to the displayed precision. div div In mathematics , the factorial of a non negative integer n , denoted ... Mathematics , Addison Wesley, Reading MA. ISBN 0 201 14236 8, p. 111 ref The factorial operation ... The definition of the factorial function can also be Extension of factorial to non integer values of argument ... more advanced mathematics, notably techniques from mathematical analysis. TOC clr Definition The factorial ... all n elements among a set of n is math tbinom nn tfrac n n 0 1 math . The factorial function can ... of factorial to non integer values of argument section below . This more generalized definition is used ... . Applications Although the factorial function has its roots in combinatorics , formulas involving factorials ... n . The only factorial that is also a prime number is 2, but there are many primes of the form n 1, called factorial prime s. All factorials greater than 1 are Parity mathematics ... thumb right Plot of the natural logarithm of the factorial As n grows, the factorial n nowiki nowiki ... more than 700 bits, so no reasonable specification of a factorial function using fixed size types ..., and the largest factorial that fits is then 69 , because 69 10 sup 100 sup ... factorials up to 170 , which is the largest factorial whose floating point approximation can be represented ... applications will compute small factorials by direct multiplication or table lookup. Larger factorial ... efficient factorial algorithms, with or without the use of a prime sieve . ref Peter Luschny, http www.luschny.de math factorial FastFactorialFunctions.htm Fast Factorial Functions The Homepage of Factorial Algorithms . ref Extension of factorial to non integer values of argument The Gamma and Pi functions Main Gamma function Image Generalized factorial function.svg thumb right 325px The factorial ... integers, the factorial function can also be defined for non integer values, but this requires more advanced tools from mathematical analysis . One function that fills in the values of the factorial ... more details
In probability theory , the n th factorial moment of a probability distribution , also called the n th factorial moment of any random variable X with that probability distribution, is ref cite book last Riordan first John title Introduction to Combinatorial Analysis year 1958 publisher Dover pages 30 ref ref http www.staff.city.ac.uk ra359 X3MathFinance Newby2006 mathematical 20modelling 20for 20finance 5Bpart 201 5D.pdf ref math operatorname E bigl X n bigr math where math x n x x 1 x 2 cdots x n 1 math is the falling factorial confusingly, this same notation, the Pochhammer symbol x sub n sub , is used by some mathematicians, especially in the theory of special function s, to denote the rising factorial x x 1 x 2 ... x n &minus 1 the present notation is used by combinatorics combinatorialists . For example, if X has a Poisson distribution with expected value , then the n th factorial moment of X is math operatorname E bigl X n bigr lambda n. math One context in which factorial moments occur naturally is at an initial stage in the use of probability generating function s to derive the moments of discrete distributions. See also moment mathematics cumulant Factorial moment generating function References Reflist DEFAULTSORT Factorial Moment Category Probability distributions Category Factorial and binomial topics hu Faktori lis momentum pl Moment silni tr Fakt riyel moment ... more details
An exponential factorial is a positive integer n exponentiation raised to the power of n &minus 1, which in turn is raised to the power of n &minus 2, and so on and so forth, that is, math n n 1 n 2 cdots . , math The exponential factorial can also be defined with the recurrence relation math a 0 1, quad a n n a n 1 . , math The first few exponential factorials are 1 number 1 , 1 number 1 , 2 number 2 , 9 number 9 , 262144, etc. OEIS id A049384 . So, for example, 262144 is an exponential factorial since math 262144 4 3 2 1 . , math The exponential factorials grow much more quickly than regular factorial s or even hyperfactorial s. The exponential factorial of 5 is 5 sup 262144 sup which is approximately 6.206069878660874 × 10 sup 183230 sup . The sum of the reciprocals of the exponential factorials from 1 onwards is the irrational number 1.6111149258083767361111... OEIS2C id A080219 . Like tetration , there is currently no accepted method of extension of the exponential factorial function to real number real and complex number complex values of its argument, unlike the factorial function, for which such an extension is provided by the gamma function . Numtheory stub References Jonathan Sondow, http mathworld.wolfram.com ExponentialFactorial.html Exponential Factorial From Mathworld , a Wolfram Web resource Category Integer sequences Category Factorial and binomial topics Category Large integers es Factorial exponencial he uk ... more details
Image Response surface metodology.jpg thumb Designed experiments with full factorial design left , response surface with second degree polynomial right In statistics , a full factorial experiment is an experiment .... A full factorial design may also be called a fully crossed design . Such an experiment allows ... statistics interaction s between factors on the response variable. For the vast majority of factorial ..., a factorial experiment would have four treatment combinations in total, and is usually called a 2 2 factorial design . If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations usually at least half are omitted. History Factorial designs were used in the 19th century ... that complex designs such as factorial designs were more efficient than studying one factor at a time ... suggests, will best respond to a logical and carefully thought out questionnaire . A factorial design ..., by the Yates analysis . The term factorial may not have been used in print before 1935, when ... factorial experiment contains two levels for each of two factors. Suppose an engineer wishes ... speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental units motor ... sup 2 sup or 2x2 factorial experiment, so named because it considers two levels the base for each of two factors the power or superscript , or levels sup factors sup , producing 2 sup 2 sup 4 factorial points. File Factorial Design.svg thumb left Designs can involve many independent variables. As a further ... float right margin 0 0 10px 1em text align center width 9em 2 2 factorial experiment A B 1 &minus &minus a &minus b &minus ab To save space, the points in a two level factorial experiment are often ... math , math math , math math , and math math . The factorial points can also be abbreviated by 1 ... values. Implementation For more than two factors, a 2 sup k sup factorial experiment can be usually ... more details
A factorial prime is a prime number that is one less or one more than a factorial all factorials above 1 are even . The first few factorial primes are 2 number 2 0 1 or 1 1 , 3 number 3 2 1 , 5 number 5 3 &minus 1 , 7 number 7 3 1 , 23 number 23 4 &minus 1 , 719 6 &minus 1 , 5039 7 &minus 1 , 39916801 11 1 , 479001599 12 &minus 1 , 87178291199 14 &minus 1 , ... OEIS id A088054 n &minus 1 is prime for OEIS id A002982 n 3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, 1963, 3507, 3610, 6917, 21480, 34790, 94550, 103040, ... n 1 is prime for OEIS id A002981 n 0, 1, 2, 3, 11, 27, 37, 41, 73, 77, 116, 154, 320, 340, 399, 427, 872, 1477, 6380, 26951, 110059, ... No other factorial primes are known as of 13 June 2011. Absence of primes to both sides of a factorial n implies a relatively lengthy run of consecutive composite number s, since n k is divisible by k for 2 &le k &le n . For example, the next prime following 6227020777 13 &minus 23 is 6227020867 13 67 a run of 89 consecutive composites here the run is substantially longer than implied merely by the absence of factorial primes. Note that this is not the most efficient way to find large prime gap s. E.g., there are 95 consecutive composites between the primes 360653 and 360749. See also Primorial prime External links MathWorld urlname FactorialPrime title Factorial Prime http primes.utm.edu top20 page.php?id 30 List of largest known factorial primes from the Prime Pages http www.primegrid.com forum thread.php?id 3008&nowrap true 30721 Factorial Prime Search from PrimeGrid Prime number classes state collapsed Category Integer sequences Category Classes of prime numbers Category Factorial and binomial topics da Fakultetsprimtal de Fakult tsprimzahl fr Nombre premier factoriel it Primo fattoriale ja fi Kertoma ... more details
In mathematics , an alternating factorial is the absolute value of the alternating sum of the first n factorial s. This is the same as their sum, with the odd indexed factorials multiplied by 1 number &minus 1 if n is even, and the even indexed factorials multiplied by &minus 1 if n is odd, resulting in an alternation of signs of the summands or alternation of addition and subtraction operators, if preferred . To put it algebraically, math mathrm af n sum i 1 n 1 n i i math or with the recurrence relation math mathrm af n n mathrm af n 1 math in which af 1 1. The first few alternating factorials are 1, 1 number 1 , 5 number 5 , 19 number 19 , 101 number 101 , 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019 OEIS id A005165 For example, the third alternating factorial is 1 &minus 2 3 . The fourth alternating factorial is &minus 1 2 3 4 19. Regardless of the parity of n , the last n sup th sup summand, n , is given a positive sign, the n 1 sup th sup summand is given a negative sign, and the signs of the lower indexed summands are alternated accordingly. This pattern of alternation ensures the resulting sums are all positive integers. Changing the rule so that either the odd or even indexed summands are given negative signs regardless of the parity of n changes the signs of the resulting sums but not their absolute values. Miodrag Zivkovi proved in 1999 that there are only a finite number of alternating factorials that are also prime number s, since 3612703 divides af 3612702 and therefore divides af n for all n &ge 3612702. As of 2006 , the known primes and probable prime s are af n for OEIS id A001272 n 3, 4, 5, 6, 7, 8, 10, 15, 19, 41, 59, 61, 105, 160, 661, 2653, 3069, 3943, 4053, 4998, 8275, 9158, 11164 Only the values up to n 661 have ... MathWorld urlname AlternatingFactorial title Alternating Factorial Yves Gallot, http perso.wanadoo.fr ... search for primes of form n n 1 n 2 n 3 ... 1 Category Integer sequences Category Factorial and binomial ... more details
This is a list of factorial and binomial topics in mathematics , by Wikipedia page. See also binomial disambiguation . Abel s binomial theorem Alternating factorial Antichain Beta function Binomial coefficient Binomial distribution Binomial proportion confidence interval Binomial QMF Daubechies wavelet filters Binomial series Binomial theorem Pascal s triangle Binomial transform Binomial type Carlson s theorem Catalan number Central binomial coefficient Combination De Polignac s formula Difference operator Difference polynomials Digamma function Erd s Ko Rado theorem Euler Mascheroni constant Fa di Bruno s formula FactorialFactorial moment Factorial prime Gamma distribution Gamma function Gaussian binomial coefficient Hyperfactorial Hypergeometric distribution Hypergeometric function identities Hypergeometric series Incomplete beta function Incomplete gamma function Lah number Lanczos approximation Lozani s triangle Mahler s theorem Multinomial distribution Multinomial coefficient , Multinomial formula , Multinomial theorem Multiplicities of entries in Pascal s triangle Multiset Multivariate gamma function Narayana numbers Negative binomial distribution N rlund Rice integral Pascal matrix Pascal s pyramid Pascal s simplex Pascal s triangle Permutation List of permutation topics Pochhammer symbol also falling, lower, rising, upper factorials Poisson distribution Polygamma function Primorial Proof of Bertrand s postulate Sierpinski triangle Star of David theorem Stirling number Stirling transform Stirling s approximation Subfactorial Table of Newtonian series Taylor series Trinomial expansion Vandermonde s identity Wilson prime Wilson s theorem Wolstenholme prime Category Mathematics related lists Factorial and binomial topics Category Factorial and binomial topics ... more details
Refimprove date December 2009 In probability theory and statistics , the factorial moment generating function of the probability distribution of a real number real valued random variable X is defined as math M X t operatorname E bigl t X bigr math for all complex number s t for which this expected value exists. This is the case at least for all t on the unit circle math t 1 math , see characteristic function probability theory characteristic function . If X is a discrete random variable taking values only in the set 0,1, ... of non negative integer s, then math M X math is also called probability generating function of X and math M X t math is well defined at least for all t on the closed set closed unit disk math t le1 math . The factorial moment generating function generates the factorial moment s of the probability distribution . Provided math M X math exists in a neighbourhood mathematics neighbourhood of t 1, the n th factorial moment is given by ref http homepages.nyu.edu bpn207 Teaching 2005 Stat Generating Functions.pdf ref math operatorname E X n M X n 1 left. frac mathrm d n mathrm d t n right t 1 M X t , math where the Pochhammer symbol x sub n sub is the falling factorial math x n x x 1 x 2 cdots x n 1 . , math Confusingly, some mathematicians, especially in the field of special function s, use the same notation to represent the rising factorial . Example Suppose X has a Poisson distribution with expected value , then its factorial moment generating function is math M X t sum k 0 infty t k underbrace operatorname P X k , lambda ke lambda k e lambda sum k 0 infty frac t lambda k k e lambda t 1 , qquad t in mathbb C , math use the Exponential function Formal definition definition of the exponential function and thus we have math operatorname E X n lambda n. math See also Moment mathematics Moment generating function Cumulant generating function Reflist DEFAULTSORT Factorial Moment Generating Function Category Factorial and binomial topics ... more details
numeral systems In combinatorics , the factorial number system , also called factoradic , is a mixed radix numeral system adapted to numbering permutation s. It is also called factorial base , although factorial s do not function as base, but as place value of digits. By converting a number less than n to factorial representation, one obtains a sequence of n digits that can be converted to a permutation ... Mathematik und Physik volume 14 year 1869 . ref The term factorial number system is used by Donald ... 16 176 0 volume 16 year 1888 . ref The term factoradic , which is a portmanteau of factorial and mixed ... library aa302371.aspx year 2003 . ref Definition The factorial number system is a mixed radix numeral ..., and so on. The factorial number system is sometimes defined with the rightmost digit omitted, because it is always zero OEIS id A007623 . In this article a factorial number representation will be flagged ... systems apply to the factorial number system as well. For instance, one can convert a number into factorial ... Vector ref which are reflected factorial numbers below them. Another column shows the inversion sets. The digit sums of the inversion vectors or factorial numbers and the cardinalities of the inversion ... permutations and their inversion vectors br compare File Symmetric group 4 permutohedron factorial number system.svg version with factorial numbers br The arrows indicate the bitwise less or equal math ... 662px height 34px decimal factorial 0 0 sub sub 1 10 sub sub 2 100 sub sub 3 110 sub sub 4 200 sub ... factorial number representation after 543210 sub sub is 1000000 sub sub which designates 6 ... expression above, is equal to 6 1. The factorial number system provides a unique representation for each ... factorial minus one math sum i 0 n i cdot i n 1 1. math This can be easily proved with mathematical ... digit by its base, also given in decimal . In fact the factorial number system itself is not truly a numeral ... s 0, ..., n &minus 1 or equivalently the numbers with n digits in factorial ... more details
rely on statistical reference books to supply the standard fractional factorial designs, consisting ... factorial experiment is generated from a full factorial experiment by choosing an alias structure ... factor 2 sup 5 &minus 2 sup can be generated by using a full three factor factorial experiment ... pri section3 pri334.htm Fractional Factorial Designs National Institute of Standards and Technology ... Fractional Factorial Design Experimental design Statistics Category Design of experiments Category ... more details
Multifactorial can refer to The factorial Multifactorials multifactorial in mathematics. Multifactorial inheritance , a pattern of predisposition for a disease process. disambig ... more details
source Demonstrating while loops These while loops will calculate the factorial of the number 5 ActionScript ActionScript 3.0 ActionScript 3 source lang actionscript var counter int 5 var factorial int 1 while counter 1 factorial counter counter trace Factorial , factorial source Ada programming language Ada Wikibooks Ada Programming Control source lang ada with Ada.Integer Text IO procedure Factorial is Counter Integer 5 Factorial Integer 1 begin while Counter 0 loop FactorialFactorial Counter Counter Counter 1 end loop Ada.Integer Text IO.Put Factorial end Factorial source Bash Unix shell Bash source lang bash counter 5 factorial 1 while counter gt 0 do factorialfactorial counter counter counter 1 done echo factorial source QBasic or Visual Basic source lang vb Dim counter As Integer 10 ... 0 source C programming language C or C source lang c unsigned int counter 5 unsigned long factorial 1 while counter 0 factorial counter Multiply and decrement printf lu , factorial source Fortran source lang fortran program FactorialProg integer counter 5 integer factorial 1 do while counter 0 factorialfactorial counter counter counter 1 end do print , factorial end program FactorialProg source ... for the loop is the same for Java, C and D source lang csharp int counter 5 long factorial 1 while counter 1 factorial counter source For Java the result is printed as follows source lang java System.out.println factorial source The same in C source lang csharp System.Console.WriteLine factorial source And finally in D source lang d writefln factorial source JavaScript source lang javascript var counter 5 var factorial 1 while counter 1 factorial counter document.write factorial source Lua programming language Lua source lang lua counter 5 factorial 1 while counter 0 do factorialfactorial counter counter counter 1 end print factorial source MATLAB source lang matlab counter 5 factorial 1 while counter 0 factorialfactorial counter Multiply counter counter 1 Decrement end factorial source ... more details
loops These example programs calculate the factorial of 5 using their respective languages syntax for a do while loop. ActionScript 3 source lang actionscript var counter int 5 var factorial int 1 do factorial counter Multiply, then decrement. while counter 0 trace factorial source Ada Ada demonstrates ... Text IO procedure Factorial is Counter Integer 5 Factorial Integer 1 begin loop FactorialFactorial Counter Counter Counter 1 exit when Counter 0 end loop Ada.Integer Text IO.Put Factorial end Factorial source C or C C demonstrates the canonical do while syntax. source lang c unsigned int counter 5 unsigned long factorial 1 do factorial counter Multiply, then decrement. while counter 0 printf lu n , factorial source C source lang c int counter 5 int factorial 1 do factorial counter Multiply, then decrement. while counter 0 System.Console.WriteLine factorial source Fortran Free form source ... program FactorialProg integer counter 5 integer factorial 1 do factorialfactorial counter counter counter 1 if counter 0 exit end do print , factorial end program FactorialProg source With Fortran 90 ... program FactorialProg integer counter 5 integer factorial 1 factorialfactorial counter counter counter 1 do while counter 0 factorialfactorial counter counter counter 1 end do print , factorial end program FactorialProg source Java source lang java int counter 5 int factorial 1 do factorial counter Multiply, then decrement. while counter 0 System.out.println factorial source JavaScript source lang javascript var counter 5 var factorial 1 do factorial counter while counter 0 document.body.appendChild document.createTextNode factorial source Perl source lang perl counter 5 factorial 1 do factorial counter while counter 0 print factorial source PHP source lang php ?php counter 5 factorial 1 do factorial counter while counter 0 echo factorial ? source Racket In Racket, as in other Scheme ... lang scheme lang racket define counter 5 define factorial 1 let loop set factorialfactorial counter ... more details
About a functional programming language used primarily by students the scripting language created by IBM REXX Orphan date February 2009 lowercase title rex rex is a functional programming language developed by Robert M. Keller for use in teaching functional programming to Harvey Mudd College students. The rex interpreter is written in Prolog . Example The Hello world program Hello World of functional languages is the factorial function. Expressed in rex factorial 0 1 factorial X X factorial X 1 The name rex derives from rewriting expressions , which is the basic principle underlying the implementation replace an instantation of an expression on the left hand side of a rule with the instantiated right hand side. External links http www.cs.hmc.edu keller rex Documentation for the rex Language and Interpreter Category Functional languages Category Educational programming languages it Rex linguaggio ... more details
Compile time function execution or compile time function evaluation , CTFE is the ability of a compiler , that would normally compile a function to machine code and execute it at Run time program lifecycle phase run time , to execute the function at compile time . This is possible if the arguments to the function are known at compile time, and the function does not make any reference to or attempt to modify any global state is a pure function . Even if the value of only some of the arguments are known, the compiler may still be able to perform some level of compile time function execution partial evaluation , possibly producing more optimized code than if no arguments were known. Example In earlier versions of C , template metaprogramming is often used to compute values at compile time, such as source lang CPP template int N struct Factorial enum value N Factorial N 1 value template struct Factorial 0 enum value 1 Factorial 4 value 24 Factorial 0 value 1 void foo int x Factorial 0 value 1 int y Factorial 4 value 24 source Using compile time function evaluation, code used to compute the factorial would be exactly the same as what one would write for run time evaluation. Here s an example of CTFE in the D programming language ref http d programming language.org function.html interpretation D 2.0 language specification Functions ref source lang D int factorial int n if n 0 return 1 return n factorial n 1 computed at compile time const int y factorial 0 1 const int x factorial 4 24 source This example specifies a valid D function called factorial which would typically be evaluated at run time. The use of code const code tells the compiler that the initializer for the variables must be computed at compile time. Note that the arguments to the function must be able to be resolved at compile time as well. ref http d programming language.org attribute.html const D 2.0 language specification Attributes ref CTFE can be used to populate data structures at compile time in a simp ... more details
final results. One example of a commonly encountered hylomorphism is the canonical factorial function. source lang haskell factorial Integer Integer factorial n n 0 1 n 0 n factorial n 1 source ... factorial 5 5 factorial 4 120 factorial 4 4 factorial 3 24 factorial 3 3 factorial 2 6 factorial 2 2 factorial 1 2 factorial 1 1 factorial 0 1 factorial 0 1 In this example, the anamorphic part ... mathematics elements of this list. Thus, in the notation given above, the factorial function may be written math text factorial 1, times , g, p math where math g n n, n 1 math and math p n n 0 math ... more details
dabconcept Should describe the history and usage of the character, with existing links as examples wiktionary a double exclamation mark may refer to A Punctuation chess Brilliant move brilliant move in chess notation The factorial Double factorial double factorial operator in mathematics A convert to Boolean data type Boolean pseudo operator in some computer languages This is through a computer type of double negative , where its Boolean value is negated, then negated again, converting to the value to either true or false An operator for getting the n th element of a list in the programming language Haskell programming language Haskell A retroflex clicks retroflex click , a family of click consonants found only in Juu languages of southern Africa and in the Damin ritual jargon of Australia The double exclamation mark is present in Unicode as the single character U 203C DOUBLE EXCLAMATION MARK and Code page 437 at 19. See also disambiguation disambiguation de es eo fr ko it ru zh ... more details
In mathematics , two different function mathematics functions are known as the pi or Pi function math pi x , math pi function &ndash the prime counting function math Pi x , math Pi function &ndash the Gamma function when offset to coincide with the factorial disambig th ... more details
In the design of experiments and analysis of variance , a main effect is the effect of an independent variable on a dependent variable averaging across the levels of any other independent variables. The term is frequently used in the context of factorial design s and regression analysis regression models to distinguish main effects from interaction statistics interaction effects. For example, in factorial designs, the main effect is what the independent variables elicit when averaged out over each other. References McBurney, D.M., White, T.L. 2004 . Research Methods . CA Wadsworth Learning. Mook, Douglas G. 2001 . Psychological Research The Ideas Behind the Methods . NY W. W. Norton & Company. statistics stub Category Research Category Analysis of variance ... more details
represent either the rising factorial or the falling factorial as defined below. Care needs to be taken ... factorial sometimes called the descending factorial , ref name Steffensen falling sequential product , lower factorial math x n x x 1 x 2 cdots x n 1 math In this article the symbol math x sup n sup is used for the rising factorial sometimes called the Pochhammer function , Pochhammer polynomial , ascending factorial , ref name Steffensen Citation last Steffensen first J. F. authorlink ... product or upper factorial math x n x x 1 x 2 cdots x n 1 . math These conventions are used in combinatorics ... function the Pochhammer symbol math x sub n sub is used to represent the rising factorial ... on binomial coefficients carry over to the falling and rising factorials. A rising factorial can be expressed as a falling factorial that starts from the other end math x n x n 1 n . math This is a special ... with complex coefficients, or any complex valued function. The rising factorial can be extended ... can the falling factorial math x n frac Gamma x 1 Gamma x n 1 . math If math D denotes derivative differentiation ... calculus The falling factorial occurs in a formula which represents polynomial s using the forward difference ... and in many other places, the falling factorial math x sub k sub in the calculus of finite difference ... factorial. The study of analogies of this type is known as umbral calculus . A general theory covering such relations, including the falling and rising factorial functions, is given by the theory ... factorial math x overline m overbrace x x 1 ldots x m 1 m mathrm factors qquad mbox for integer m ge0, math and for the falling factorial math x underline m overbrace x x 1 ldots x m 1 m mathrm ... factorial include math P x , n , math sup x sup P sub n sub , math P sub x , n sub , or math ... factorial math x sup n sup is the less common math x sup sup sub n sub . When the notation math x sup sup sub n sub is used for the rising factorial, the notation math x sup &ndash sup sub n sub is typically ... more details
Orphan date February 2009 In computing , Fudgets is a graphical user interface toolkit for the functional programming language Haskell programming language Haskell and the X Window System . Fudgets makes it easy to create client server applications that communicate via the Internet . Most of the work on Fudgets was done in 1991 1996 by Thomas Hallgren and Magnus Carlsson. The authors claim that many of the advantages of Fudgets come from the fact that they are programmed in a Non strict programming language lazy functional programming language . The main entity of toolkit is fudget implemented on low level through stream processors which has its own input and output. Fudgets can be composed in parallel or sequence yielding new fudget which can be used in code as any other fudget. Example factorialF stdoutF mapF show . factorial . read stdinF factorial Integer Integer factorial n product 1..n The code is self describing considering that is sequential fudget plumbing and mapF is fudget that takes a function of one argument and makes a fudget which output is input applied to that function. Note that fudget composition must be read from right to left, as a simple function composition. Now you can simply write main fudlogue factorialF compile and run. For every given integer value it will print its factorial. License The license of Fudgets claims that this software is Freeware free for non commercial use only. External links http www.altocumulus.org Fudgets Fudgets home page http www.cse.chalmers.se hallgren Thesis Fudgets Phd thesis by Hallgren and Carlsson http hsffig.sourceforge.net repos FudgetsNew darcs repository for Cabal software cabal izing fudgets does not contain any Fudgets source code Category Widget toolkits Category X based libraries Category Haskell software compu lang stub ... more details
LCFC can stand for Lancaster City F.C. Lancaster City Football Club , an English football club Leicester City F.C. Leicester City Football Club , an English football club Lincoln City F.C. Lincoln City Football Club , an English football club Liverpool County Football Combination , an English football league London Caledonians F.C. , a former English football club Lowest Common Factorial of Crime , a modern form of mathematical, criminal justice disambig ... more details
lowercase expert Computing date May 2010 wikibooks 1 Common Lisp 2 First steps Experienced tutorial Defining functions 3 Defining functions in Common Lisp defun short for de fine fun ction is a Macro computer science macro in the Lisp programming language Lisp family of programming languages that defines a Subroutine function in the global variable global environment ref http www.lispworks.com documentation HyperSpec Body m defun.htm Macro DEFUN ref that uses the form ref http www.sftw.umac.mo fstmcjr sftw120 lisp.html ref source lang lisp defun function name parameter1 parameter2 ... parameterN functionbody source Defining the function code addnumbers code that adds two numbers source lang lisp Define a function that adds two numbers together defun addnumbers number1 number2 number1 number2 addnumbers 5 4 9 source defining function code square code that squares a number source lang lisp Define a function that squares a number defun square x x x source and defining a function that returns the code factorial code of a code number code source lang lisp defun factorial number if number 1 1 number factorial number 1 factorial 6 720 source See also tt Scheme programming language define tt tt Common Lisp Macros defmacro tt tt Lambda Lambda.2C the word lambda tt in Lisp programming language Lisp References references External links http www.gnu.org software emacs emacs lisp intro html node defun.html code defun code in Emacs Lisp Compu lang stub Category Articles with example Lisp code ... more details
The sparsity of effects principle states that a system is usually dominated by main effect s and low order interactions. Thus it is most likely that main single factor effects and two factor interactions are the most significant responses see factorial experiment . In other words, higher order interactions such as three factor interactions are very rare. Formally, C.F. Jeff Wu and Hamada 2000, page 112 refer to this as the hierarchical ordering principle . They state that the effect sparsity principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant. br Note the Wu Hamada principle is only valid on the assumption of a factor space far from a stationary point Statistics for experimenters Box, Hunter, Hunter 2005 page 208 See also Occam s Razor References Wu, C. F. Jeff and Hamada, Michael 2000 Experiments Planning, analysis, and parameter design optimization, New York Wiley, ISBN 0 471 25511 4. Category Design of experiments Category Social sciences methodology Category Statistical principles ... more details
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