Using Yacas, function reference by the Yacas team 1 Yacas version: 1.3.6 generated on November 25, 2014 This document describes the functions that are useful in the context of using Yacas as an end user. 1This text is part of the Yacas software package. Copyright 2000{2002. Principal documentation authors: Ayal Zwi Pinkus, Serge Winitzki, Jitse Niesen. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts and no Back-Cover Texts. A copy of the license is included in the section entitled \GNU Free Documentation License". Contents 1 Introduction 10 2 Arithmetic and other operations on numbers 11 + | arithmetic addition . 11 - | arithmetic subtraction or negation . 11 * | arithmetic multiplication . 11 / | arithmetic division . 11 ^ | arithmetic power . 12 Div | Determine divisor of two mathematical objects . 12 Mod | Determine remainder of two mathematical objects after dividing one by the other . 12 Gcd | greatest common divisor . 12 Lcm | least common multiple . 13 << | binary shift left operator . 13 >> | binary shift right operator . 13 FromBase | conversion of a number from non-decimal base to decimal base . 13 ToBase | conversion of a number in decimal base to non-decimal base . 13 N | try determine numerical approximation of expression . 13 Rationalize | convert floating point numbers to fractions . 14 ContFrac | continued fraction expansion . 14 Decimal | decimal representation of a rational . 14 Floor | round a number downwards . 15 Ceil | round a number upwards . 15 Round | round a number to the nearest integer . 15 Min | minimum of a number of values . 15 Max | maximum of a number of values . 16 Numer | numerator of an expression . 16 Denom | denominator of an expression . 16 Pslq | search for integer relations between reals . 16 3 Predicates relating to numbers 17 < | test for \less than" . 17 > | test for \greater than" . 17 <= | test for \less or equal" . 17 >= | test for \greater or equal" . 18 IsZero | test whether argument is zero . 18 IsRational | test whether argument is a rational . 18 4 Calculus and elementary functions 19 Sin | trigonometric sine function . 19 Cos | trigonometric cosine function . 19 Tan | trigonometric tangent function . 19 ArcSin | inverse trigonometric function arc-sine . 20 ArcCos | inverse trigonometric function arc-cosine . 20 ArcTan | inverse trigonometric function arc-tangent . 20 Exp | exponential function . 21 Ln | natural logarithm . 21 Sqrt | square root . 21 Abs | absolute value or modulus of complex number . 21 Sign | sign of a number . 22 1 D | take derivative of expression with respect to variable . 22 Curl | curl of a vector field . 22 Diverge | divergence of a vector field . 23 Integrate | integration . 23 Limit | limit of an expression . 23 5 Random numbers 24 Random, RandomSeed | (pseudo-) random number generator . 24 RngCreate | manipulate random number generators as objects . 24 RngSeed | manipulate random number generators as objects . 24 Rng | manipulate random number generators as objects . 24 RandomIntegerMatrix | generate a matrix of random integers . 25 RandomIntegerVector | generate a vector of random integers . 25 RandomPoly | construct a random polynomial . 25 6 Series 26 Add | find sum of a list of values . 26 Sum | find sum of a sequence . 26 Factorize | product of a list of values . 26 Taylor | univariate Taylor series expansion . 26 InverseTaylor | Taylor expansion of inverse . 27 ReversePoly | solve h (f (x)) = g (x) + O (xn) for h ............................... 27 BigOh | drop all terms of a certain order in a polynomial . 27 LagrangeInterpolant | polynomial interpolation . 28 7 Combinatorics 29 ! | factorial . 29 !! | factorial and related functions . 29 *** | factorial and related functions . 29 Subfactorial | factorial and related functions . 29 Bin | binomial coefficients . 29 Eulerian | Eulerian numbers . 30 LeviCivita | totally anti-symmetric Levi-Civita symbol . 30 Permutations | get all permutations of a list . 30 8 Special functions 31 Gamma | Euler's Gamma function . 31 Zeta | Riemann's Zeta function . 31 Bernoulli | Bernoulli numbers and polynomials . 31 Euler | Euler numbers and polynomials . 32 LambertW | Lambert's W function . 32 9 Complex numbers 33 Complex | construct a complex number . 33 Re | real part of a complex number . ..