2542.sagews

money=10000;year=0

while money<20000:
  years=years+1
money=money*1.0069

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_7.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("d2hpbGUgbW9uZXk8MjAwMDA6CiAgeWVhcnM9eWVhcnMrMQptb25leT1tb25leSoxLjAwNjk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmps3MT5U/___code___.py", line 4, in <module> years=years+_sage_const_1 NameError: name 'years' is not defined

#!/usr/bin/env sage

n=10

m=0

x=range(n)

while x<100:
  p=random() 
  if p<0.2:
     x[m]=1 
  else:
     x[m]=0 
  m=m+1

x

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

epsilion=0.01

x_pre=infinity

x=0.0

while abs(x-x_pre)>epsilion: 
  x_pre=x
  x=x_pre**3-x_pre+1

x

1.00000000000000

x=0;x+=1;x

1

x=2;x**=2;x

4

x=[123,'xyz'];x+=[011];x

[123, 'xyz', 9]

x=y=z=123

x

123

y

123

z

123

x,y,z=1,2,3

x

1

y

2

z

3

x=666;y=888

x,y=y,x

x

888

y

666

#!/usr/bin/env sage

x=1

x+=100

x

101

load myadd.sage

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_76.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("bG9hZCBteWFkZC5zYWdl"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpvgeEJw/___code___.py", line 2, in <module> exec compile(u'sage.misc.preparser.load(sage.misc.preparser.base64.b64decode("bXlhZGQuc2FnZQ=="),globals(),False)' + '\n', '', 'single') File "", line 1, in <module> File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/misc/preparser.py", line 1503, in load exec(preparse_file(open(filename).read()), globals) IOError: [Errno 2] No such file or directory: 'myadd.sage'

x

101

attach myadd.sage

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_78.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("YXR0YWNoIG15YWRkLnNhZ2U="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpnjCzga/___code___.py", line 2, in <module> exec compile(u'sage.misc.preparser.load(sage.misc.preparser.base64.b64decode("bXlhZGQuc2FnZQ=="),globals(),True)' + '\n', '', 'single') File "", line 1, in <module> File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/misc/preparser.py", line 1503, in load exec(preparse_file(open(filename).read()), globals) IOError: [Errno 2] No such file or directory: 'myadd.sage'

x

101

x

101

#!/usr/bin/env sage

n=10

x=[int(random()*100) for each in range(n)]

print "random numbers is ",x

random numbers is [19, 19, 75, 94, 66, 19, 63, 58, 88, 4]

for each in range(n-1):
   for k in range(n-1): 
      if x[k]<x[k+1]: 
         x[k],x[k+1]=[k+1],x[k]
print "sorted is",x

sorted is [[1], [1], [1], [1], [1], [1], 19, 19, 19, 4]

sage:load bubble_sort.py

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_92.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("YnViYmxlX3NvcnQucHk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpzHE3d0/___code___.py", line 2, in <module> exec compile(u'bubble_sort.py' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'bubble_sort' is not defined

random number is [94,15,90,85,29,19,11,77,55,13]

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_93.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cmFuZG9tIG51bWJlciBpcyBbOTQsMTUsOTAsODUsMjksMTksMTEsNzcsNTUsMTNd"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpB8HcZg/___code___.py", line 3 random number is [_sage_const_94 ,_sage_const_15 ,_sage_const_90 ,_sage_const_85 ,_sage_const_29 ,_sage_const_19 ,_sage_const_11 ,_sage_const_77 ,_sage_const_55 ,_sage_const_13 ] ^ SyntaxError: invalid syntax

sorted is [94,190,85,77,55,29,19,15,13,11]

False

n=var('n')

a_n=(1+1/n)**n

a_n.limit(n=oo)

e

limit(sin(n*pi/3),n=oo)

ind

n=var('n')

limit((n**2-1)/(n+5),n=oo)

+Infinity

x=var('x')

diff(sin(x),x)

cos(x)

diff(sin(x),x,2)

-sin(x)

x,y=var('x,y')

f=x^2*y+x*exp(y)

f.diff(x,y)

2*x + e^y

var('x,a')

(x, a)

f=exp(sin(a-x^2))/x

f.derivative(x)

-2*e^(sin(-x^2 + a))*cos(-x^2 + a) - e^(sin(-x^2 + a))/x^2

x=var('x')

f=sin(x)

taylor(f,x,0,6)

1/120*x^5 - 1/6*x^3 + x

a=matrix(ZZ,[[3,1,1],[2,1,2]])

B=matrix(ZZ,[[1,-2,3],[4,5,-6]])

a+b

[ 4 -1 4] [ 6 6 -4]

a-b

[ 2 3 -2] [-2 -4 8]

a.transpose()

[3 2] [1 1] [1 2]

transpose(a.transpose())

[3 1 1] [2 1 2]

a*b.transpose()

[ 4 11] [ 6 1]

transpose(b)*a

[11 5 9] [ 4 3 8] [-3 -3 -9]

A=matrix(QQ,3,range(9));A

[0 1 2] [3 4 5] [6 7 8]

b=matrix(QQ,3,1,[1,2,3]);b

[1] [2] [3]

x=A\b;x

[-2/3] [ 1] [ 0]

A*x

[1] [2] [3]

A=matrix(QQ,3,range(9));A[0,0]=2;A

[2 1 2] [3 4 5] [6 7 8]

b=matrix(QQ,1,3,[1,2,3]);b

[1 2 3]

x=b*A^(-1);x

[ 0 5/3 -2/3]

x*A

[1 2 3]

(8*a)*b.transpose()

[64] [80]

8*(a*transpose(b))

[64] [80]

Q=matrix([[2,1,0,0,0],[0,2,1,0,0],[0,0,2,1,0],[0,0,0,2,1],[0,0,0,0,2]])

Q^3

[ 8 12 6 1 0] [ 0 8 12 6 1] [ 0 0 8 12 6] [ 0 0 0 8 12] [ 0 0 0 0 8]

rank(Q)

5

Q.inverse()

[ 1/2 -1/4 1/8 -1/16 1/32] [ 0 1/2 -1/4 1/8 -1/16] [ 0 0 1/2 -1/4 1/8] [ 0 0 0 1/2 -1/4] [ 0 0 0 0 1/2]

Q^(-1)*Q

[1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1]

A=matrix(RR,[[1,2,3],[1,3,-2],[3,7,8],[1,4,-9]])

b=matrix(RR,[[1],[1],[3],[1]])

rank(A)

3

var('a,b,c,d')

(a, b, c, d)

D=matrix\
([[a^2,(a+1)^2,(a+2)^2,(a+3)^2],[b^2,(b+1)^2,(b+2)^2,(b+3)^2],\
[c^2,(c+1)^2,(c+2)^2,(c+3)^2],[d^2,(d+1)^2,(d+2)^2,(d+3)^2]])

D

[ a^2 (a + 1)^2 (a + 2)^2 (a + 3)^2] [ b^2 (b + 1)^2 (b + 2)^2 (b + 3)^2] [ c^2 (c + 1)^2 (c + 2)^2 (c + 3)^2] [ d^2 (d + 1)^2 (d + 2)^2 (d + 3)^2]

det(D)

0

y=matrix(RR,[[1,2],[3,4]]);y

[1.00000000000000 2.00000000000000] [3.00000000000000 4.00000000000000]