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Algorithm to solve the discrete logarithm problem
mathematics, the Function Field Sieve is one of the most efficient algorithms to solve the Discrete Logarithm Problem (DLP) in a finite field. It has heuristic
Function_field_sieve
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
Factorization algorithm
In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically
General_number_field_sieve
Special-purpose integer factorization algorithm
mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from
Special_number_field_sieve
Best results achieved to date
variant of the medium-sized base field function field sieve, for binary fields, to compute a discrete logarithm in a field of 21971 elements. In order to
Discrete_logarithm_records
Topics referred to by the same term
Function field may refer to: Function field of an algebraic variety Function field (scheme theory) Algebraic function field Function field sieve Function
Function_field
Integer factorization algorithm
quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field sieve).
Quadratic_sieve
Algorithm for generating prime numbers
In mathematics, the sieve of Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up
Sieve_of_Sundaram
Algorithms to generate prime numbers
prime. A prime sieve or prime number sieve is a fast type of algorithm for finding primes. There are many prime sieves. The simple sieve of Eratosthenes
Generation_of_primes
Algorithm for generating prime numbers
mathematics, the sieve of Atkin is a modern algorithm for finding all prime numbers up to a specified integer. Compared with the ancient sieve of Eratosthenes
Sieve_of_Atkin
Problem of inverting exponentiation in groups
the size of the group). Baby-step giant-step Function field sieve Index calculus algorithm Number field sieve Pohlig–Hellman algorithm Pollard's rho algorithm
Discrete_logarithm
theorem Brun sieve Function field sieve General number field sieve Large sieve Larger sieve Quadratic sieve Selberg sieve Sieve of Atkin Sieve of Eratosthenes
List_of_number_theory_topics
Ways to estimate the size of sifted sets of integers
sophisticated sieves also do not work directly with sets per se, but instead count them according to carefully chosen weight functions on these sets (options
Sieve_theory
Factorization method based on the difference of two squares
Fermat's factorization method are the basis of the quadratic sieve and general number field sieve, the best-known algorithms for factoring large semiprimes
Fermat's_factorization_method
Integer factorization algorithm
the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field sieve. While it is
Rational_sieve
Algorithm for generating prime numbers
In mathematics, the sieve of Pritchard is an algorithm for finding all prime numbers up to a specified bound. Like the ancient sieve of Eratosthenes, it
Sieve_of_Pritchard
Quantum algorithm for integer factorization
the most scalable classical factoring algorithm, the general number field sieve, which works in sub-exponential time: O ( e 1.9 ( log N ) 1 / 3 ( log
Shor's_algorithm
Integer factorization algorithm
such cases other methods are used such as the quadratic sieve and the general number field sieve (GNFS). Because these methods also have superpolynomial
Trial_division
Largest integer that divides given integers
gcd(a/d, b/d) = 1. The GCD is a commutative function: gcd(a, b) = gcd(b, a). The GCD is an associative function: gcd(a, gcd(b, c)) = gcd(gcd(a, b), c). Thus
Greatest_common_divisor
Probabilistic algorithm for computing discrete logarithms
{\displaystyle p} is large compared to q {\displaystyle q} , the function field sieve, L q [ 1 / 3 , 32 / 9 3 ] {\textstyle L_{q}\left[1/3,{\sqrt[{3}]{32/9}}\
Index_calculus_algorithm
Algorithm for solving the discrete logarithm problem
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Baby-step_giant-step
Decomposition of a number into a product
completed with a highly optimized implementation of the general number field sieve run on hundreds of machines. No algorithm has been published that can
Integer_factorization
Method for computing the relation of two integers with their greatest common divisor
compute the multiplicative inverse in algebraic field extensions and, in particular in finite fields of non-prime order. It follows that both extended
Extended_Euclidean_algorithm
Algorithm for integer multiplication
low=345. */ function split_at(num, d) hi = num / (BASE ^ d) low = num % (BASE ^ d) /* remainder of division */ return hi, low function karatsuba(num1
Karatsuba_algorithm
Exponentation in modular arithmetic
exponent e when given b, c, and m – is believed to be difficult. This one-way function behavior makes modular exponentiation a candidate for use in cryptographic
Modular_exponentiation
Algorithm for computing logarithms
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Pohlig–Hellman_algorithm
System of rapid mental calculation
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Trachtenberg_system
Algorithm in computational number theory
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Pollard's_kangaroo_algorithm
Algorithm for checking if a number is prime
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Lucas_primality_test
Algorithm in computational number theory
Mathematica as the function LatticeReduce Number Theory Library (NTL) as the function LLL PARI/GP as the function qflll Pymatgen as the function analysis
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Integer factorization algorithm
125–131. Describes the improvements available from different iteration functions and cycle-finding algorithms. Katz, Jonathan; Lindell, Yehuda (2007).
Pollard's_rho_algorithm
Probabilistic primality test
\left(2^{b}\right)-\pi \left(2^{b-1}\right)}{2^{b-2}}}} where π is the prime-counting function. Using an asymptotic expansion of π (an extension of the prime number theorem)
Miller–Rabin_primality_test
Mathematical procedure
helped find new identities involving multiple zeta functions and their appearance in quantum field theory; and in identifying bifurcation points of the
Integer_relation_algorithm
Algorithm for generating numbers coprime with first few primes
the halfway point. Sieve of Sundaram Sieve of Atkin Sieve of Pritchard Sieve theory Pritchard, Paul, "Linear prime-number sieves: a family tree," Sci
Wheel_factorization
Probabilistic primality testing algorithm
isprime function, Mathematica's PrimeQ function (that already uses 2020's version of Baillie–PSW), PARI/GP's isprime and ispseudoprime functions, and SageMath's
Baillie–PSW_primality_test
Algorithm for computing greatest common divisors
0) = rN−1. function gcd(a, b) if b = 0 return a else return gcd(b, a mod b) (As above, if negative inputs are allowed, or if the mod function may return
Euclidean_algorithm
Standard division algorithm for multi-digit numbers
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Long_division
Multiplication algorithm
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Ancient Egyptian multiplication
Ancient_Egyptian_multiplication
Algorithm for integer factorization
second-fastest is the multiple polynomial quadratic sieve, and the fastest is the general number field sieve. The Lenstra elliptic-curve factorization is named
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Algorithm checking for prime numbers
{\tilde {O}}(\log(n)^{10.5})} , later reduced using additional results from sieve theory to O ~ ( log ( n ) 7.5 ) {\displaystyle {\tilde {O}}(\log(n)^{7
AKS_primality_test
≤ j < i ≤ n {\displaystyle 1\leq j<i\leq n} . Also define projection functions π i ( x ) = ∑ j ≥ i ⟨ x , b j ∗ ⟩ ⟨ b j ∗ , b j ∗ ⟩ b j ∗ {\displaystyle
Korkine–Zolotarev lattice basis reduction algorithm
Korkine–Zolotarev_lattice_basis_reduction_algorithm
2307/2005475. JSTOR 2005475. Pomerance, Carl (December 1996). "A Tale of Two Sieves" (PDF). Notices of the AMS. Vol. 43, no. 12. pp. 1473–1485. Samuel S. Wagstaff
Continued fraction factorization
Continued_fraction_factorization
Greatest integer less than or equal to square root
Documentation 2.1". Chapel Documentation - Chapel Documentation 2.1. "CLHS: Function SQRT, ISQRT". Common Lisp HyperSpec (TM). "Math - Crystal 1.13.2". The
Integer_square_root
Algorithm to multiply two numbers
multiplication algorithm that some students will ever need. Lattice, or sieve, multiplication is algorithmically equivalent to long multiplication. It
Multiplication_algorithm
Probabilistic primality test
bound for the number of Carmichael numbers is lower than the prime number function n/log(n)) there are enough of them that Fermat's primality test is not
Fermat_primality_test
Algorithm used in modular arithmetic
computations in the Rabin signature algorithm and in the sieving step of the quadratic sieve. Tonelli–Shanks can be generalized to any cyclic group (instead
Tonelli–Shanks_algorithm
Fast greatest common divisor algorithm
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Lehmer's_GCD_algorithm
Special-purpose algorithm for factoring integers
can be modelled as a random number of size less than √n. By the Dickman function, the probability that the largest factor of such a number is less than
Pollard's_p_−_1_algorithm
Algorithm for determining whether a number is prime
Pomerance, and Robert Rumely. The test involves arithmetic in cyclotomic fields. It was later improved by Henri Cohen and Hendrik Willem Lenstra, commonly
Adleman–Pomerance–Rumely primality test
Adleman–Pomerance–Rumely_primality_test
Study of algorithms for performing number theoretic computations
Peter Stevenhagen, eds. (2008). Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography. MSRI Publications. Vol. 44. Cambridge University
Computational_number_theory
Method for division with remainder
remainder given two positive integers using only subtractions and comparisons: function divide_unsigned(N, D) if D = 0 then error(DivisionByZero) end R := N Q
Division_algorithm
Probabilistic primality test
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Solovay–Strassen primality test
Solovay–Strassen_primality_test
Mathematical for factoring integers
=293\cdot 3413\,} function Euler_factorize(int n) -> list[int] if is_prime(n) then print("Number is not factorable") exit function for-loop from a=1 to
Euler's_factorization_method
Mathematical algorithm
β b i {\displaystyle x_{i}=\alpha ^{a_{i}}\beta ^{b_{i}}} , where the function f : x i ↦ x i + 1 {\displaystyle f:x_{i}\mapsto x_{i+1}} is assumed to
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Multiplication algorithm
recursively, provide K as parameter. Otherwise, use some other multiplication function like T3MUL and reduce modulo 2 K + 1 {\displaystyle 2^{K}+1} afterwards
Schönhage–Strassen_algorithm
Primality test for Fermat numbers
Pollard's rho p − 1 p + 1 Quadratic sieve (QS) General number field sieve (GNFS) Special number field sieve (SNFS) Rational sieve Fermat's Shanks's square forms
Pépin's_test
Number-theoretic algorithm
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Cornacchia's_algorithm
Pre-generalisation of the fundamental lemma of sieve theory
In the field of number theory, the Brun sieve (also called Brun's pure sieve) is a technique for estimating the size of "sifted sets" of positive integers
Brun_sieve
Algorithm for computing the greatest common divisor
integers, Eisenstein integers, quadratic rings, and integer rings of number fields. An algorithm for computing the GCD of two numbers was known in ancient
Binary_GCD_algorithm
Primality test for certain numbers
prime searchers and some distributed computing projects including Riesel Sieve and PrimeGrid. A revised version, LLR2 was deployed in 2020. This generates
Lucas–Lehmer–Riesel_test
Test if a Mersenne number is prime
\end{aligned}}} where the first equality uses the Binomial Theorem in a finite field, which is ( x + y ) M p ≡ x M p + y M p ( mod M p ) {\displaystyle (x+y)^{M_{p}}\equiv
Lucas–Lehmer_primality_test
Integer factorization algorithm
factors. It uses Lucas sequences to perform exponentiation in a quadratic field. It is analogous to Pollard's p − 1 algorithm. In fact, it is also able
Williams's_p_+_1_algorithm
Number-theoretic algorithm
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Pocklington_primality_test
Primality test for numbers of a certain form
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Proth's_theorem
Algorithm for multiplying large numbers
close to 1 by increasing k {\displaystyle k} , the constant term in the function grows very rapidly. The growth rate for mixed-level Toom–Cook schemes was
Toom–Cook_multiplication
Algorithm in number theory
computing gcd ( x − y , n ) {\displaystyle \gcd(x-y,n)} . The quadratic sieve is an optimization of Dixon's method. It selects values of x close to the
Dixon's_factorization_method
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Pocklington's_algorithm
Cyclic algorithm to solve indeterminate quadratic equations
by more than a thousand years. But no European performances in the whole field of algebra at a time much later than Bhaskara's, nay nearly equal up to
Chakravala_method
Function representing relative sizes of particles in a system
normally only collect very large particles, those that can be separated using sieve trays. Centrifugal collectors will normally collect particles down to about
Particle-size_distribution
Natural number
ISBN 0198503415. Gaitsgory, Dennis; Lurie, Jacob (2019). Weil's Conjecture for Function Fields (Volume I). Annals of Mathematics Studies. Vol. 199. Princeton: Princeton
1
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Quadratic_Frobenius_test
Mathematical lemma
giant-step Pollard rho Pollard kangaroo Pohlig–Hellman Index calculus Function field sieve Greatest common divisor Binary Euclidean Extended Euclidean Lehmer's
Bhaskara's_lemma
Efficient algorithm to count points on elliptic curves
is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it
Schoof's_algorithm
Analytic function in mathematics
The Riemann zeta function or Euler–Riemann zeta function, denoted by the lowercase Greek letter ζ (zeta), is a mathematical function of a complex variable
Riemann_zeta_function
Methods to test or prove primality
primality testing (and proving) followed quickly. Primality testing is a field that has been around since the time of Fermat, in whose time most algorithms
Elliptic_curve_primality
Group of similar cells performing a specific function
cells that are nestled between sieve-tube members that function in some manner bringing about the conduction of food. Sieve-tube members that are alive contain
Tissue_(biology)
Number divisible only by 1 and itself
depend on the size of its factors include the quadratic sieve and general number field sieve. As with primality testing, there are also factorization
Prime_number
odd prime. Here F p {\displaystyle \mathbf {F} _{p}} denotes the finite field with p {\displaystyle p} elements; { 0 , 1 , … , p − 1 } {\displaystyle
Cipolla's_algorithm
Branch of pure mathematics
important tools of analytic number theory are the circle method, sieve methods and L-functions (or, rather, the study of their properties). The theory of modular
Number_theory
Diameter of a sphere of the same volume as an irregularly-shaped subject
the equivalent sieve diameter, or the diameter of a sphere that just passes through a defined sieve pore. Of note, the equivalent sieve diameter can be
Equivalent_spherical_diameter
Provides an asymptotic formula for counting the number of prime ideals of a number field
Alina Carmen Cojocaru; M. Ram Murty (8 December 2005). An introduction to sieve methods and their applications. London Mathematical Society Student Texts
Landau_prime_ideal_theorem
Integer having only small prime factors
factorization algorithms, for example: the general number field sieve), the VSH hash function is another example of a constructive use of smoothness to
Smooth_number
Norwegian mathematician (1917–2007)
turned to sieve theory, a previously neglected topic which Selberg's work brought into prominence. In a 1947 paper he introduced the Selberg sieve, a method
Atle_Selberg
American mathematician
correlation conjecture on the zeros of the Riemann zeta function, is known for his development of large sieve methods, and is the author of multiple books on
Hugh_Lowell_Montgomery
Formal power series
function Generating function transformation Stanley's reciprocity theorem Integer partition Combinatorial principles Cyclic sieving Z-transform Umbral
Generating_function
Technique in cryptography
curve from 676 bits to 923 bits. In 2016, the Extended Tower Number Field Sieve algorithm allowed to reduce the complexity of finding discrete logarithm
Pairing-based_cryptography
Topics referred to by the same term
theory Quadratic residue, an integer that is a square modulo n Quadratic sieve, a modern integer factorization algorithm Quadratic convergence, in which
Quadratic
Potential counterexample to the generalized Riemann hypothesis
generalized Riemann hypothesis, on the zeros of Dirichlet L-functions associated to quadratic number fields. Roughly speaking, these are possible zeros very near
Siegel_zero
Notation describing limiting behavior in computational number theory
c=(64/9)^{1/3}\approx 1.923} . The best such algorithm prior to the number field sieve was the quadratic sieve which has running time L n [ 1 / 2 , 1 ] = e ( 1 + o ( 1
L-notation
Method in number theory
algorithm, is the probabilistic method of finding roots of polynomials over the field F p {\displaystyle \mathbb {F} _{p}} with p {\displaystyle p} elements.
Berlekamp–Rabin_algorithm
2 ≡ q ( mod n ) . {\displaystyle x^{2}\equiv q{\pmod {n}}.} sieve of Eratosthenes Sieve of Eratosthenes square-free integer A square-free integer is
Glossary_of_number_theory
Polish-American mathematician (born 1947)
He has made deep contributions to the field of analytic number theory, mainly in modular forms on GL(2) and sieve methods." He became a fellow of the American
Henryk_Iwaniec
wound signaling also function in signaling other defense responses. Cross-talk events regulate the activation of different roles. Sieve elements are very
Wound_response_in_plants
Number
zero function (or zero map) on a domain D. This is the constant function with 0 as its only possible output value, that is, it is the function f defined
0
Integer factorization algorithm
41 ⋅ 271 {\displaystyle N=11111=41\cdot 271} . Below is an example of C function for performing SQUFOF factorization on unsigned integer not larger than
Shanks's square forms factorization
Shanks's_square_forms_factorization
Problem easily dividable into parallel tasks
particle physics. The marching squares algorithm. Sieving step of the quadratic sieve and the number field sieve. Tree growth step of the random forest machine
Embarrassingly_parallel
Agricultural machine
A stone picker (or rock picker) is an implement to sieve through the top layer of soil to separate and collect rocks and soil debris from good topsoil
Stone_picker
dry sieving A method of sifting artefacts from excavated sediments by shaking it through sieves or meshes of varying sizes. As opposed to wet sieving, which
Glossary_of_archaeology
British mathematician
(1974). Sieve Methods. London: Academic Press. ISBN 0-12-318250-6. MR 0424730. Zbl 0298.10026.Halberstam, Heini; Richert, Hans-Egon (2011). Sieve Methods
Heini_Halberstam
Mathematics award
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical
Fields_Medal
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
Girl/Female
Japanese American
Valley field.
Boy/Male
Indian
Friction
Boy/Male
English
In the field.
Boy/Male
Buddhist, Indian, Japanese
Mysterious Function
Boy/Male
English
Gathering field; meeting field.
Girl/Female
Indian
Hay field
Surname or Lastname
English
English : topographic name for someone who lived on land which had been cleared of forest, but not brought into cultivation, from Old English feld ‘pasture’, ‘open country’, as opposed on the one hand to æcer ‘cultivated soil’, ‘enclosed land’ (see Acker) and on the other to weald ‘wooded land’, ‘forest’ (see Wald).Possibly also Scottish or Irish : reduced form of McField (see McPhail).Jewish (American) : Americanized and shortened form of any of the many Jewish surnames containing Feld.
Girl/Female
Tamil
Hay field
Girl/Female
Hindu, Indian
Fraction of the Cosmos
Boy/Male
African, American, Anglo, Australian, British, Christian, English, Jamaican
Battlefield; Spear Field; Triangular Field
Surname or Lastname
English
English : topographic name from Middle English feldes, plural or possessive of feld ‘open country’. This name is also found as a translation of equivalent names in other languages, in particular French Deschamps, Duchamp.
Girl/Female
Bengali, Indian
Fraction of Time
Boy/Male
English
Fern field.
Boy/Male
English
Pasture; field.
Girl/Female
Afghan, Arabic, Australian, Indian, Muslim
Fiction; Romance; Story
Boy/Male
Australian, British, English
A Field
Surname or Lastname
English
English : variant of Field.
Boy/Male
English
Pasture; field.
Boy/Male
Anglo, British, English
Field with Ferns; Fern Field
Boy/Male
Anglo, British, English
Field with Ferns; Fern Field
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
Boy/Male
Muslim/Islamic
Friend
Girl/Female
Welsh
White wave. Also a Blessed reconciliation.
Surname or Lastname
English (chiefly Devon and Cornwall)
English (chiefly Devon and Cornwall) : variant of Laver, which was also used as a personal name in the 17th century.
Boy/Male
Hindu, Indian, Sanskrit, Telugu
Of Good Fortune; The Lord
Girl/Female
Hindu, Indian, Marathi
Mother of Warrior
Male
Danish
, Christian, follower of Christ.
Boy/Male
Hindu, Indian, Marathi, Telugu
Written
Male
English
 Unisex pet form of English Robert and Roberta, ROBIN means "bright fame." This name is also sometimes given as a bird name.
Male
Egyptian
, a mystical serpent of evil.
Girl/Female
Tamil
Rossini | ரோஸஸீநீÂ
Light, Bright
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
FUNCTION FIELD-SIEVE
a.
Pertaining to, or connected with, a function or duty; official.
v. i.
To take the field.
n.
The place or point of union, meeting, or junction; specifically, the place where two or more lines of railway meet or cross.
v. t.
The act of uniting, or the state of being united; junction.
a.
Open, like a field.
v. t.
To use with full command or power, as a thing not too heavy for the holder; to manage; to handle; hence, to use or employ; as, to wield a sword; to wield the scepter.
v. t.
To give sanction to; to ratify; to confirm; to approve.
n.
The act of joining, or the state of being joined; union; combination; coalition; as, the junction of two armies or detachments; the junction of paths.
v. t.
To sell by auction.
n.
The things sold by auction or put up to auction.
v. t.
To permit; to grant; as, to yield passage.
n.
A quantity so connected with another quantity, that if any alteration be made in the latter there will be a consequent alteration in the former. Each quantity is said to be a function of the other. Thus, the circumference of a circle is a function of the diameter. If x be a symbol to which different numerical values can be assigned, such expressions as x2, 3x, Log. x, and Sin. x, are all functions of x.
a.
Pertaining to the function of an organ or part, or to the functions in general.
v. t.
To supply with an organ or organs having a special function or functions.
a.
Relating to an open fields; drowing in a field; growing in a field, or open ground.
n.
The act of anointing, smearing, or rubbing with an unguent, oil, or ointment, especially for medical purposes, or as a symbol of consecration; as, mercurial unction.
v. i.
To stand out in the field, ready to catch, stop, or throw the ball.
n.
The appropriate action of any special organ or part of an animal or vegetable organism; as, the function of the heart or the limbs; the function of leaves, sap, roots, etc.; life is the sum of the functions of the various organs and parts of the body.
adv.
To, in, or on the field.
n.
The whole surface of an escutcheon; also, so much of it is shown unconcealed by the different bearings upon it. See Illust. of Fess, where the field is represented as gules (red), while the fess is argent (silver).