SAGE

1. Sage Quick Reference by William Stein (March 2009) - quickref.pdf download (and the source quickref.tar.bz2)

2. Sage Linear Algebra Quick Reference by Robert A. Beezer (December 2011, Sage 4.8) - quickref-linalg.pdf download (source quickref-linalg.tex)

3. Sage Elementary Number Theory Quick Reference by William Stein (April 2009) - quickref-nt.pdf download (and the source quickref-nt.tar.bz2)

4. Sage Calculus Quick Reference by William Stein (April 2009) - quickref-calc.pdf download (and the source quickref-calc.tar.bz2)

5. Basic Math by Peter Jipsen, version 1.1 (January 2008) - sage-quickref.pdf download (and the source sage-quickref.tex)

6. Graph Theory by Steven Rafael Turner, version 4.7 (July 2011) - quickref-graphtheory.pdf download (and the source quickref-graphtheory.tex)

7. Abstract Algebra by B. Balof, T. W. Judson, D. Perkinson, R. Potluri, version 1.0 (June 2012) - quickref-algebra.pdf download (and the source quickref-algebra.tar.bz2)

8. Dynamical Systems by B. Hutz and J. Silverman, version 1.0 (Auguts 2016) - dynamics_ref.pdf download (and the source download).

9.Constructing Small groups: See here.

10.Filter on graph database: Sometimes you need to query something on the database of small graphs. 

from itertools import ifilter

f = lambda g: g."filter1" and not g."filter2"

for g in ifilter(f, graphs(6)):

   print(g)

Or you can use the following command:

import six 

f = lambda g: g."filter1" and not g."filter2"

for g in six.moves.filter(f, graphs(6)):

   print(g)

Or you can use the following command:

from sage.graphs.connectivity import is_connected

Q = GraphQuery(display_cols=['graph6'], num_vertices=9)

for g in Q:

    if is_connected(g) and g.is_vertex_transitive():

        print(diameter(g, algorithm='standard'))

Or you can use the following command:

for g in graphs(6):

        if is_connected(g) and g.is_vertex_transitive():

11.Multiplicities of Eigenvalues: 

For algebraic multiplicities, you can use the following command:

sage: G.charpoly().roots(AA, multiplicities=True)

sage: A = G.am()

sage: for (l, E) in A.right_eigenspaces():

          print('Eigenvalue', l, 'geometric multiplicity', E.dimension())

12.graph6 <--> sage format: 

with the following command you can convert your graph in the sage format to graph6 format.

sage: your_graph.graph6_string()

Also for digraphs with digraph6.

sage: your_graph.dig6_string()

Conversely convert graph6 format to sage format

sage: d6 = "C?"

sage: G = Graph(d6, format='graph6')

Also for digraphs with digraph6.

sage: d6 = "C?"

sage: G = DiGraph(d6, format='dig6')

13.Creating .sage file: In Jupyter Notebook, the click on "New" pop-down menu.