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 (integer exponent), integer arithmetic expressions,
N M (space = multiply)

What you input, result, number name, visual representation


Sqrt(N), Cbrt(N) or N^(M) (fractional exponent)

Input, Decimal Representation with arbitrary precision, Continued Fraction format


Fractional Arithmetic Expressions (1/4)*(4–(1/2))

Input, Exact Result, Decimal Conversion, Prime Factorization, Egyptian Fraction Expansion


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


N!/(R! (N-R)! ) for Combinations; 
N! /(R!) for Permutations

Input, Result, Number Name, Alternative representations, Integral representations

Absolute Value


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

i.e. expand (x+4)(x-5)
i.e.  factor  x^2 – x – 20


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


Plot 3x + 4y < 5

Input, (Inequality) Plot(s)