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sql server reporting services barcode font Basic Concepts in Software
Basic Concepts Reading QR In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. QR Code Drawer In None Using Barcode creation for Software Control to generate, create QR Code 2d barcode image in Software applications. A positive integer is prime if it is divisible only by itself and 1. For technical reasons, 1 is not considered prime; the smallest prime is 2. Read QRCode In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Encode QR Code JIS X 0510 In Visual C#.NET Using Barcode generation for .NET framework Control to generate, create QR Code image in .NET framework applications. Prime[n] returns the nth prime. RandomPrime[n] returns a pseudorandom prime number between 2 and n. RandomPrime[{m, n}] returns a pseudorandom prime number between m and n. RandomPrime[ { m, n } , k] returns a list of k pseudorandom primes, each between m and n. QR Code 2d Barcode Creator In VS .NET Using Barcode generator for ASP.NET Control to generate, create QR image in ASP.NET applications. Quick Response Code Encoder In VS .NET Using Barcode encoder for .NET framework Control to generate, create QR Code ISO/IEC18004 image in .NET framework applications. EXAMPLE 10 Find the 7th prime.
Print Denso QR Bar Code In Visual Basic .NET Using Barcode drawer for Visual Studio .NET Control to generate, create Denso QR Bar Code image in Visual Studio .NET applications. Bar Code Creator In None Using Barcode maker for Software Control to generate, create bar code image in Software applications. Prime[7] 17 RandomPrime[{7, 47}] 29 RandomPrime[{7, 47}, 10] {31, 29, 41, 47, 43, 13, 31, 17, 37, 7} Bar Code Printer In None Using Barcode creator for Software Control to generate, create barcode image in Software applications. EAN13 Printer In None Using Barcode generator for Software Control to generate, create EAN13 Supplement 5 image in Software applications. The Fibonacci numbers are defined by
Encode GS1  12 In None Using Barcode creation for Software Control to generate, create UCC  12 image in Software applications. Paint Data Matrix In None Using Barcode generator for Software Control to generate, create ECC200 image in Software applications. f1 = 1, f2 = 1, fn = fn 2 + fn 1 n 3
GS1  12 Maker In None Using Barcode printer for Software Control to generate, create GS1  12 image in Software applications. Create 1D In VB.NET Using Barcode generator for .NET Control to generate, create Linear 1D Barcode image in .NET framework applications. Thus, the first few Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, GTIN  12 Printer In Visual Studio .NET Using Barcode creation for Reporting Service Control to generate, create GS1  12 image in Reporting Service applications. Painting UCC.EAN  128 In ObjectiveC Using Barcode creation for iPhone Control to generate, create UCC  12 image in iPhone applications. Fibonacci[n] returns the nth Fibonacci number.
Reading DataMatrix In .NET Framework Using Barcode reader for .NET Control to read, scan read, scan image in .NET framework applications. Drawing UPCA In None Using Barcode drawer for Online Control to generate, create UPCA image in Online applications. EXAMPLE 11
Barcode Creator In Java Using Barcode encoder for Java Control to generate, create barcode image in Java applications. Printing Code128 In VS .NET Using Barcode generation for ASP.NET Control to generate, create Code 128B image in ASP.NET applications. Fibonacci[7] 13 There are three Mathematica functions that convert real numbers to nearby integers.
Round[x] returns the integer closest to x. If x lies exactly between two integers (e.g., 5.5), Round returns the nearest even integer. Floor[x] returns the greatest integer which does not exceed x. This is sometimes known as the greatest integer function and is represented in many textbooks by x . Ceiling[x] returns the smallest integer not less than x. Many textbooks represent this by x . EXAMPLE 12
Round[5.75] 6 Floor[5.75] 5 Ceiling[5.75] 6 A decimal number can be broken up into two parts, the integer portion (number to the left of the decimal point) and the fractional portion. IntegerPart[x] gives the integer portion of x (decimal point excluded). FractionalPart[x] gives the fractional portion of x (decimal point included). Observe that IntegerPart[x]+ FractionalPart[x]= x.
Basic Concepts
EXAMPLE 13
IntegerPart[4.67] 4 FractionalPart[4.67] 0.67 IntegerPart[4.67] + FractionalPart[4.67] 4.67 If m and n are positive integers, there exist unique integers q and r such that m = qn + r with 0 r<n This result is known as the Division Algorithm. q is called the quotient and r is the remainder. The Mathematica functions Quotient and Mod return the quotient and remainder, respectively. Quotient[m, n] returns the quotient when m is divided by n. Mod[m, n] returns the remainder when m is divided by n. EXAMPLE 14
Quotient[17, 3] 5 Mod[17, 3] 2 Suppose a and b are two integers. If there exists an integer, k, such that a = kb, we say that b divides a. Alternatively, a is a multiple of b. Let m and n be two integers. If b divides both m and n, we say that b is a common divisor of m and n. The largest common divisor of m and n is called their greatest common divisor (GCD). If a is a multiple of both m and n, we say a is a common multiple of m and n. The smallest common multiple of m and n is called their least common multiple (LCM). GCD[m, n] returns the greatest common divisor of m and n. LCM[m, n] returns the least common multiple of m and n. The functions GCD and LCM extend to more than two arguments.
EXAMPLE 15 Find the greatest common divisor and least common multiple of 24, 40, and 48.
GCD[24, 40, 48] 8 LCM[24, 40, 48] 240 The Fundamental Theorem of Arithmetic guarantees that every positive integer can be factored into primes in a unique way. The function FactorInteger[n] gives the prime factors of n together with their respective exponents.
EXAMPLE 16
FactorInteger[2 381 400] {{2, 3} ,{3, 5}, {5, 2}, {7, 2}} The prime factors of 2,381,400 are 2, 3, 5, and 7 with exponents, respectively, 3, 5, 2, 2. In other words, 2,381,400 = 23355272. The result of this operation produces a nested sequence of lists. (A list is a Mathematica object, enclosed within braces, { }, which will be discussed in detail in 3.) Basic Concepts
In order to estimate computational efficiency, it is useful to be able to determine how long an operation or sequence of operations takes to execute. Timing[expression] evaluates expression, and returns a list of time used, in seconds, together with the result obtained. Timing counts only the CPU time spent in the Mathematica kernel. It does not include overhead time spent in the front end.

