# Mathematics

do basic arithmetic

125 + 375
do exact arithmetic with fractions

1/4 * (4 - 1/2)
compute a decimal approximation of a specified number of digits

pi to 1000 digits
convert a decimal number to another base

219 to binary
plot a function

plot x^3 - 6x^2 + 4x + 12
plot a region satisfying multiple inequalities

plot x^2+y^2<1 and y>x
solve an equation

x^3 - 4x^2 + 6x - 24 = 0
factor a polynomial

factor 2x^5 - 19x^4 + 58x^3 - 67x^2 + 56x - 48
compute eigenvalues and eigenvectors of a matrix

eigenvalues {{4,1},{2,-1}}
compute an integral

integrate sin x dx from x=0 to pi
calculate a derivative

derivative of x^4 sin x
solve an ordinary differential equation

y'' + y = 0
compute properties of a geometric figure

annulus, inner radius=2, outer radius=5
plot a conic section and identify its type

2x^2 - 3xy + 4y^2 + 6x - 3y - 4 = 0
compute properties of a polyhedron

dodecahedron
compute a prime factorization

factor 70560
solve a Diophantine equation

solve 3x+4y=5 over the integers
compute a possible formula and continuation for a sequence

5, 14, 23, 32, 41, ...
analyze a graph specified by adjacency rules

1->2, 2->3, 3->1, 3->4, 4->1
solve a recurrence

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2
minimize or maximize a function

maximize x(1-x)e^x
numerically integrate functions that cannot be integrated symbolically

integrate sin(cos x) from x=0 to 1
compute a truth table

P && (Q || R)
generate a Venn diagram

(complement S) intersect (A union B)
do computations with special functions

d/dx Si(x)^2
do computations with number-theoretic functions

phi(110)
find representations for a function

gamma(x) integral representation
compute properties of a function of a complex variable (use the variable <i>z</i>)

e^z
do vector analysis computations

div (x^3 y, y^3 z, z^3 x)
compute properties of a knot

8_1 knot
find information about a math concept

tangram
get a brief definition

basic definition of prime number
get information about a mathematical conjecture

Riemann Hypothesis
get historical information about a theorem

Fermat's little theorem
find the continued fraction representation of a number

continued fraction pi
find definitions of continued fraction terminology

what is a regular continued fraction
find continued fraction papers by author

continued fraction papers by Stern