1. Tabular layout

Computational questions
How do I construct ... group?
--
permutation 5.1
the conjugacy classes of a 5.2

Given a group G, how do I compute ... ?
--
all normal subgroups of G 5.3
the center/group id/random element of G5.4

How do I compute the ... of a matrix?
--
eigenvectors/values
row reduced echelon form 6.3
6.2 kernel
6.4 characteristic polynomial
How do I find the ... of a group's representations?
--
9.1character table
9.2Brauer character table
How do I compute $ A^n \pmod m$ , where A is ...?
--
11.1 an integer
11.2 a square matrix
11.3 a polynomial

How do I ... a polynomial?
--
12.1 factor
12.3 find roots of 12.4 evaluate
12.5 Groebner basis of ideal of

Given an elliptic curve $ E$ , how do I compute ...?
--
15.1 its conductor
15.2 its j-invariant (and discriminant)
14.2 its associated modular form
15.3 its points defined over GF(q)

Given a space of modular symbols M, how do I compute ... ?
--
14.3 Hecke operators action

For a number field, how do I compute ...?
--
16.1 those ramified at a given prime
16.2 the class number
16.3 an integral basis for its ring of integers

Given a congruence subgroup $ \Gamma$ , how do I compute ... ?
--
14.1 the dimension of the space of cusp forms for Gamma
a list of coset reps of $ SL_2(\mathbf{Z})/\Gamma$

How do I construct ... vector space?
--
6.1 a basis of a
a linear code, as a

How do I construct the ring of ... ?
--
10.1 matrices
10.2 polynomials
10.2 polynomials modulo an ideal
10.3 p-adic numbers

How do I plot a ...?
--
3 function (like $ \sin(x)$ or $ [(\sin(t),\cos(t)]$ or $ x^2-y^2$ )
17.1 curve (over the reals)
17.2 surface (over the reals)
piecewise-defined function

How do I compute the ... ?
--
13.1 discrete log of $ x$
13.2 next prime after $ x$
13.3 sigma function
quadratic residues mod p 13.4

How do I compute ... curve over a finite field?
--
17.3 the rational points of
a basis for the Riemann-Roch space of a 17.4

How do I compute ... graph?
--
8.1 a Cayley
8.2 an adjacency matrix

Interface questions

18.1 Can I run a SAGE job in the background?
I used SAGE in a research paper. 18.2 How should I reference it?
18.3 Can I log my SAGE session?
18.4 Can I output my results into LaTex?
18.5 How do I compute ... in Pari, GAP, Singular, MAGMA?
18.6 Given a SAGE or Python object foo, how do I figure out what functions I can call on it?
18.7 How do I read a file into SAGE?
18.11 What is SAGE? What calculations can SAGE do?
18.8 How do I (a very impatient person) install SAGE and the databases as fast as possible?
18.9 How do I read the Python code for the SAGE command (fill in your favorite command)?
18.10 How do I compute the value of (favorite special function) in SAGE?

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