3916.sagews

def is_even(n):
    return n%2 == 0

is_even(2)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{True}

is_even(3)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{False}

def is_divisible_by(number, divisor=2):
    return number%divisor ==0

is_divisible_by(13,7)

\newcommand{\Bold}[1]{\mathbf{#1}}\mathrm{False}

def even(n):
    v=[]
    for i in range(3,n):
        if i%2==0:
            v.append(i)
    return v

even(3)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\right]

even(10)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[4, 6, 8\right]

range(3)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, 1, 2\right]

range(3.1)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[0, 1, 2\right]

for i in range(5):
    print '%6s %6s %6s'%(i, i^2, i^3)

0 0 0 1 1 1 2 4 8 3 9 27 4 16 64

x=var('x')
solve(x^2+3*x+2,x)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = \left(-2\right), x = \left(-1\right)\right]

b,c=var('b c')
solve([x^2+b*x+c==0],x)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[x = -\frac{1}{2} \, b - \frac{1}{2} \, \sqrt{b^{2} - 4 \, c}, x = -\frac{1}{2} \, b + \frac{1}{2} \, \sqrt{b^{2} - 4 \, c}\right]

y=var('y')
solve([x+y==6,x-y==4],x,y)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[x = 5, y = 1\right]\right]

var('x y p q')
eq1=p+q==9
eq2=q*y+p*x==-6
eq3=q*y^2+p*x^2==24
solve({eq1,eq2,eq3,p==1],p,q,x,y)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_75.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dmFyKCd4IHkgcCBxJykKZXExPXArcT09OQplcTI9cSp5K3AqeD09LTYKZXEzPXEqeV4yK3AqeF4yPT0yNApzb2x2ZSh7ZXExLGVxMixlcTMscD09MV0scCxxLHgseSk="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpHG7KOF/___code___.py", line 7 solve({eq1,eq2,eq3,p==_sage_const_1 ],p,q,x,y) ^ SyntaxError: invalid syntax

var('x y p q')

\newcommand{\Bold}[1]{\mathbf{#1}}\left(x, y, p, q\right)

eq1=p+q==9

eq1

\newcommand{\Bold}[1]{\mathbf{#1}}p + q = 9

eq2=q*y+p*x==-6

eq2

\newcommand{\Bold}[1]{\mathbf{#1}}p x + q y = \left(-6\right)

eq3=q*y^2+p*x^2==24

eq3

\newcommand{\Bold}[1]{\mathbf{#1}}p x^{2} + q y^{2} = 24

solve([eq1,eq2,eq3,p==1],p,q,x,y)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[p = 1, q = 8, x = -\frac{4}{3} \, \sqrt{10} - \frac{2}{3}, y = \frac{1}{6} \, \sqrt{2} \sqrt{5} - \frac{2}{3}\right], \left[p = 1, q = 8, x = \frac{4}{3} \, \sqrt{10} - \frac{2}{3}, y = -\frac{1}{6} \, \sqrt{2} \sqrt{5} - \frac{2}{3}\right]\right]

solns = solve([eq1,eq2,eq3,p==1],p,q,x,y, solution_dict=True)
[[s[p].n(30), s[q].n(30), s[x].n(30), s[y].n(30)] for s in solns]

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\left[1.0000000, 8.0000000, -4.8830369, -0.13962039\right], \left[1.0000000, 8.0000000, 3.5497035, -1.1937129\right]\right]

var('theta')

\newcommand{\Bold}[1]{\mathbf{#1}}\theta

solve(cos(theta)==sin(theta),theta)

\newcommand{\Bold}[1]{\mathbf{#1}}\left[\sin\left(\theta\right) = \cos\left(\theta\right)\right]

find_root(cos(theta)==sin(theta),0,pi/2)

\newcommand{\Bold}[1]{\mathbf{#1}}0.785398163397

diff(sin(theta))

\newcommand{\Bold}[1]{\mathbf{#1}}\cos\left(\theta\right)

diff(sin(theta^2))

\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \theta \cos\left(\theta^{2}\right)

diff(sin(x^2),x,4)

\newcommand{\Bold}[1]{\mathbf{#1}}16 \, x^{4} \sin\left(x^{2}\right) - 48 \, x^{2} \cos\left(x^{2}\right) - 12 \, \sin\left(x^{2}\right)

f=x^2+17*y^2
f.diff(x),f.diff(y)

\newcommand{\Bold}[1]{\mathbf{#1}}\left(2 \, x, 34 \, y\right)

integral(x*sin(x^2),x,0,1)

\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{1}{2} \, \cos\left(1\right) + \frac{1}{2}

var('t')
x=function('x',t)
DE=diff(x,t)+x-1
desolve(DE,[x,t])

\newcommand{\Bold}[1]{\mathbf{#1}}{\left(c + e^{t}\right)} e^{\left(-t\right)}

bessel_I(1,1)

\newcommand{\Bold}[1]{\mathbf{#1}}0.565159103992485

cos(pi)

\newcommand{\Bold}[1]{\mathbf{#1}}-1