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Factorial - Wikipedia, the free encyclopedia

The primorial is similar to the factorial, but with the product taken only over the prime numbers.
The double factorial is the most commonly used variant, but one can similarly define the triple factorial (n!!!) and so on.
The factorial function can also be defined for non-integer values, but this requires more advanced tools from mathematical analysis.

http://en.wikipedia.org/wiki/Factorial (1184 words)



Factorial Analysis of Variance

The means plot indicates an inverse relationship between the daytime and late shifts.
The default ANOVA model includes only the main effects (that is, the terms representing shift and day).
Select shift and day as the independent variables.

http://www.okstate.edu/sas/v8/sashtml/analyst/chap10/sect4.htm (598 words)



5.3.3.4. Fractional factorial designs

The following sections will show you how to choose an appropriate fraction of a full factorial design to suit your purpose at hand.
We use various strategies that ensure an appropriate choice of runs.
Later sections will show how to choose the "right" fraction for 2-level designs - these are both balanced and orthogonal

http://www.itl.nist.gov/div898/handbook/pri/section3/pri334.htm (298 words)



Factorial experiment - Wikipedia, the free encyclopedia

This may not be feasible due to high cost or insufficient resources.
However, the number of experimental runs required for three-level factorial designs can be much greater than for their two-level counterparts.
Factorial experiments can be used when there are more than two levels of each factor.

http://en.wikipedia.org/wiki/Factorial_experiment (681 words)



February 1992/Arithmetic In Factorial-Base

Note that it is not necessary to actually calculate the value of 3!
Now, assume the number is represented an array of longs and LONG_MAX is 2147483647.
On systems that allot a fixed amount of memory for use as a program stack, it may be necessary to declare all or most of the temporary numbers as static arrays, rather than the default to auto.

http://www.tcnj.edu/~hernande/cujv5/html/10.02/hegeman/hegeman.htm (1673 words)



factorial - a Whatis.com definition

The factorial value of 0 is defined as equal to 1.
The factorial is of interest to number theorists.
The factorial, symbolized by an exclamation mark (!), is a quantity defined for all integers greater than or equal to 0.

http://whatis.techtarget.com/definition/0,,sid9_gci945482,00.html (206 words)



Factorial ANOVA

Factorial ANOVA means you have 2 or more independent variables.
Factorial ANOVA increases the power by adding another factor.
A second factor is added to a one-way ANOVA design to increase power.

http://carbon.cudenver.edu/~lsherry/rem/factorial_anova.html (632 words)



PSY290AC - Lesson 8

Interactions occur when the effect of one independent variable is dependent on the level of another independent variable.
The first independent variable has two levels (indicated by the number 2) and the second independent variable has three levels (indicated by the number 3).
When developing a report for results of a factorial design, a matrix should always be included for ease of communicating; the goal is to have the results of the experiment as clear as possible for the reader.

http://www.rio.maricopa.edu/classes/psy/psy290ac/011303/lessons/lesson08.shtml (1895 words)



Prolog Tutorial -- 2.2

The Prolog goal to calculate the factorial of the number 3 responds with a value for W, the goal variable:
How do the two programs differ with regard to how they compute factorial?
Two predicate definitions that calculate the factorial function are in file 2_2.pl, which the reader can view by clicking on the 'Code' link at the bottom of this page.

http://www.csupomona.edu/~jrfisher/www/prolog_tutorial/2_2.html (813 words)



Introduction.

Notice that when a value of greater than 21 is entered the factorial calculated is a large negative number, can you explain why this might be?
Perhaps the simplest example of recursion is the factorial function.
This process of breaking the factorial problem down into finding a smaller factorial and multiplying until the smaller number is 0, i.e.

http://www.iol.ie/~jmchugh/csc302/simple/fact (376 words)



Java: Example - Factorial

Recursion is a great tool, but using it where it's not appropriate doesn't set a great example.
Even the iterative solution has problems because the large numbers that factorial generates cannot be represented in the limited range of integers, or limited precision of floating-point numbers.
Programs using these primitive types are very dangerous because they will produce garbage results without comment.

http://leepoint.net/notes-java/data/numbers/60factorial.html (269 words)



Halfbakery: Inverse Factorial '?'

Browse anonymously, or get an account and write.
Mathematics is a field slightly larger than factorial calculations, as I recall.
But that would be ugly with the factorial.

http://www.halfbakery.com/idea/Inverse_20Factorial_20_27_3f_27 (672 words)



The Top Twenty: Factorial

Factorial primes come in two flavors: factorial plus one: n!+1, and factorial minus one: n!-1.
The chronology of prime number records' Factorial/Primorial Prime Records by year
There is more information of primorial and factorial primes in [Dubner87] and [Dubner89a].

http://primes.utm.edu/top20/page.php?id=30 (198 words)



Factorial Designs

Whenever we are interested in examining treatment variations, factorial designs should be strong candidates as the designs of choice.
You may also want to examine how we approach the statistical analysis of factorial experimental designs.
Finally, factorial designs are the only effective way to examine interaction effects.

http://www.socialresearchmethods.net/kb/expfact.htm (1421 words)



PlanetMath: falling factorial

Watson [5] credits this notation to Pochhammer [6], and indeed the special functions literature eschews ``falling factorial'' in favour of ``Pochhammer symbol''.
Works of combinatorics [1,2,3] give greater focus to the falling factorial because of its role in defining the Stirling numbers.
Works focusing on special functions [4,5] universally use

http://planetmath.org/encyclopedia/RisingFactorial.html (322 words)



Factorial

Problem Statement: Write a FORTRAN program to calculate the factorial of a given number.
Problem Statement: Write a QBasic program to calculate the factorial of a given number.
c ---------------------------------------------------------------------- c Calculate the factorial of a given number c Variables used: c n...

http://www.glue.umd.edu/~nsw/ench250/fact.htm (204 words)



The Factorial Tutorial

The factorial function does not benefit from an optimistic implementation, and so should not be written in E. It can be implemented more efficiently in Java.
The factorial function is used in the study of permutations.
This use of E can be beneficial in the case where there is a math server available that could compute the function while the requestor goes on doing other useful work.

http://www.crockford.com/ec/factorial.html (930 words)



Numbers: glossary

Factorials of other numbers are calculated in the same way.
Factorials are useful in working out the number of different ways you can arrange things.
It is just a convenient way of writing 'factorial 5'.

http://richardphillips.org.uk/number/gl/facto.htm (187 words)



Factorial Limited Multimedia and Web Site Development

Factorial is a design and production studio founded in 1999 by principals Daniel Deverell, Jonathan Schnapp, and Kris Luhrssen.
Unlike many multimedia content developers, Factorial has a long history of designing print for publishing houses, ad and public relations agencies, and the technology sector.
When I first started Factorial I was known for creating CD-ROMs and video for marketing purposes.

http://factorial.net (183 words)



GLM: 2-way factorial

In a factorial analysis of variance design each level of a treatment occurs under each level of every other treatment.
Move the variable score to the Dependent Variable: window.
The Simple Factorial procedure cannot handle repeated measures designs, nor can you make planned comparisons with the Simple Factorial procedure.

http://web.uccs.edu/lbecker/SPSS80/glm_2way_80.htm (5385 words)



Factorial Algorithm

factorial := 1; { initialise running product variable }
Factorial is often used as a (very poor) example of recursion since n!
The factorial of an integer is the product of all the positive integers less than or equal to it.

http://portal.newman.wa.edu.au/technology/12infsys/html/KWH2003/SBP6Fact.htm (1064 words)



CHAPTER 9 BETWEEN-SUBJECTS FACTORIAL DESIGNS

The authors explain that researchers measure main effects (the action of each independent variable on a dependent variable) and interaction effects (a change in the effect of one independent variable across the levels of another independent variable) in factorial experiments.
They review the advantages of using these more complex designs, which include efficiency and measurement of interactions.
This chapter extends chapter eight’s coverage of between-subjects designs and examines between-subjects factorial designs in which two or more independent variables (factors) are studied in the same experiment.

http://www2.truman.edu/shaffer/266ch9_2002.htm (937 words)



factorial

From these values, the true effects can be separated from the effects which are within the experimental error.
A two-level, full factorial design was implemented in these experiments to compare the effects of four different species on the corrosion parameters.
Figure 2a shows a sample printout of the sum of the squares, the mean squares, the F ratios and the probabilities for this factorial analysis.

http://www.virginia.edu/cese/vol1/paper4/factor.htm (507 words)



Factorial Frequencies

Unlike palm-reading, however, she can't just conjure up these frequencies, so she has employed you to detemine these values.
As she expects to use either the day of the week, the day of the month, or the day of the year as the value of n, you must be able to determine the number of occurrences of each decimal digit in numbers as large as 366 factorial (366!), which has 781 digits.
In an attempt to bolster her sagging palm-reading business, Madam Phoenix has decided to offer several numerological treats to her customers.

http://acm.uva.es/p/v3/324.html (287 words)



Two Way ANOVA

Although the number of subjects is the same in both designs, with the factorial design, we obtain the additional information about the relationship of previous experience with the drug to memory performance.
Furthermore, the analysis would show that the two control groups were not significantly different at any age.
The design provides more information from the same amount of work.

http://www.uwsp.edu/psych/stat/13/anova-2w.htm (3497 words)



Factorial Analysis of Variance

One-way factorial analysis - one independent variable (IV) and one dependent variable (DV Two-way factorial analysis - two IVs and one DV.
Three-way factorial analysis - three IVs and one DV.

http://www.chsbs.cmich.edu/k_han/psy612/anova-twoway.htm (519 words)



The Evolution of a Haskell Programmer

KRC may or may not be a trademark of Research Software, Ltd.,
The code shown here is based on an account by Thomas Hallgren (see [7]), extended to include factorial.
I attended Iavor’s excellent presentation and remarked that I found the end of the paper rather anti-climactic: after much categorical effort and the definition of several generalized recursion combinators, the main examples were the factorial and Fibonacci functions.

http://www.willamette.edu/~fruehr/haskell/evolution.html (2890 words)



PlanetMath: factorial

In this way the notion of factorial can be generalized to all complex values except the negative integers.
(Combinatorics :: Enumerative combinatorics :: Factorials, binomial coefficients, combinatorial functions)
Alternatively, the factorial can be defined recursively by

http://planetmath.org/encyclopedia/Factorial.html (98 words)



factorial

Factorial is often used as a (poor) example of recursion, since n!
Peter Luschny's 14 fast factorial algorithms (Java and C#) including benchmarks and advice.
Paul E. Black, "factorial", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.

http://www.nist.gov/dads/HTML/factorial.html (106 words)



The Prime Glossary: factorial

The factorial of a positive integer is the product of all the positive integers less than or equal to it.
The factorial of n is usually denoted n!

http://primes.utm.edu/glossary/page.php?sort=Factorial (88 words)



5.3.3.3. Full factorial designs

As shown by the above table, when the number of factors is 5 or greater, a full factorial design requires a large number of runs and is not very efficient.
A common experimental design is one with all input factors set at two levels each.
If there are k factors, each at 2 levels, a full factorial design has 2

http://www.itl.nist.gov/div898/handbook/pri/section3/pri333.htm (157 words)



Factorial

It is! But the EL-9600 can only do up to the factorial of 69, 70 is to high for it to calculate.
This is the problem: The EL-9600 is only programmed to do up to X*10e99, any number of factorial over 69 will exceed the limit of the 99 max exponent.
Therefore to get around this, I simply make up my own exponent type thing.

http://www.angelfire.com/ca/cdrmrc/Factorial.html (192 words)



factorial

[n] the product of all the integers up to and including a given integer; "1, 2, 6, 24, and 120 are factorials".

http://lookwayup.com/lwu.exe/lwu/d?s=f&w=factorial (22 words)



ABC-Dir: Factorial

[Win] Co-Word Mapping, Cluster Analysis and FAC (factorial analysis of correspondence) software and glossary on Coocurrence and Graph Methods by...
Technical paper describing the conditions for biosynthesis of the Aspergillus Niger IBT-90 enzyme by a mathematical method of factorial planning...
Factorial function, iterative computation of the square root, nonadvancing I/O, dynamic arrays, Towers of Hanoi, and other topics.

http://www.abc-directory.com/view/factorial (123 words)



Fractional Factorial DOE

A fractional factorial DOE is useful when the number of potential factors is relatively large because they reduce the total number of runs required.
By reducing the number of runs, a fractional factorial DOE will not be able to evaluate the impact of some of the factors independently.
A fractional factorial design of experiment (DOE) includes selected combinations of factors and levels.

http://www.isixsigma.com/dictionary/Fractional_Factorial_DOE-245.htm (254 words)



The American Statistician: Plotting p(super k) factorial or p(super n-k) fractional factorial data.@ HighBeam Research

The raw data are displayed in a tree structure where the order of the tree is determined by increasing sums of squares from an analysis of variance model.
Search for more information on HighBeam Research for.
A computer code written is S that produces the factorial data plot is available from the author.

http://www.highbeam.com/library/doc0.asp?DOCID=1G1:19027721&refid=ip_encyclopedia_hf (235 words)



factorial. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.

The product of all the positive integers from 1 to a given number: 4 factorial, usually written 4!, is equal to 24 (1 × 2 × 3 × 4 = 24).
Of or relating to a factor or factorial.

http://www.bartleby.com/61/77/F0007700.html (103 words)



[No title]

The simple case in our Factorial problem is Factorial (0) which can be solved with the answer of 1.
1; --i) { product = product * i; } /* Return function result */ return (product); } ¡VZAXDB&ðH ð@ ð0“Þ½h”¿ÿ ?ð ÿÿÿÌ33ÌÌÌÿ²²²î×ï ððDðð( ð ðDð0¢ ðD ð0ë’¿¿ÀÿðàððK ðÐ¨To solve the Factorial problem using recursion (or any other recursive solution) the function must include the following: 1) statements to solve the simple case.
The general case contains the logic needed to reduce the size of the problem which would be n * Factorial (n - 1).¡S `^—(h¦¸ð§¢ ðD £ð

http://grail.cba.csuohio.edu/~jomalone/Wk15Notes.ppt (184 words)



Chapter 12 p 1

Factorial ANOVA: Models with Multiple Categorical Predictors and Product Terms
Unfortunately, in the traditional approach to ANOVA it is usually the only test that is presented in the source table.
In this chapter we investigate models with two or more categorical predictors.

http://espse.ed.psu.edu/espse/hale/507Mat/Chapt12/Chapt12p1.html (819 words)



Factorial Design Analysis

Here is the regression model statement for a simple 2 x 2 Factorial Design.
In this model, the main effects are the statistics associated with the beta values that are adjacent to the Z-variables.
Purchase a printed copy of the Research Methods Knowledge Base

http://www.socialresearchmethods.net/kb/statfact.htm (234 words)



factorial randomness

Compare these results a = 0.89874592240, b = -0.4.8940098622 and R = 0.99661451810 with the results from the Factorial First Digit Distribution for n = 10
So with that formula it is possible to gess better than change what the next number of the factorial sequence will be.
The answer is: Yes for now because the discribed results also indicate that there maybe a mathematical formula possible from wich you can calulate the factors from a given number.

http://home.zonnet.nl/galien8/factor/factor.html (1936 words)



Factorial and Gamma Functions

is a bigfloat version of the factorial function.
gives the highest factorial which is automatically expanded.

http://starship.python.net/crew/mike/maxima/html/macref/node24.html (441 words)



Fast Factorial Functions

Though of no practical importance (because it is slow), it has the fascination of an unexpected solution.
Browse the Java and C# sources, including tables counting the number of operations.
A short description of 21 algorithms for computing the factorial function n!.

http://www.luschny.de/math/factorial/FastFactorialFunctions.htm (150 words)



Permutations

So that computing it would take a lot of activity.
and finally, 0=0 followed by zero factorials - a result of doing nothing.

http://www.cut-the-knot.org/do_you_know/permutation.shtml (455 words)



AskOxford: factorial

4 &mul; 3 &mul; 2 &mul; 1 (factorial 4, denoted by 4!
• adjective relating to a factor or factorial.

http://www.askoxford.com/concise_oed/factorial?view=uk (117 words)



factorial

\* e.g use of functions factorials *\ \* fact(n) = n*(n-1)*....2*1 *\ #include main() { int n, m; printf("Enter a number: "); scanf("%d", andn); m = fact(n); printf("The factorial of %d is %d.\n", n, m); exit(0); } fact(n) int n; { if (n == 0) return(1); return(n * fact(n-1)); }

http://www.cs.cf.ac.uk/Dave/C/section2_22_8.html (51 words)



factorial

the product of a given positive integer multiplied by all lesser positive integers: The quantity four factorial (4!) = 4 · 3 · 2 · 1 = 24.
of or pertaining to a factor or a factory.

http://www.infoplease.com/dictionary/factorial (54 words)



Yan Tran's Factorial Calculator

Enter number you wish to find the factorial of:
Click here to go back to the MAIN MENU

http://www.cs.uml.edu/~ytran/factorial.html (18 words)



Factorial Based (FB) Numbers v0.2

add a class to join integer with factorial

http://efsa.sourceforge.net/archive/waquier/factoria.htm (413 words)