2534.sagews

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

f=sin(x*y)

taylor(f,(x,0),(y,-1),4)

-1/2*(y + 1)*x^3 + 1/6*x^3 + (y + 1)*x - x

plot(sin,(0,2*pi),color='red')

m1=matrix(ZZ,[[1,2,3,],[4,5,6]])

m1.parent()

Full MatrixSpace of 2 by 3 dense matrices over Integer Ring

m1

[1 2 3] [4 5 6]

m1/2

[1/2 1 3/2] [ 2 5/2 3]

p.is_irreducible()

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_20.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cC5pc19pcnJlZHVjaWJsZSgp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpk0gwFM/___code___.py", line 2, in <module> exec compile(u'p.is_irreducible()' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'p' is not defined

q2=x^3-9*x^2+20*x-12;q2

x^3 - 9*x^2 + 20*x - 12

gcd(q1,q2)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_22.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("Z2NkKHExLHEyKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpoxDM2_/___code___.py", line 2, in <module> exec compile(u'gcd(q1,q2)' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'q1' is not defined

lcm(q1,q2)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_24.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("bGNtKHExLHEyKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpSh6glo/___code___.py", line 2, in <module> exec compile(u'lcm(q1,q2)' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'q1' is not defined

q1.factor()

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_25.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("cTEuZmFjdG9yKCk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpTsEPrr/___code___.py", line 2, in <module> exec compile(u'q1.factor()' + '\n', '', 'single') File "", line 1, in <module> NameError: name 'q1' is not defined

q2.factor()

(x - 6)*(x - 2)*(x - 1)

n=var('n')

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

a_n.limit(n=oo)

e

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

ind

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