Integers

Compute properties of an integer:

28

Do exact arithmetic with integers:

141(2^141) + 1

Compute a prime factorization:

factor 70560

Rational Numbers

Compute properties of a rational number:

12/17

Compute the exact value of a repeating decimal:

.03571428571428...

Irrational Numbers

Compute properties of an irrational number:

sqrt(13)

Determine whether a number is irrational:

Is cbrt(3) an irrational number?

Algebraic Numbers

Determine whether a number is algebraic:

Is sin(pi/17) an algebraic number?

Identify algebraic integers and units:

Is 1/(1+sqrt(5)) an algebraic integer?

Transcendental Numbers

Determine whether a number is transcendental:

Is sqrt(2)^sqrt(2) transcendental?

Get information about a transcendental number:

Champernowne constant

Complex Numbers

Do basic arithmetic on complex numbers:

1/(12+7i)

Find roots of complex numbers:

(1+i)^(1/5)

Apply functions to complex numbers:

exp(24+2i)

Arbitrary Precision

Do exact arithmetic with large numbers:

1927508279017230597 + 278789278723478925

Find a decimal approximation:

(1+e)/2

Compute a decimal approximation to a specified number of digits:

pi to 1000 digits

Mathematical Constants

Compute the value of a mathematical constant:

feigenbaum alpha

Do computations involving constants:

golden ratio - 1/(golden ratio)

Number Recognition

Find possible closed forms for an approximate number:

-0.283882181415

Represent an approximate number in terms of specified constants:

express 4.8675 through pi and e

Base Conversions

Convert a decimal number to another base:

1275 to base 7

Convert a number in a given base to decimal:

100011010 base 2

Do mixed-base computations:

(28 base 16) + (30 base 5)

Historical Numbers

Do computations with Roman numerals:

XLVIII + LXXII

Convert a decimal number to Mayan numerals:

365 to Mayan

Number Names

Find the English name of a large number:

10^39

Specify a number by name:

49 tredecillion