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Introduction to Sage and Python

Worksheet

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A worksheet is made of cells. Some contain text and some contain code that you can run directly.

5+12

Sage as a calculator

4/5
12//5
(4/5).n()
4./5.
.8

pi.n(digits=300)

x = var('x')
expr = 1 / (1-x^2)
expr

show(expr)

latex(expr)

expr2 = - expr + expr^3
show(expr2)

show(expr2.simplify_rational())

expr2.subs(x = pi)

expr2.subs(x = pi).n()

The help system

How can you find what you are looking for?

--> The tab key and the "?"

A = matr

A = matrix([[1,2],[3,4]])

type(A)

A.parent()

A.

A.rank

A.rank?

A.rank??

A._rank_linbox

Some simple things

f(x) = x^3 + x - 4
f

f(7)

f.derivative()

plot(f)

Some code

b = 8
if b%2==0:
    a = b/2
else:
    a = 3*b +1

for i in xrange(3):
    print i

l = [2,4,5,68]
for i in l:
    print i

a = 5
while a!=1:
    print a
    if a%2==0:
        a/=2
    else:
        a=a*3+1

def my_function(a):
    if(a%2):
        return a*3+1
    else:
        return a/2

my_function(5)

Some combinatorics

P = Permutations(4)
P

list(P)

P = Permutations(10)
P

P.cardinality()

P.random_element()

P.identity()

p = Permutation([1,5,3,4,2,7,6])

p.parent()

p.

p.number_of_descents()

Lets compute the average number of fixed points...

p.number_of_fixed_points()

P5 = Permutations(5)

mean([p.number_of_fixed_points() for p in P5])

P6 = Permutations(6)

mean([p.number_of_fixed_points() for p in P6])

P100 = Permutations(100)

mean([P100.random_element().number_of_fixed_points() for i in range(100)])

Some useful links


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