Sharedex_intro.sagewsOpen in CoCalc
A = matrix([
        [2,0,0,0,0,89],
        [0,2,0,0,0,243],
        [0,0,2,0,0,212],
        [0,0,0,2,0,150],
        [0,0,0,0,2,245],
        [1,1,1,1,1,546]
    ])
#A
#type(A)
A.LLL()
[-1 1 -1 1 -1 0] [ 1 -1 -1 1 -1 -1] [-1 -1 -1 1 1 2] [ 1 -1 -1 -1 -1 2] [-2 -2 4 0 -2 0] [-6 -4 -6 -6 0 -3]
2 + 2
2*2
a = 2
b = 4
a*b
type(b)
# just adding a comment
p = "this is a string"
p
t = "r"
type(t)
t
4 4 8 <type 'sage.rings.integer.Integer'> 'this is a string' <type 'str'> 'r'
a = 3
b = 5
c = 0
if a > b:
    c = 2*(a+b)
    # indented in the if statement
elif a == b:
    c = 3*(a + b)
else:
    c = -2*(a+b)
# end if
# not indented not in the if statement
c
-16
# observe the upper bound
for i in range(1,7):
    print "the value of i = " + str(i) + "and the value of i + 1 = " + str(i+1)
the value of i = 1and the value of i + 1 = 2 the value of i = 2and the value of i + 1 = 3 the value of i = 3and the value of i + 1 = 4 the value of i = 4and the value of i + 1 = 5 the value of i = 5and the value of i + 1 = 6 the value of i = 6and the value of i + 1 = 7
a = 0
while a <= 7:
    a = a + 1
    print a
print "I have exited the while loop"
1 2 3 4 5 6 7 8 I have exited the while loop
gcd(7, 26)
inverse_mod(7, 26)
mod(7*15, 26)
1 15 1
#G = graphs.DiamondGraph()
#G.show() # long time
#G = graphs.LollipopGraph(13,4); 

#G = graphs.StarGraph(23)
#g = graphs.TadpoleGraph(13, 4); g
#g.show()
G = graphs.PetersenGraph()
G.plot().show()    # or G.show()
M = G.adjacency_matrix()
M
[0 1 0 0 1 1 0 0 0 0] [1 0 1 0 0 0 1 0 0 0] [0 1 0 1 0 0 0 1 0 0] [0 0 1 0 1 0 0 0 1 0] [1 0 0 1 0 0 0 0 0 1] [1 0 0 0 0 0 0 1 1 0] [0 1 0 0 0 0 0 0 1 1] [0 0 1 0 0 1 0 0 0 1] [0 0 0 1 0 1 1 0 0 0] [0 0 0 0 1 0 1 1 0 0]
A = matrix([
        [3,2],
        [4,3]
    ])
A
B = matrix([
        [3,1],
        [7,2]
    ])
B
AB = A*B
print "AB = "
AB
AB.transpose()

print "B^T = "
B.transpose()
print "A^T = "
A.transpose()
B.transpose()*A.transpose()
[3 2] [4 3] [3 1] [7 2] AB = [23 7] [33 10] [23 33] [ 7 10] B^T = [3 7] [1 2] A^T = [3 4] [2 3] [23 33] [ 7 10]