Wolfram|Alpha introduces a fundamentally new way to get knowledge and answers—

not by searching the web, but by doing dynamic computations based on a vast collection

of built-in data, algorithms, and methods.

**PART 2 : Lets look at the mathematical searches and plotting**

**The following is not intended to be a handbook,**

but only a listing of search examples

but only a listing of search examples

**Plotting & Graphics**

plot a function of one variable

plot x^3 - 6x^2 + 4x + 12

graph sin t + cos (sqrt(3)t)

plot 4/(9*x^(1/4))

specify an explicit range for the variable

plot e^x from x=0 to 10

plot a function where it is real-valued

real plot -(sqrt(25-y^2))

plot a special function

plot Ai(x)

plot multiple functions

plot sin x, cos x, tan x

plot a function on a logarithmic scale

log plot e^x-x

plot on a log-linear scale

log-linear plot x^2 log x, x=1 to 10

**3D Plots**

plot a function of two variables

plot sin x cos y

specify explicit ranges for the variables

plot x^2 y^3, x=-1..1, y=0..3

**Equations**

plot the solution to an equation in two variables

plot 3x^2-2xy+y^2=1

**Inequalities**

plot the region satisfying an inequality in two variables

plot |x|^3+|y|^3<1

plot a region satisfying multiple inequalities

plot x^2+y^2<1 and y>x

**Polar Plots**

draw a polar plot

polar plot r=1+cos theta

specify a range for the variable theta

polar plot r=theta, theta=0 to 8 pi

Parametric Plots

Parametric Plots

draw a parametric plot

parametric plot (cos^3 t, sin^3 t)

specify a range for the parameter

parametric plot (sin 10t, sin 8t), t=0..2pi

Number Lines

Number Lines

visualize a set of real numbers on a number line

number line 2, 3, 5, 7, 11, 13

show multiple sets on a number line

number line x^2>5, 0<=x<3

**Algebra**

**Equation Solving**

solve a polynomial equation

x^3 - 4x^2 + 6x - 24 = 0

solve a system of linear equations

x+y=10, x-y=4

solve an equation with parameters

solve a x^2 + b x + c = 0 for x

**Polynomials**

compute properties of a polynomial in several variables

x^3 + x^2 y + x y^2 + y^3

factor a polynomial

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48

**Rational Functions**

compute properties of a rational function

(x^2-1)/(x^2+1)

compute a partial fraction decomposition

partial fractions (x^2-4)/(x^4-x)

Simplification

Simplification

simplify an expression

simplify x^5-20x^4+163x^3-676x^2+1424x-1209

simplify cos(arcsin(x)/2)

**Vectors**

compute properties of a vector

vector {2, -5, 4}

compute a cross product

{1/4, -1/2, 1} cross {1/3, 1, -2/3}

**Matrices & Linear Algebra**

do basic arithmetic on matrices

{{0,-1},{1,0}}.{{1,2},{3,4}}+{{2,-1},{-1,2}}

compute eigenvalues and eigenvectors of a matrix

eigenvalues {{4,1},{2,-1}}

**Quaternions**

compute quaternions

quaternion: 0+2i-j-3k

do calculations with quaternions

quaternion -Sin[Pi]+3i+4j+3k multiplied by -1j+3.9i+4-+3k

**Finite Groups**

get information about a finite group

alternating group A_5

ask about a property of a group

order of the monster group

do algebra with permutations

perm (1 2 3 4)^3(1 2 3)^-1

**Finite Fields**

compute properties of a finite field

Z/7Z

compute a specific property

number of primitive polynomials of GF(3125)

**Domain & Range**

compute the domain of a function

domain of f(x) = x/(x^2-1)

compute the range of a function

range of e^(-x^2)