Wolframalpha.com

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)