithms such as the Number Field Sieve or the index calculus algorithm. Instead of numbers one sieves through
Function_field_sieve
Best results achieved to date
than 550 CPU-hours. This computation was performed using the same index calculus algorithm as in the recent computation in the field with 24080 elements.
Discrete_logarithm_records
Specialized notation for multivariable calculus
while the tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups
Matrix_calculus
Differential calculus on function spaces
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and
Calculus_of_variations
Operation in mathematical calculus
integral, called integration, is one of the two fundamental operations of calculus, along with differentiation. Integration was initially used to solve problems
Integral
Small set of prime numbers used in sieving algorithms
between these algorithms is essentially the methods used to generate (x, y) candidates. Factor bases are also used in the Index calculus algorithm for computing
Factor_base
Branch of mathematical analysis
Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number
Fractional_calculus
Collection of random variables
processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical
Stochastic_process
Overview of and topical guide to algorithms
Lambda calculus — formal system used in the study of computation Von Neumann architecture — computer architecture influencing practical algorithm implementation
Outline_of_algorithms
Rafael E. Núñez Algebra — Serge Lang Algebra: Chapter 0 — Paolo Aluffi Calculus on Manifolds — Michael Spivak Principles of Mathematical Analysis — Walter
List_of_mathematics_books
Infinitesimal calculus on functions defined on a geometric algebra
In mathematics, geometric calculus extends geometric algebra to include differentiation and integration. The formalism is powerful and can be shown to
Geometric_calculus
Algorithms to complete a sudoku
computer programs that will solve Sudoku puzzles using a backtracking algorithm, which is a type of brute force search. Backtracking is a depth-first
Sudoku_solving_algorithms
Number, approximately 3.14
definition because, as Remmert 2012 explains, differential calculus typically precedes integral calculus in the university curriculum, so it is desirable to
Pi
Mathematical notation
Multi-index notation is a mathematical notation that simplifies formulas used in multivariable calculus, partial differential equations and the theory
Multi-index_notation
Method in computational algebra
Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields). The algorithm consists mainly
Berlekamp's_algorithm
Mathematical-logic system based on functions
In mathematical logic, the lambda calculus (also written as λ-calculus) is a formal system for expressing computation based on function abstraction and
Lambda_calculus
Mathematical notion of infinitesimal difference
differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives
Differential_(mathematics)
{\textstyle {\frac {n}{p}}\leq 4} usually suffices. The index calculus algorithm is another algorithm that can be used to solve DLP under some circumstances
Hyperelliptic curve cryptography
Hyperelliptic_curve_cryptography
Algorithm that employs a degree of randomness as part of its logic or procedure
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random
Randomized_algorithm
Extension of propositional modal logic
theoretical computer science, the modal μ-calculus (Lμ, Lμ, or propositional mu-calculus, sometimes just μ-calculus, although this can have a more general
Modal_μ-calculus
Decomposition of a number into a product
efficient non-quantum integer factorization algorithm is known. However, it has not been proven that such an algorithm does not exist. The presumed difficulty
Integer_factorization
Algebraic object with geometric applications
Elwin Bruno Christoffel, and others – as part of the absolute differential calculus. The concept enabled an alternative formulation of the intrinsic differential
Tensor
Programming language designed 1942 to 1945
1938, Zuse discovered that the calculus he had independently devised already existed and was known as propositional calculus. What Zuse had in mind needed
Plankalkül
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Operation on differential forms
in its current form by Élie Cartan in 1899. The resulting calculus, known as exterior calculus, allows for a natural, metric-independent generalization
Exterior_derivative
Number of times a curve wraps around a point in the plane
study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics
Winding_number
Theorem in computability theory
represents an algorithm Fb and P(b) = "yes". We can then define an algorithm H(a, i) as follows: 1. construct a string t that represents an algorithm T(j) such
Rice's_theorem
Notation of differential calculus
In differential calculus, there is no single standard notation for differentiation. Instead, several notations for the derivative of a function or a dependent
Notation_for_differentiation
writing definitions for existing ones. This glossary of calculus is a list of definitions about calculus, its sub-disciplines, and related fields. Contents:
Glossary_of_calculus
Discrete (i.e., incremental) version of infinitesimal calculus
Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of
Discrete_calculus
Problem in computer science
in its computational power to Turing machines, such as Markov algorithms, Lambda calculus, Post systems, register machines, or tag systems. What is important
Halting_problem
Straight path on a curved surface or a Riemannian manifold
the space), and then minimizing this length between the points using the calculus of variations. This has some minor technical problems because there is
Geodesic
Calculus for temporal reasoning (relating to time instances) of events
Allen's interval algebra is a calculus for temporal reasoning that was introduced by James F. Allen in 1983. The calculus defines possible relations between
Allen's_interval_algebra
Association of one output to each input
concept of algorithm, several models of computation have been introduced, the old ones being general recursive functions, lambda calculus, and Turing
Function_(mathematics)
Calculus of functions generalization
In mathematics, calculus on Euclidean space is a generalization of calculus of functions in one or several variables to calculus of functions on Euclidean
Calculus_on_Euclidean_space
Rational number sequence
Jordan, Charles (1950), Calculus of Finite Differences, New York: Chelsea Publ. Co.. Kaneko, M. (2000), "The Akiyama-Tanigawa algorithm for Bernoulli numbers"
Bernoulli_number
Algorithm for factoring polynomials over finite fields
the Cantor–Zassenhaus algorithm is a method for factoring polynomials over finite fields (also called Galois fields). The algorithm consists mainly of exponentiation
Cantor–Zassenhaus_algorithm
Mathematical identities
are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional
Vector_calculus_identities
Alternative form of government or social ordering
also referred to as algorithmic regulation, regulation by algorithms, algorithmic governance, algocratic governance, algorithmic legal order, or algocracy
Government_by_algorithm
Type of logical system
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system used in mathematics, philosophy
First-order_logic
Theoretical model of computation
related to lambda calculus, namely head reduction and call by name. A redex (one says also β-redex) is a term of the lambda calculus of the form (λ x.
Krivine_machine
problem Index of coincidence Bible code Spurious relationship Monty Hall problem Probable prime Probabilistic algorithm = Randomised algorithm Monte Carlo
List_of_probability_topics
Formula for the derivative of a product
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions
Product_rule
Algorithm to compare text strings using wildcard syntax
§ Implementations. Pattern matching Pattern calculus Glob (programming) Wildcard character List of algorithms "Wildcard characters". ScienceDirect. 2018
Matching_wildcards
Computer system for solving algebra problems
structured Gaussian elimination and Lanczos algorithms for reducing sparse systems which arise in index calculus methods, while Magma uses Markowitz pivoting
Magma (computer algebra system)
Magma_(computer_algebra_system)
Addition of several numbers or other values
telescoping series and is the analogue of the fundamental theorem of calculus in calculus of finite differences, which states that: f ( n ) − f ( m ) = ∫ m
Summation
Certain vector fields are the sum of an irrotational and a solenoidal vector field
the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that certain differentiable vector fields can be resolved into the
Helmholtz_decomposition
Leibniz also develops his version of infinitesimal calculus. 1675—Isaac Newton invents an algorithm for the computation of functional roots. 1680s – Gottfried
Timeline_of_mathematics
Generalization of the product rule in calculus
In calculus, the general Leibniz rule, named after Gottfried Wilhelm Leibniz, generalizes the product rule for the derivative of the product of two functions
General_Leibniz_rule
Index of articles associated with the same name
polynomial of degree at most one), as in first-order approximation and other calculus uses, where it is contrasted with "polynomials of higher degree", or "without
First-order
Theorem in calculus
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through
Divergence_theorem
Relationship between programs and proofs
forms in lambda calculus matches Prawitz's notion of normal deduction in natural deduction, from which it follows that the algorithms for the type inhabitation
Curry–Howard_correspondence
Mathematical function, inverse of an exponential function
commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They help to describe frequency
Logarithm
Vector operator in vector calculus
In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters
Divergence
Academic subfield of computer science
deals with what problems can be solved on a model of computation using an algorithm, how efficiently they can be solved and to what degree (e.g., approximate
Theory_of_computation
Ranges of numbers contained in each other
predecessors of calculus (differentiation and integration). In computer science, sequences of nested intervals is used in algorithms for numerical computation
Nested_intervals
Pattern defining an infinite sequence of numbers
theorem (analysis of algorithms) Mathematical induction Orthogonal polynomials Recursion Recursion (computer science) Time scale calculus Jacobson, Nathan
Recurrence_relation
Matrix of binary truth values
— The algorithm relies on addition being idempotent, cf. p.134 (bottom). Copilowish, Irving (December 1948). "Matrix development of the calculus of relations"
Logical_matrix
Branch of algebraic geometry
characteristic classes, and both its algorithmic aspects and applications remain of current interest. The term Schubert calculus is sometimes used to mean the
Schubert_calculus
Academic journal
journal. Milner, Robin; Parrow, Joachim; Walker, David (1992-09-01). "A calculus of mobile processes, I". Information and Computation. 100 (1): 1–40. doi:10
Information_and_Computation
Algebraic operation on coordinate vectors
order by 2), see Tensor contraction for details. The straightforward algorithm for calculating a floating-point dot product of vectors can suffer from
Dot_product
theory topics Index of wave articles The fields of mathematics and computing intersect both in computer science, the study of algorithms and data structures
Lists_of_mathematics_topics
Infinite sum
many terms, one after the other. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most
Series_(mathematics)
of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives
List_of_theorems
Attempts to formalize the concept of algorithms
Algorithm characterizations are attempts to formalize the word algorithm. Algorithm does not have a generally accepted formal definition. Researchers
Algorithm_characterizations
Mathematical operation in linear algebra
{T}}} Scalar multiplication Matrix calculus, for the interaction of matrix multiplication with operations from calculus Nykamp, Duane. "Multiplying matrices
Matrix_multiplication
Array of numbers
Orthonormalization of a set of vectors Irregular matrix Matrix calculus – Specialized notation for multivariable calculus Matrix function – Function that maps matrices
Matrix_(mathematics)
statistics Bühlmann model Buzen's algorithm BV4.1 (software) c-chart Càdlàg Calculating demand forecast accuracy Calculus of predispositions Calibrated probability
List_of_statistics_articles
Algebraic manipulation of "true" and "false"
propositional calculus have an equivalent expression in Boolean algebra. Thus, Boolean logic is sometimes used to denote propositional calculus performed
Boolean_algebra
Topological space that locally resembles Euclidean space
manifolds are differentiable manifolds; their differentiable structure allows calculus to be done. A Riemannian metric on a manifold allows distances and angles
Manifold
Statement relating differentiable symmetries to conserved quantities
statistical mechanics. Noether's theorem is used in theoretical physics and the calculus of variations. It reveals the fundamental relation between the symmetries
Noether's_theorem
Matrix operation which flips a matrix over its diagonal
be performed on the columns, for example in a fast Fourier transform algorithm, transposing the matrix in memory (to make the columns contiguous) may
Transpose
Array data structure that compactly stores bits
relation may be represented by a bit array called a logical matrix. In the calculus of relations, these arrays are composed with matrix multiplication where
Bit_array
Indexing". 1994. John W. Wheeler; Guarionex Jordan. "An Empirical Study of Term Indexing in the Darwin Implementation of the Model Evolution Calculus"
Term_indexing
Scheduling algorithm for tasks or data flows
w i {\displaystyle w_{i}} emissions opportunities. The different WRR algorithms differ in the distribution of these opportunities in the cycle. In classical
Weighted_round_robin
converse is not necessarily true. Grantham's stated goal when developing the algorithm was to provide a test that primes would always pass and composites would
Quadratic_Frobenius_test
Overview of and topical guide to trigonometry
formula Haversine formula mnemonics in trigonometry All Students Take Calculus List of integrals of trigonometric functions List of integrals of inverse
Outline_of_trigonometry
Class of mathematical software
Calculus is a Mathematica package for doing tensor and exterior calculus on differentiable manifolds. EDC and RGTC, "Exterior Differential Calculus"
Tensor_software
Problem optimization method
Dynamic programming (DP) is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and
Dynamic_programming
Mathematical method in calculus
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product
Integration_by_parts
Manifold upon which it is possible to perform calculus
allow one to apply calculus. Any manifold can be described by a collection of charts (atlas). One may then apply ideas from calculus while working within
Differentiable_manifold
Conditions for switching order of integration in calculus
true if the function is continuous on the rectangle; in multivariable calculus, this weaker result is sometimes also called Fubini's theorem). Tonelli's
Fubini's_theorem
Branch of mathematics
quantitative methods of approximation and convergence. It grew out of calculus, especially the use of derivatives and integrals to study variable quantities
Mathematical_analysis
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
property 3 of the functional calculus, the operator e i ( T ) {\displaystyle e_{i}(T)} is a projection. Moreover, let νi be the index of λi and f ( z ) = ( z
Jordan_normal_form
French mathematician (born 1956)
contributions to the fields of partial differential equations and the calculus of variations. He was a recipient of the 1994 Fields Medal. Lions entered
Pierre-Louis_Lions
Arithmetical operation
Multiplication algorithm Karatsuba algorithm, for large numbers Toom–Cook multiplication, for very large numbers Schönhage–Strassen algorithm, for huge numbers
Multiplication
Polish-born American mathematician (born 1949)
and Gian-Carlo Rota) of one of the founding papers of the modern umbral calculus. In 1985 he and Herman te Riele disproved the Mertens conjecture. In mathematics
Andrew_Odlyzko
The index of physics articles is split into multiple pages due to its size. To navigate by individual letter use the table of contents below. !$@ 0–9
Index_of_physics_articles_(R)
Derivative of a function with multiple variables
variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f ( x
Partial_derivative
Digital signature scheme
. Working in an elliptic curve group provides some defense against index calculus attacks (with the caveat that such attacks are still possible in the
BLS_digital_signature
Swiss mathematician (1707–1783)
mathematics, such as analytic number theory, complex analysis, and infinitesimal calculus. He also introduced much of modern mathematical terminology and notation
Leonhard_Euler
Formula for systems of linear equations
1016/S0024-3795(01)00469-4. Levi-Civita, Tullio (1926). The Absolute Differential Calculus (Calculus of Tensors). Dover. pp. 111–112. ISBN 9780486634012. {{cite book}}:
Cramer's_rule
English polymath (1642–1727)
Gottfried Wilhelm Leibniz for formulating infinitesimal calculus, although he developed calculus years before Leibniz. Newton contributed to and refined
Isaac_Newton
Church, the λ-calculus is strong enough to describe all mechanically computable functions (see Church–Turing thesis). Lambda-calculus is thus effectively
Computable_topology
constraints: Constraint algorithm — for solving Newton's equations with constraints Pantelides algorithm — for reducing the index of a DEA Methods for solving
List of numerical analysis topics
List_of_numerical_analysis_topics
German polymath (1646–1716)
empty set. He anticipated Lagrangian interpolation and algorithmic information theory. His calculus ratiocinator anticipated aspects of the universal Turing
Gottfried_Wilhelm_Leibniz
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
Girl/Female
Welsh
Legendary daughter of GanKy.
Girl/Female
Indian
Light of Lord Inder
Boy/Male
Indian, Punjabi, Sikh
Pushp means Flower and Inder is a God; Better
Girl/Female
American, Australian, British, English
The Country India
Boy/Male
Bengali, Celebrity, Gujarati, Hindu, Indian, Kannada, Marathi, Punjabi, Sanskrit, Sikh, Sindhi, Traditional
The God of Weather and War; Lord of the Devas; King of Gods
Girl/Female
Indian, Sikh
Love with (God) Inder
Boy/Male
Sikh
Ruler of all that is wild and untamed., Born of tooth and fang
Boy/Male
Sikh
Lakh-w-inder-meaning is the Man who has defeated lakhs of inders indian Lord Indra)
Boy/Male
Hindu
Indra devta
Surname or Lastname
English
English : nickname for a virile man, from Middle English male ‘masculine’ (Old French masle, madle, Latin masculus).Belgian (van Male) : habitational name from any of a number of places in Flanders named Male.
Surname or Lastname
English and Scottish
English and Scottish : probably a variant of Sewatt, which is from the common Old Norse personal name Sigvarðr, composed of sigr ‘victory’ + varðr ‘guardian’. The International Genealogical Index records several UK ancestors called Suit(t), though the name is hardly found in Britain today.
Surname or Lastname
English
English : occupational name for an officer of justice or a nickname for a solemn and authoritative person thought to behave like a judge, from Middle English, Old French juge (Latin iudex, from ius ‘law’ + dicere to say), which replaced the Old English term dēma. Compare Dempster.Irish : part translation of Gaelic Mac an Bhreitheamhain, later Mac an Bhreithimh ‘son of the judge (breitheamhnach)’. Compare Brain.
Boy/Male
Sikh
Protector of Indra, Variant of Inder
Male
French
Variant spelling of French Adrien, ANDRION means "from Hadria." This form of the name can be found in An Index to the Given Names in the 1292 Census of Paris, by Colm Dubh.Â
Male
Celtic
, Mars, the divinity.
Boy/Male
Tamil
Inder Kant | இநà¯à®¤à®°à®•à®¾à®¨à¯à®¤
Indra devta
Inder Kant | இநà¯à®¤à®°à®•à®¾à®¨à¯à®¤
Girl/Female
Hindu, Indian
Index Finger
Boy/Male
Hindi
Supreme god.
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Scholar
Girl/Female
Muslim
Queen. Empress.
Boy/Male
French
This French name is based on the Latin 'caelestis' meaning 'heavenly'. Five popes have been named...
Female
Scandinavian
 Scandinavian form of Old Norse Hulð, HULDA means "hidden, obscure, secret." Compare with another form of Hulda.
Girl/Female
Arabic, Muslim, Sindhi
Well-built; Attractive
Girl/Female
Indian, Punjabi, Sikh
Ray of Holy Light
Girl/Female
Australian, Christian
Dark
Girl/Female
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
God's Grace
Male
Icelandic
Icelandic form of Old Norse Guðleifr, GUÃLEIFUR means "divine heir."
Girl/Female
Arabic, Muslim
Sublimity
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
INDEX CALCULUS-ALGORITHM
pl.
of Calculus
a.
Caused, or characterized, by the presence of a calculus or calculi; a, a calculous disorder; affected with gravel or stone; as, a calculous person.
n. pl.
See Index.
n.
A concretion, or calculus, formed in the gall bladder or biliary passages. See Calculus, n., 1.
n. pl.
See Calculus.
a.
Of the nature of a calculus; like stone; gritty; as, a calculous concretion.
n.
A calculous concretion, especially one in the kidneys or bladder; the disease arising from a calculus.
n.
Any solid concretion, formed in any part of the body, but most frequent in the organs that act as reservoirs, and in the passages connected with them; as, biliary calculi; urinary calculi, etc.
n.
A urinary calculus.
n.
Index; indication.
v. t.
To provide with an index or table of references; to put into an index; as, to index a book, or its contents.
n.
The second digit, that next pollex, in the manus, or hand; the forefinger; index finger.
pl.
of Index
imp. & p. p.
of Index
a.
Of or pertaining to the center of gravity. See Barycentric calculus, under Calculus.
pl.
of Index
n.
A method of computation; any process of reasoning by the use of symbols; any branch of mathematics that may involve calculation.
p. pr. & vb. n.
of Index
n.
The calculus; fluxions.
pl.
of Index