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Efficient algorithm to count points on elliptic curves
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography
Schoof's_algorithm
The Schoof–Elkies–Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a
Schoof–Elkies–Atkin_algorithm
Surname list
football player Schoof cabinet Schoofs 17958 Schoof, a main-belt asteroid Schoof–Elkies–Atkin algorithm, extension of Schoof's algorithm by Noam Elkies
Schoof
trace the developments up to Schoof's definitive work on the subject, while also listing the improvements to Schoof's algorithm made by Elkies (1990) and
Counting points on elliptic curves
Counting_points_on_elliptic_curves
Methods to test or prove primality
E using Schoof's algorithm, which is the preferred algorithm for the Goldwasser–Kilian algorithm. However, the original algorithm by Schoof is not efficient
Elliptic_curve_primality
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
Quantum algorithm for integer factorization
Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor
Shor's_algorithm
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
central role in the study of counting points on elliptic curves in Schoof's algorithm. The set of division polynomials is a sequence of polynomials in Z
Division_polynomials
Algorithm in computational number theory
Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and
Lenstra–Lenstra–Lovász lattice basis reduction algorithm
Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
Method for computing the relation of two integers with their greatest common divisor
and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common
Extended_Euclidean_algorithm
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
Algorithm to multiply two numbers
multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient
Multiplication_algorithm
Dutch mathematician
a professor at the University Tor Vergata in Rome. In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite
René_Schoof
Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Approach to public-key cryptography
curve and use a general point-counting algorithm, for example, Schoof's algorithm or the Schoof–Elkies–Atkin algorithm, Select a random curve from a family
Elliptic-curve_cryptography
American mathematician (born 1966)
Harvard's history. He and A. O. L. Atkin extended Schoof's algorithm to create the Schoof–Elkies–Atkin algorithm. Elkies also studies the connections between
Noam_Elkies
Mathematical procedure
a_{1}x_{1}+a_{2}x_{2}+\cdots +a_{n}x_{n}=0.\,} An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real
Integer_relation_algorithm
Integer factorization algorithm
Pollard's rho algorithm is an algorithm for integer factorization. It was invented by John Pollard in 1975. It uses only a small amount of space, and
Pollard's_rho_algorithm
Mathematical algorithm
Pollard's rho algorithm for logarithms is an algorithm introduced by John Pollard in 1978 to solve the discrete logarithm problem, analogous to Pollard's
Pollard's rho algorithm for logarithms
Pollard's_rho_algorithm_for_logarithms
Special-purpose algorithm for factoring integers
Pollard's p − 1 algorithm is a number theoretic integer factorization algorithm, invented by John Pollard in 1974. It is a special-purpose algorithm, meaning
Pollard's_p_−_1_algorithm
Algebraic curve in mathematics
Z/36Z. The number of points on a specific curve can be computed with Schoof's algorithm. Studying the curve over the field extensions of Fq is facilitated
Elliptic_curve
Algorithm in computational number theory
kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced
Pollard's_kangaroo_algorithm
Multiplication algorithm
The Schönhage–Strassen algorithm is an asymptotically fast multiplication algorithm for large integers, published by Arnold Schönhage and Volker Strassen
Schönhage–Strassen_algorithm
British-American mathematician
Chicago. Atkin, along with Noam Elkies, extended Schoof's algorithm to create the Schoof–Elkies–Atkin algorithm. Together with Daniel J. Bernstein, he developed
A._O._L._Atkin
Algorithm for computing logarithms
theory, the Pohlig–Hellman algorithm, sometimes credited as the Silver–Pohlig–Hellman algorithm, is a special-purpose algorithm for computing discrete logarithms
Pohlig–Hellman_algorithm
Algorithm for computing the greatest common divisor
The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor
Binary_GCD_algorithm
Algorithm used in modular arithmetic
The Tonelli–Shanks algorithm (referred to by Shanks as the RESSOL algorithm) is used in modular arithmetic to solve for r in a congruence of the form r2
Tonelli–Shanks_algorithm
Estimates the number of points on an elliptic curve over a finite field
proved by André Weil in the case of curves. Sato–Tate conjecture Schoof's algorithm Weil's bound Artin, Emil (1924), "Quadratische Körper im Gebiete der
Hasse's theorem on elliptic curves
Hasse's_theorem_on_elliptic_curves
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
Integer factorization algorithm
theory, Williams's p + 1 algorithm is an integer factorization algorithm, one of the family of algebraic-group factorisation algorithms. It was invented by
Williams's_p_+_1_algorithm
Fast greatest common divisor algorithm
GCD algorithm, named after D. H. Lehmer, is a fast GCD algorithm for multiple-precision arithmetic, which improves on the simpler Euclidean algorithm by
Lehmer's_GCD_algorithm
Probabilistic primality test
or Rabin–Miller primality test is a probabilistic primality test: an algorithm which determines whether a given number is likely to be prime, similar
Miller–Rabin_primality_test
Public university in Rome, Italy
professor of Probability Calculus René Schoof, mathematician who published the homonymous algorithm (Schoof's Algorithm), professor of Mathematics Pietro Trifone
University of Rome Tor Vergata
University_of_Rome_Tor_Vergata
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
Method in number theory
In number theory, Berlekamp's root finding algorithm, also called the Berlekamp–Rabin algorithm, is the probabilistic method of finding roots of polynomials
Berlekamp–Rabin_algorithm
Multiplication algorithm
ancient Egypt the concept of base 2 did not exist, the algorithm is essentially the same algorithm as long multiplication after the multiplier and multiplicand
Ancient Egyptian multiplication
Ancient_Egyptian_multiplication
Algorithm in number theory
(also Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method
Dixon's_factorization_method
Algorithm checking for prime numbers
test and the cyclotomic AKS test) is a deterministic primality-proving algorithm created and published by Manindra Agrawal, Neeraj Kayal, and Nitin Saxena
AKS_primality_test
In computational number theory, Cipolla's algorithm is a technique for solving a congruence of the form x 2 ≡ n ( mod p ) , {\displaystyle x^{2}\equiv
Cipolla's_algorithm
Probabilistic primality test
composite return probably prime Using fast algorithms for modular exponentiation, the running time of this algorithm is O(k·log3 n), where k is the number
Solovay–Strassen primality test
Solovay–Strassen_primality_test
Pocklington's algorithm is a technique for solving a congruence of the form x 2 ≡ a ( mod p ) , {\displaystyle x^{2}\equiv a{\pmod {p}},} where x and
Pocklington's_algorithm
Largest integer that divides given integers
|a|. This case is important as the terminating step of the Euclidean algorithm. The above definition is unsuitable for defining gcd(0, 0), since there
Greatest_common_divisor
Algorithm for multiplying large numbers
introduced the new algorithm with its low complexity, and Stephen Cook, who cleaned the description of it, is a multiplication algorithm for large integers
Toom–Cook_multiplication
Number-theoretic algorithm
In computational number theory, Cornacchia's algorithm is an algorithm for solving the Diophantine equation x 2 + d y 2 = m {\displaystyle x^{2}+dy^{2}=m}
Cornacchia's_algorithm
Integer factorization algorithm
The quadratic sieve algorithm (QS) is an integer factorization algorithm and, in practice, the second-fastest method known (after the general number field
Quadratic_sieve
Greatest integer less than or equal to square root
y {\displaystyle y} and k {\displaystyle k} be non-negative integers. Algorithms that compute (the decimal representation of) y {\displaystyle {\sqrt {y}}}
Integer_square_root
Standard division algorithm for multi-digit numbers
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand. It breaks
Long_division
Algorithm for integer factorization
elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose
Lenstra elliptic-curve factorization
Lenstra_elliptic-curve_factorization
Method in speedcubing
119 algorithms in total to learn the full method, with 41 for F2L, 57 for full OLL, and 21 for full PLL. On top of that, there are other algorithm sets
CFOP_method
Integer factorization algorithm
x-y} will give a non-trivial factor of N {\displaystyle N} . A practical algorithm for finding pairs ( x , y ) {\displaystyle (x,y)} which satisfy x 2 ≡
Shanks's square forms factorization
Shanks's_square_forms_factorization
Korkine–Zolotarev (KZ) lattice basis reduction algorithm or Hermite–Korkine–Zolotarev (HKZ) algorithm is a lattice reduction algorithm. For lattices in R n {\displaystyle
Korkine–Zolotarev lattice basis reduction algorithm
Korkine–Zolotarev_lattice_basis_reduction_algorithm
Algorithm for solving the discrete logarithm problem
branch of mathematics, the baby-step giant-step is a meet-in-the-middle algorithm for computing the discrete logarithm or order of an element in a finite
Baby-step_giant-step
Problem of inverting exponentiation in groups
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 for generating prime numbers
Sundaram is a variant of the sieve of Eratosthenes, a simple deterministic algorithm for finding all the prime numbers up to a specified integer. It was discovered
Sieve_of_Sundaram
System of rapid mental calculation
This article presents some methods devised by Trachtenberg. Some of the algorithms Trachtenberg developed are for general multiplication, division and addition
Trachtenberg_system
Algorithms to generate prime numbers
In computational number theory, a variety of algorithms make it possible to generate prime numbers efficiently. These are used in various applications
Generation_of_primes
Special-purpose integer factorization algorithm
number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general number field sieve (GNFS) was derived from it. The special
Special_number_field_sieve
Integer factorization algorithm
most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests to see if an integer n
Trial_division
Integer factorization algorithm
In mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. It is a special case of the general number field
Rational_sieve
Algorithm for determining whether a number is prime
Adleman–Pomerance–Rumely primality test is an algorithm for determining whether a number is prime. Unlike other, more efficient algorithms for this purpose, it avoids the
Adleman–Pomerance–Rumely primality test
Adleman–Pomerance–Rumely_primality_test
Algorithm for generating prime numbers
In 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
Factorization algorithm
the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity
General_number_field_sieve
Exponentation in modular arithmetic
multiplicative inverse d of b modulo m (for instance by using extended Euclidean algorithm). More precisely: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1
Modular_exponentiation
Primality test for certain numbers
based on the Lucas–Lehmer primality test. It is the fastest deterministic algorithm known for numbers of that form.[citation needed] For numbers of the form
Lucas–Lehmer–Riesel_test
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,
Sieve_of_Pritchard
Cyclic algorithm to solve indeterminate quadratic equations
The chakravala method (Sanskrit: चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. It is commonly
Chakravala_method
Algorithm for checking if a number is prime
exponentiation algorithm like binary or addition-chain exponentiation). The algorithm can be written in pseudocode as follows: algorithm lucas_primality_test
Lucas_primality_test
factorization method (CFRAC) is an integer factorization algorithm. It is a general-purpose algorithm, meaning that it is suitable for factoring any integer
Continued fraction factorization
Continued_fraction_factorization
Study of algorithms for performing number theoretic computations
mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating
Computational_number_theory
Test if a Mersenne number is prime
odd prime. The primality of p can be efficiently checked with a simple algorithm like trial division since p is exponentially smaller than Mp. Define a
Lucas–Lehmer_primality_test
Probabilistic primality test
no value. Using fast algorithms for modular exponentiation and multiprecision multiplication, the running time of this algorithm is O(k log2n log log
Fermat_primality_test
Mathematical lemma
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenberg system Italics indicate that algorithm is for numbers of special forms
Bhaskara's_lemma
German mathematician (1912–1991)
(3): 153–156. 1960. doi:10.1090/S0002-9904-1960-10414-4. Schoof, René (1993). "Review: Algorithmic algebraic number theory, by M. Pohst and H. Zassenhaus"
Hans_Zassenhaus
Wioletta; Magro, Giuseppe; Mairani, Andrea; Parodi, Katia; Sala, Paola R.; Schoofs, Philippe; Tessonnier, Thomas; Vlachoudis, Vasilis (2016). "The FLUKA Code:
FLUKA
Probabilistic primality testing algorithm
primality test is a probabilistic or possibly deterministic primality testing algorithm that determines whether a number is composite or is a probable prime.
Baillie–PSW_primality_test
Factorization method based on the difference of two squares
of the quadratic sieve and general number field sieve, the best-known algorithms for factoring large semiprimes, which are the "worst-case". The primary
Fermat's_factorization_method
Mathematical for factoring integers
made Euler's factorization method disfavoured for computer factoring algorithms, since any user attempting to factor a random integer is unlikely to know
Euler's_factorization_method
Algorithm to solve the discrete logarithm problem
In 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
Function_field_sieve
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
Dutch mathematician (born 1949)
Lenstra–Lenstra–Lovász lattice basis reduction algorithm (in 1982); Developing a polynomial-time algorithm for solving a feasibility integer programming
Hendrik_Lenstra
Algorithm for generating numbers coprime with first few primes
list of initial prime numbers constitute complete parameters for the algorithm to generate the remainder of the list. These generators are referred to
Wheel_factorization
Topics referred to by the same term
since 2011 .sea, a StuffIt Expander archive (or application) Schoof–Elkies–Atkin algorithm Search engine advertising, also referred to as search engine
Sea_(disambiguation)
Belief that HIV does not cause AIDS
and to nearly all journalists, with the exception of Mark Schoofs of the Village Voice. Schoofs reported that David Rasnick, another AIDS denialist member
HIV/AIDS denialism in South Africa
HIV/AIDS_denialism_in_South_Africa
American mathematician
improvements to the Schoof–Elkies–Atkin algorithm that led to new point-counting records, and average polynomial-time algorithms for computing zeta functions
Andrew Sutherland (mathematician)
Andrew_Sutherland_(mathematician)
Scientific and musical study of bells
Physics of Musical Instruments, p. 685. ISBN 978-0-387-98374-5. Cites Schoofs et al., 1987 for major-third bell. Rossing, Thomas D. (2000). Science of
Campanology
Novel type of computer memory
displacing existing memory technologies. Shi, J.; Ha, S. D.; Zhou, Y.; Schoofs, F.; Ramanathan, S. (2013). "A correlated nickelate synaptic transistor"
Electrochemical_RAM
Primality test for numbers of a certain form
in contrast to the probably prime results typical of other Monte Carlo algorithms such as the Miller-Rabin test. An approximate upper bound error probability
Proth's_theorem
Group-like structure appearing in global fields
of a real quadratic number field and applied his baby-step giant-step algorithm to compute the regulator of such a field in O ( D 1 / 4 + ε ) {\displaystyle
Infrastructure (number theory)
Infrastructure_(number_theory)
American internet media and news company
appointment of Ben Smith as editor-in-chief. In 2013, Pulitzer Prize winner Mark Schoofs of ProPublica was hired as head of investigative reporting. By 2016, BuzzFeed
BuzzFeed
SAML • SAVILLE • SC2000 • Schnorr group • Schnorr signature • Schoof–Elkies–Atkin algorithm • SCIP • Scott Vanstone • Scrambler • Scramdisk • Scream (cipher)
Index of cryptography articles
Index_of_cryptography_articles
cannot always be avoided. In the case of an elliptic curve there is an algorithm of John Tate describing it. For abelian varieties such as Ap, there is
Arithmetic of abelian varieties
Arithmetic_of_abelian_varieties
Number-theoretic algorithm
relation (LLL; KZ) Modular exponentiation Montgomery reduction Schoof Trachtenberg system Italics indicate that algorithm is for numbers of special forms
Pocklington_primality_test
2010 environmental disaster
November 2014. Marghany, Maged (15 December 2014). "Utilization of a genetic algorithm for the automatic detection of oil spill from RADARSAT-2 SAR satellite
Deepwater_Horizon_oil_spill
Primality test for Fermat numbers
F_{n}} by repeated squaring. This makes the test a fast polynomial-time algorithm. However, Fermat numbers grow so rapidly that only a handful of Fermat
Pépin's_test
Approach to design that considers human needs at every step of development
ISSN 1944-3900. Carayon, Pascale; Wooldridge, Abigail; Hoonakker, Peter; Hundt, Ann Schoofs; Kelly, Michelle M. (April 1, 2020). "SEIPS 3.0: Human-centered design
Human-centered_design
Washington Post. Retrieved January 11, 2017. Bensinger, Ken; Elder, Miriam; Schoofs, Mark (January 10, 2017). "These Reports Allege Trump Has Deep Ties To
Russian interference in the 2016 United States elections
Russian_interference_in_the_2016_United_States_elections
Street Journal team); former reporter who writes on defense topics Mark Schoofs (B.A. 1985), reporter, 2000 Pulitzer Prize for international reporting
List of Yale University people
List_of_Yale_University_people
Retrieved 22 March 2019. Schoof, René (2008). "Computing Arakelov class groups". In Buhler, J.P.; P., Stevenhagen (eds.). Algorithmic Number Theory: Lattices
Glossary of arithmetic and diophantine geometry
Glossary_of_arithmetic_and_diophantine_geometry
) – three-time Putnam Fellow; mathematician, co-creator of Schoof–Elkies–Atkin algorithm; chess master Joseph Engelberger ( B.S. 1946, M.S. 1949) – engineer
List of Columbia University alumni and attendees
List_of_Columbia_University_alumni_and_attendees
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
Boy/Male
Hindu
Young shoots and leaves
Girl/Female
Muslim
A noble hearted, Generous lady, Had this name, She built a religious school (Daughter of al-muzaffar)
Girl/Female
Muslim/Islamic
Name of a liberal woman of Baghdad who founded a religious school
Boy/Male
Arabic, Muslim
School Follower; Name of Muslim Cast
Girl/Female
Indian
Name of a liberal woman of baghdad who founded a religious school
Boy/Male
Muslim
School follower
Surname or Lastname
English
English : from Anglo-Norman French chivere, chevre ‘goat’ (Latin capra ‘nanny goat’), applied as a nickname for an unpredictable or temperamental person, or a metonymic occupational name for a goatherd.Born in London in about 1614, the son of spinner William Cheaver, Ezekiel Cheever came to Boston in June 1637. After a brief sojourn in New Haven, CT, he was master of the Boston Latin School from 1670 until his death in 1708. He had twelve children; his youngest son, also called Ezekiel, was the clerk to the court in the infamous Salem witchcraft trials of 1692.
Surname or Lastname
English
English : patronymic from a short form of the personal name Simon.Jewish (from Ukraine; Symes, Symis) : metronymic from the Yiddish female personal name Sime (see Sima).Benjamin Syms was a planter and philanthropist, probably the earliest inhabitant of any North American colony to bequeath property for the establishment of a free school. His name was spelled variously as Sims, Simes, Sym, Symms, Syms, and Symes. He was probably born in England, but was reported in the VA census of 1624/25 as age 33 and living at Basse’s Choice in what was later known as Isle of Wight County.
Boy/Male
Tamil
Young shoots and leaves
Girl/Female
Muslim
Name of a liberal woman of baghdad who founded a religious school
Boy/Male
Gujarati, Hindu, Indian, Jain, Kannada, Malayalam, Marathi, Telugu
Young Shoots and Leaves; New Leave
Girl/Female
Arabic, Muslim
A Noble Hearted; Generous Lady; Daughter of Al-muzaffar had this Name; She Built a Religious School
Girl/Female
Muslim/Islamic
A noble hearted generous lady, daughter of al-Muzaffar, had this name; she built a religious school
Boy/Male
Arabic, Muslim
Founder of the Hanafi School of Thought or Islamic Law
Girl/Female
Indian
A noble hearted, Generous lady, Had this name, She built a religious school (Daughter of al-muzaffar)
Boy/Male
Hindu, Indian, Traditional
Young Shoots and Leaves
Girl/Female
Arabic
School Mistress; Woman Learned in Law and Divinity
Boy/Male
Indian
School follower
Boy/Male
Arabic, Muslim
Founder of the Hanafi School of Thought / Islamic Law
Surname or Lastname
English
English : occupational name for a marksman, from an agent derivative of Middle English schoot(en) ‘to shoot’.Americanized spelling of German and Dutch Schutter.
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
Girl/Female
Indian
Wealthy, Lord of wealth
Boy/Male
Indian, Sanskrit
Ray; Strength; Majesty
Boy/Male
Czechoslovakian, Hindu, Indian
Instrument
Girl/Female
Hindu, Indian, Malayalam
Name of Lord Ganesh
Girl/Female
Indian
Happy, Precious, Generous
Boy/Male
Tamil
Pious
Girl/Female
Hindu
Victory, Good character
Girl/Female
Biblical
Sight of the valley, a walled valley.
Boy/Male
Biblical
Desert.
Girl/Female
Greek
Hyacinth.
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
SCHOOFS ALGORITHM
n.
A house appropriated for the use of a school or schools, or for instruction.
n.
A school for the higher branches of literature and science; a preparatory school for the university; -- used esp. of German schools of this kind.
a.
Antagonistic; opposing; counteracting; as, antagonist schools of philosophy.
n.
A shoal; a multitude; as, a school of fish.
n.
The course of sciences read in the schools.
v. t.
To train in an institution of learning; to educate at a school; to teach.
imp. & p. p.
of School
n.
Figuratively, any means of knowledge or discipline; as, the school of experience.
a.
Pertaining to, or suiting, a scholar, a school, or schools; scholarlike; as, scholastic manners or pride; scholastic learning.
n.
One who teaches or instructs a school.
a.
Collecting or running in schools or shoals.
n.
A place of primary instruction; an establishment for the instruction of children; as, a primary school; a common school; a grammar school.
n.
A place for learned intercourse and instruction; an institution for learning; an educational establishment; a place for acquiring knowledge and mental training; as, the school of the prophets.
p. pr. & vb. n.
of School
n.
In universities, schools, etc., a definite continuous period during which instruction is regularly given to students; as, the school year is divided into three terms.
n.
The canons, precepts, or body of opinion or practice, sanctioned by the authority of a particular class or age; as, he was a gentleman of the old school.
n.
An assemblage of scholars; those who attend upon instruction in a school of any kind; a body of pupils.
n.
School.
adv.
Toward school.
n.
A book used in schools for learning lessons.