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Summation method for hypergeometric terms
In mathematics, Gosper's algorithm, due to Bill Gosper, is a procedure for finding sums of hypergeometric terms that are themselves hypergeometric terms
Gosper's_algorithm
American mathematician and programmer (born 1943)
of pride in the Lisp community. The Gosper curve and Gosper's algorithm are named after him. In high school, Gosper was interested in model rockets until
Bill_Gosper
An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem
List_of_algorithms
On finding a repeating loop in a sequence
Brent's algorithm. While Brent's algorithm uses a single tortoise, repositioned every time the hare passes a power of two, Gosper's algorithm uses several
Cycle_detection
Algorithm for speeding up cellular automaton simulations
using alternative algorithms that simulate each time step of each cell of the automaton. The algorithm was first described by Bill Gosper in the early 1980s
Hashlife
Mathematical software
algorithm Root-finding algorithms Symbolic integration via e.g. Risch algorithm or Risch–Norman algorithm Hypergeometric summation via e.g. Gosper's algorithm
Computer_algebra_system
Numbering of combinations of items
non-negative integer was observed by Lehmer (1964). Indeed, a greedy algorithm finds the k-combination corresponding to N: take ck maximal with ( c k
Combinatorial_number_system
Scientific area at the interface between computer science and mathematics
the F5 algorithm) Gosper's algorithm: find sums of hypergeometric terms that are themselves hypergeometric terms Knuth–Bendix completion algorithm: for
Computer_algebra
Pair of functions in combinatorics
Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a method to find a function's WZ counterpart, and can be
Wilf–Zeilberger_pair
Polyhedral number representing a tetrahedron
{(n+1)(n+2)(n+3)}{6}}.\end{aligned}}} The formula can also be proved by Gosper's algorithm. Tetrahedral and triangular numbers are related through the recursive
Tetrahedral_number
Equalities involving sums over the coefficients occurring in hypergeometric series
Definite sums: Sister Celine's Method, Zeilberger's algorithm Indefinite sums: Gosper's algorithm The book A = B by Marko Petkovšek, Herbert Wilf and
Hypergeometric_identity
Software algorithm book
a software algorithm book by Henry S. Warren, Jr. first published in 2002. It presents fast bit-level and low-level arithmetic algorithms for common tasks
Hacker's_Delight
Visualisation method for hierchical data
must define a tiling algorithm, that is, a way to divide a region into sub-regions of specified areas. Ideally, a treemap algorithm would create regions
Treemapping
Two-dimensional cellular automaton
programs often do not store cells as a two-dimensional arrays, instead using algorithms such as Hashlife which represent patterns as a tree structure. The Game
Conway's_Game_of_Life
(n)} . The Petkovšek algorithm uses as key concept that this rational function has a specific representation, namely the Gosper-Petkovšek normal form
Petkovšek's_algorithm
Number represented as a0+1/(a1+1/...)
Bill Gosper – First exact algorithms for continued fraction arithmetic. Complete quotient Computing continued fractions of square roots – Algorithms for
Simple_continued_fraction
algebra, Abramov's algorithm computes all rational solutions of a linear recurrence equation with polynomial coefficients. The algorithm was published by
Abramov's_algorithm
Number, approximately 3.14
simple spigot algorithm in 1995. Its speed is comparable to arctan algorithms, but not as fast as iterative algorithms. Another spigot algorithm, the BBP digit
Pi
Cellular automaton neighborhood consisting of eight adjacent cells
century, and as a result an algorithm was derived from the Moore graph which was later called the Moore Neighborhood algorithm. The pseudocode for the Moore-Neighbor
Moore_neighborhood
English mathematician (1937–2020)
For calculating the day of the week, he invented the Doomsday algorithm. The algorithm is simple enough for anyone with basic arithmetic ability to do
John_Horton_Conway
Binary representation for signed numbers
are needed than for the more efficient algorithms actually implemented in computers. Some multiplication algorithms are designed for two's complement, notably
Two's_complement
Product of numbers from 1 to n
is not efficient, faster algorithms are known, matching to within a constant factor the time for fast multiplication algorithms for numbers with the same
Factorial
Curve whose range contains the unit square
Hausdorff dimension Przemyslaw Prusinkiewicz and Aristid Lindenmayer. "The Algorithmic Beauty of Plants". 2012. p. 12 Jeffrey Ventrella. "Brainfilling Curves
Space-filling_curve
Family of related bitwise operations on machine words
implement Gosper's loop-detection algorithm, which can find the period of a function of finite range using limited resources. The binary GCD algorithm spends
Find_first_set
Number of nonzero symbols in a string
of any known algorithm. However, when a value is expected to have few nonzero bits, it may instead be more efficient to use algorithms that count these
Hamming_weight
Pattern that has no predecessors
cellular automata, orphans and Gardens of Eden can be found by an efficient algorithm, but for higher dimensions this is an undecidable problem. Nevertheless
Garden of Eden (cellular automaton)
Garden_of_Eden_(cellular_automaton)
Tool for simulating cellular automata
Rokicki; it can be scripted using Lua or Python. It includes a hashlife algorithm that can simulate the behavior of very large structured or repetitive
Golly_(program)
Collection of mathematical and algorithmic hacks
AI Lab containing a wide variety of hacks, including useful and clever algorithms for mathematical computation, some number theory and schematic diagrams
HAKMEM
System composed of many interacting components
adaptation Artificial neural network Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental
Complex_system
Fractal analysis technique
inspect the object or pattern (see Figure 1). Computer based box counting algorithms have been applied to patterns in 1-, 2-, and 3-dimensional spaces. The
Box_counting
Moving pattern in Conway's Game of Life
universal constructor that starts with only 15 gliders, with a construction algorithm published in 2022. Eric S. Raymond has proposed the glider as an emblem
Glider (Conway's Game of Life)
Glider_(Conway's_Game_of_Life)
Eppstein (at PARC 1989–1990), researcher in computational geometry and graph algorithms John Ellenby (at PARC 1975–1978),[citation needed] Led AltoII development
List of people associated with PARC
List_of_people_associated_with_PARC
Non-standard positional numeral system
Implementations since then have been rare. zfp, a floating-point compression algorithm from the Lawrence Livermore National Laboratory, uses negabinary to store
Negative_base
Linux-based, open-sourced, toolkit of portable software
vector and matrix operations, Boyer–Moore–Gosper string search algorithm functions, a Smith–Waterman algorithm function, relational algebra operations and
Multidimensional hierarchical toolkit
Multidimensional_hierarchical_toolkit
NeWS Bill Gosper – Macsyma, Lisp machine, hashlife, helped Donald Knuth on Vol.2 of The Art of Computer Programming (Semi-numerical algorithms) Paul Graham
List_of_programmers
Difference between logarithm and harmonic series
of Mersenne primes. An estimation of the efficiency of the euclidean algorithm. Sums involving the Möbius and von Mangolt function. Estimate of the divisor
Euler's_constant
3927⁄1250 and 754⁄240 3.1416 3 −2.338×10−2% 1220 Fibonacci 3.141818 3 +7.173×10−3% 1320 Zhao Youqin Zhao Youqin's π algorithm 3.141592 6 −2.080×10−3%
Chronology of computation of pi
Chronology_of_computation_of_pi
Generalized Balanced Ternary (GBT) Applied to High-Performance Computational Algorithms". APS Meeting Abstracts. Bibcode:1997APS..CPC..C409D. van Roessel, Jan
Generalized_balanced_ternary
Cellular automaton neighborhood consisting of four adjacent cells
Vision Algorithms in Image Algebra (2nd ed.), CRC Press, p. 177, ISBN 9781420042382. Breukelaar, R.; Bäck, Th. (2005), "Using a Genetic Algorithm to Evolve
Von_Neumann_neighborhood
American mathematics and science writer (1914–2010)
majority of secure data transmission schemes. Since RSA is a relatively slow algorithm it is not widely used to directly encrypt data. More often, it is used
Martin_Gardner
"Inelegant" is a translation of Knuth's version of the algorithm with a subtraction-based remainder-loop replacing his use of division (or a "modulus"
Mathematical_visualization
Computing by new or unusual methods
complexity of an algorithm can be measured given a model of computation. Using a model allows studying the performance of algorithms independently of
Unconventional_computing
Formatting to make code or markup easier to read
example. The HTML example may require a series of progressive interrelated algorithms to account for various patterns of tag elements and content that conforms
Pretty-printing
Extension of the factorial function
to N {\displaystyle N} bits of precision with the above series. A fast algorithm for calculation of the Euler gamma function for any algebraic argument
Gamma_function
Discrete model of computation
or more dimensions reversibility is undecidable; that is, there is no algorithm that takes as input an automaton rule and is guaranteed to determine correctly
Cellular_automaton
2D cellular automaton similar to Conway's Game of Life
unlikely that a parallel algorithm exists for a simulation significantly faster than that obtained by a naive parallel algorithm with one processor per
Life_without_Death
Family of cellular automata to model feeding behaviour
worm is still active after 5.2×1019 timesteps. He used an algorithm based on Bill Gosper's Hashlife to simulate the worms at extraordinary speeds. This
Paterson's_worms
Fractal creation method
the generated figure extends outside the initial polygon. When r=2, the algorithm enters in a meta-stable state and generates quasi-symmetric figures. For
Chaos_game
Fractal sets in complex dynamics of mathematics
z ) . {\displaystyle \bigcup _{n}f^{-n}(z).} (This suggests a simple algorithm for plotting Julia sets, see below.) If f is an entire function, then
Julia_set
dropout) – founder of Instabase Katie Bouman (PhD 2017) – developer of the algorithm used in filtering the first images of a black hole taken by the Event
List of Massachusetts Institute of Technology alumni
List_of_Massachusetts_Institute_of_Technology_alumni
Linear recurrence equation
{\displaystyle f} is the sum of hypergeometric sequences. The algorithm makes use of the Gosper-Petkovšek normal-form of a rational function. With this specific
P-recursive_equation
Function in q-analog theory
"Evaluation of q-gamma function and q-analogues by iterative algorithms". Numerical Algorithms. 49 (1–4): 159–168. Bibcode:2008NuAlg..49..159G. doi:10
Q-gamma_function
Computer algebra system
another factor of perhaps 5–10 in speed for key algorithms. Macsyma did not have many of the basic algorithms of numerical linear algebra, such as LU decomposition
Macsyma
Australian social disruption festival
Forrest Alicia Garza (Black Lives Matter) Bates Gill Priyamvada Gopal Kevan Gosper Stan Grant (journalist) A.C. Grayling Germaine Greer Lev Grossman Tracey
Festival_of_Dangerous_Ideas
GOSPERS ALGORITHM
GOSPERS ALGORITHM
Boy/Male
Muslim
The gopels
Boy/Male
Muslim/Islamic
One who prospers
Girl/Female
German, Hebrew
Praise; Prospers in Battle
Girl/Female
Anglo, Australian, British, Czech, Danish, English, French, German, Teutonic
Little Wealthy One; Prospers in Battle; Fortunate; Heroine
Boy/Male
Muslim/Islamic
One who prospers
Boy/Male
Arabic, Muslim
One who Prospers
Boy/Male
Indian, Kannada, Tamil
Gospel
Boy/Male
Indian, Punjabi, Sikh
One who Fosters the Poor
Boy/Male
Muslim
One who prospers
Girl/Female
German
Prospers in Battle
Surname or Lastname
English (Cornwall and Devon)
English (Cornwall and Devon) : unexplained.
Male
Japanese
(æ£æ´‹) Japanese name MASAHIRO means "justice prospers."
Girl/Female
Australian, Danish, Finnish, German, Japanese, Romanian, Swedish
Wealth; Poem Child; Fortunate Maid of Battle; Prospers in Battle; Poem
Girl/Female
Australian, Finnish
Bringer of the Gospel
Girl/Female
Hindu, Indian
Gospel Love; Good
Boy/Male
Indian
The gopels
Girl/Female
Arabic, Muslim
One who Prospers
Boy/Male
Arabic, Muslim, Sindhi
One who Prospers
Girl/Female
German
Prospers in Battle; Fortunate Heroine
Girl/Female
French, German
Prospers in Battle; Wealthy
GOSPERS ALGORITHM
GOSPERS ALGORITHM
Boy/Male
English Scottish
Surname.'beloved.
Boy/Male
Arabic, Australian, Muslim
One who Spreads or Grants Prosperity
Male
English
Anglicized form of Hebrew Methuwshael, METHUSAEL means "man of God." In the bible, this is the name of a descendant of Cain.
Male
Portuguese
Portuguese form of Latin Fabianus, FABIÃO means "like Fabius."Â
Boy/Male
Hindu, Indian
Ganga River
Boy/Male
Muslim
Irritable, Impatient
Boy/Male
Hindu, Indian
Very Good; Brave
Boy/Male
Arabic
Servant of the King
Boy/Male
Indian
Sought after
Boy/Male
French
Makes garments.
GOSPERS ALGORITHM
GOSPERS ALGORITHM
GOSPERS ALGORITHM
GOSPERS ALGORITHM
GOSPERS ALGORITHM
n.
An unfertilized, rounded mass of protoplasm, produced in an oogonium.
n.
One of the little hours of the Breviary.
n.
A certain tool used by coopers.
v. i.
To preach the gospel.
n.
An analogous mass of protoplasm in the ovule of a flowering plant; an embryonic vesicle.
n.
Good news; announcement of glad tidings; especially, the gospel, or a gospel.
n.
See Gosherd.
v.
Anything propounded or accepted as infallibly true; as, they took his words for gospel.
n.
The four Gospels, by way of distinction or eminence.
v. t.
To instruct in the gospel.
n.
One who, or that which, fosters.
a.
Accordant with, or relating to, the gospel; evangelical; as, gospel righteousness.
n.
The evening song or service.
n.
The price paid for coopers; work.
v.
A selection from one of the gospels, for use in a religious service; as, the gospel for the day.
a.
Made of osiers; composed of, or containing, osiers.
n.
The ovum, after fusion with the spermatozoon in impregnation.
v.
Any system of religious doctrine; sometimes, any system of political doctrine or social philosophy; as, this political gospel.
n.
One who thrives, or prospers.
n.
One who coshers.