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User Interface and Math Keywords

Robert Katz

Last Updated August 4, 2009

 Category: Mathematics Keyword Formats Described Results Elementary Mathematics N + M N – M N*M N/M N^M (integer exponent), integer arithmetic expressions, N M (space = multiply) What you input, result, number name, visual representation Radicals Sqrt(N), Cbrt(N) or N^(M) (fractional exponent) Input, Decimal Representation with arbitrary precision, Continued Fraction format Fractions Fractional Arithmetic Expressions (1/4)*(4–(1/2)) Input, Exact Result, Decimal Conversion, Prime Factorization, Egyptian Fraction Expansion Trigonometry Use pi; Default is units of radians. To use degrees: Cos[60 Degree]    Cos[Pi/3], Sin[Pi/3], Tan[Pi/3], ArcCos[1/2], ArcSin[1/2], ArcTan[Sqrt[3]], Sec[Pi/3], Csc[Pi/3], Cot[Pi/3], ArcSec[2/Sqrt[3]] Input, (Exact) Result, Decimal Representation with arbitrary precision, Conversion to degrees, Right Triangle Picture inside Circle to show Width and Height of legs when Hypotenuse = Diameter, continued fraction, alternative representations, relations to other equivalent functions Factorial N! N!/(R! (N-R)! ) for Combinations;  N! /(R!) for Permutations Input, Result, Number Name, Alternative representations, Integral representations Absolute Value Abs(expression) Input, result, number name, visual representation, alternate representations Exponential Functions Use e^(expression) or exp(expression)  For Base 10 logs, use log(expression) and choose base 10, for Natural logs use ln(expression) or log(expression) Input, Decimal representation, Property, Plots, Series Expansion, Derivative, (In)definite Integral, Limit, Series Representation, Continued Fraction, Alternative and Integral representations Numerical Approximation N(expression, showdigits) i.e. N(pi, 50) Input, Result Simplification in Algebra expand  i.e. expand (x+4)(x-5) factor i.e.  factor  x^2 – x – 20 simplify i.e. simplify (x^2 – x –20) / (x+4) Input, Result, Plots, Expansion/Factor over a finite field,  p-adic expansion Solving equations and inequalities solve  x^2 – x – 20 = 0 solve x + 4 - 3y = 2x - 3 + y/3 for y   solve 0 < 2 - 3x < 8   solve 2x + 3y = 4 and 3x + 2y = 5 Input, Result, Root plots in real or complex plane; optional show steps to solution with solve keyword Minimize x^2 – x – 20 Input, (Global) minimum, plots Maximize -x^2 + x + 20 Input, (Global) maximum, plots Graphing Plot 3x + 4y < 5 Input, (Inequality) Plot(s)