Combinatorics

compute binomial coefficients (combinations)

30 choose 18

compute a Frobenius number

Frobenius number {4, 7, 12}

find partitions of an integer

integer partitions of 10

Graph Theory

compute properties of a named graph

Pappus graph

compare several graphs

Petersen graph, icosahedral graph

analyze a graph specified by adjacency rules

1->2, 2->3, 3->1, 3->4, 4->1

Point Lattices

compute properties of a lattice

face-centered cubic

compute properties of a root lattice

A4 root lattice

compare several lattices

simple cubic, simple hexagonal

Sequences

compute a possible formula and continuation for a sequence

1, 4, 9, 16, 25, ...

sum an incompletely specified infinite series

1/2 + 1/4 + 1/8 + 1/16 + ...

Recurrences

solve a recurrence

g(n+1)=n^2+g(n)

specify initial values

f(n)=f(n-1)+f(n-2), f(1)=1, f(2)=2

find a recurrence satisfied by a given sequence

fibonacci(n) recurrence

Ackermann Function

evaluate the Ackermann function

ackermann[2,3]

what is ackermann 4,1?

ack(2,ack(2,1))