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1VolumexFOXES TEAMReference for Xnumbers.xlaNumeric Calculusin Excel
REFERENCE FOR XNUMBERS.XLANumeric Calculusin EXCELOct 2007
Xnumbers TutorialIndexAbout this Tutorial . 8Array functions. 9What is an array-function? . 9How to insert an array function . 9How to get the help on line. 12Xnumbers installation. 13How to install . 13How to uninstall . 14Installation troubles . 14Multiprecision Floating Point Arithmetic . 15Why using extended precision numbers? . 15Multiprecision methods. 17How to store long number . 17Functions . 19General Description. 19Using Xnumbers functions . 19Using extended numbers in Excel. 20Functions Handbook . 21Precision. 22Formatting Result . 22Arithmetic Functions. 23Addition. 23Subtraction. 23Multiplication . 24Division . 24Inverse . 24Integer Division . 24Integer Remainder . 25Sum . 27Product . 27Raise to power. 27Square Root. 28Nth- Root . 28Absolute. 28Change sign. 28Integer part . 29Decimal part. 29Truncating. 29Rounding . 29Relative Rounding . 30Extended Numbers manipulation . 31Digits count . 31Significant Digits count. 31Numbers comparison. 31Extended number check . 32Format extended number. 32Check digits . 32SortRange. 33Digits sum . 33Vector flip. 33Scientific format . 34Split scientific format . 34Converting multiprecision into double . 34Macros X-Edit . 35Macro X-Converter . 36Statistical Functions . 39Factorial . 39Factorial with double-step . 392
Xnumbers TutorialCombinations. 39Permutations. 40Arithmetic Mean. 40Geometric Mean . 40Quadratic Mean . 40Standard Deviation . 40Variance. 41Probability distributions . 41Univariate Statistic . 46Linear Regression Coefficients . 47Linear Regression - Standard Deviation of Estimates . 49Linear Regression Formulas. 50Linear Regression Covariance Matrix. 51Linear Regression Statistics . 52Linear Regression Evaluation . 53Polynomial Regression - Coefficient . 54Polynomial Regression - Standard Deviation of Estimates . 54Polynomial Regression Statistics. 54Macro - Regression . 55Linear Regression with Robust Method . 59Linear Regression Min-Max . 60NIST Certification Test. 61Transcendental Functions . 62Logarithm natural (Napier’s) . 62Logarithm for any base . 62Exponential . 62Exponential for any base . 62Constant e . 63Constant Ln(2) . 63Constant Ln(10) . 63Hyperbolic Sine. 63Hyperbolic ArSine . 63Hyperbolic Cosine. 64Hyperbolic ArCosine . 64Hyperbolic Tangent. 64Hyperbolic ArTangent . 64Euler constant γ . 64Trigonometric Functions. 65Sin . 65Cos . 65Tan . 66Arcsine. 66Arccosine . 66Arctan . 66Constant π . 66Complement of right angle. 67Polynomial Rootfinder . 68Input parameters. 69Output . 70How to use rootfinder macros . 71Integer roots. 74Multiple roots . 76Polynomial Functions . 77Polynomial evaluation . 77Polynomial derivatives . 78Polynomial coefficients . 79Polynomial writing. 80Polynomial addition. 80Polynomial multiplication. 80Polynomial subtraction. 81Polynomial division quotient. 81Polynomial division remainder . 81Polynomial shift. 85Polynomial center . 85Polynomial roots radius. 86Polynomial building from roots. 87Polynomial building with multi-precision. 89Polynomial Solving . 90Integer polynomial . 903
Xnumbers TutorialPolynomial System of 2nd degree. 91Bivariate Polynomial . 92Orthogonal Polynomials evaluation . 97Weight of Orhogonal Polynomials. 99Zeros of Orthogonal Polynomials. 99Coefficients of Orthogonal Polynomials . 100Complex Arithmetic and Functions . 101How to insert a complex number . 101Complex Addition. 102Complex Subtraction . 102Complex Multiplication . 102Complex Division . 102Polar Conversion . 103Rectangular Conversion . 103Complex absolute . 103Complex power. 104Complex Roots . 104Complex Log. 105Complex Exp . 105Complex inverse . 105Complex negative . 105Complex conjugate . 105Complex Sin . 106Complex Cos . 106Complex Tangent . 106Complex ArcCos. 106Complex ArcSin . 106Complex ArcTan . 106Complex Hyperbolic Sine. 106Complex Hyperbolic Cosine. 107Complex Hyperbolic Tan. 107Complex Inverse Hyperbolic Cos. 107Complex Inverse Hyperbolic Sin. 107Complex Inverse Hyperbolic Tan. 107Complex digamma . 107Complex Exponential Integral . 107Complex Error Function . 108Complex Complementary Error Function. 108Complex Gamma Function . 108Complex Logarithm Gamma Function . 108Complex Zeta Function. 108Complex Quadratic Equation . 109Number Theory . 110Maximum Common Divisor. 110Minimum Common Multiple . 110Rational Fraction approximation . 111Continued Fraction . 112Continued Fraction of Square Root . 113Check Prime . 113Next Prime . 113Modular Addition. 114Modular Subtraction. 114Modular Multiplication . 114Modular Division . 114Modular Power. 114Perfect Square. 116Check odd/even. 116Check Integer . 116Macro - Factorize . 117Batch Factorization with Msieve . 118Factorization function. 120Macro - Prime Numbers Generator. 121Prime Test . 121Diophantine Equation . 123Brouncker-Pell Equation . 124Euler's Totient function . 125Integer relation. 126Macro Integer Relation Finder . 130Linear Algebra Functions . 133Matrix Addition . 1334
Xnumbers TutorialMatrix Subtraction. 133Matrix Multiplication . 133Matrix Inverse . 133Matrix Determinant . 133Matrix Modulus . 134Scalar Product . 134Similarity Transform . 134Matrix Power. 134Matrix LU decomposition . 135Matrix LLT decomposition . 135Vector Product . 136Solve Linear Equation System. 136Square Delta Extrapolation .
and macros contained in the Xnumbers addin. It is a printable version of the help-on-line, with a larger collection of examples. XNUMBERS.XLA is an Excel addin containing useful functions for numerical calculus in standard and multiprecision floating point arithmetic up to 200 significant digits.
