︠6de93d0c-20fc-470d-b45f-165139997c3ei︠
%html
<p><span style="font-size: medium;"><strong>Welcome to SAGE! &nbsp;</strong></span></p>
<p><span style="font-size: small;">We can do all sorts of cool things with SAGE.</span></p>
<p><span style="font-size: small;">First, let's plot a few points.</span></p>

︡337d01d7-2902-432b-99fe-ff1ab92d4adc︡{"html": "<p><span style=\"font-size: medium;\"><strong>Welcome to SAGE! &nbsp;</strong></span></p>\n<p><span style=\"font-size: small;\">We can do all sorts of cool things with SAGE.</span></p>\n<p><span style=\"font-size: small;\">First, let's plot a few points.</span></p>"}︡
︠68dd9a8c-ace5-4433-b352-666d30c6f124︠
points([(0,0), (1,1), (2,pi)], pointsize=30)
︡1dc05f22-87b1-4970-9850-bf5f1fc84308︡{"html": "<font color='black'><img src='cell://sage0.png'></font>"}︡
︠1aee9ba6-c661-41bb-880a-ececc6883e03i︠
%html
<p><span style="font-size: small;">In 3-D!</span></p>

︡8196f6d9-1070-47bb-90b5-94e119d12f76︡{"html": "<p><span style=\"font-size: small;\">In 3-D!</span></p>"}︡
︠1df02018-ee24-4064-84a7-f4f88ebc9c8f︠
points([(0,0,0), (1, 1, 1), (2, pi, -4)])
︡75091a68-f561-49b4-ae30-b34398ee2198︡︡
︠fe4fc3fd-63a1-4613-8587-a899c40f5295︠
p=vector((0,2,4))
q=vector((1,1,1))
︡f3e7c139-a1f7-44a6-a6e8-44b62c02b51e︡︡
︠28785298-24fa-4d10-b6bc-f0c9c1f3b8af︠
p-q
︡5353910d-2673-4540-9939-8ca699721c75︡{"stdout": "(-1, 1, 3)"}︡
︠04825c38-170a-4899-a9dd-93df597b4783i︠
%html
<p><span style="font-size: small;">norm gives the length of the vector</span></p>

︡21df0b33-530a-4ed4-b770-1e5d4cae0dec︡{"html": "<p><span style=\"font-size: small;\">norm gives the length of the vector</span></p>"}︡
︠653eb09d-d42b-4799-ac8a-620812ebe9e8︠
norm(p-q)
︡cf1cd517-dde1-4a32-be89-38f5554f91af︡{"stdout": "sqrt(11)"}︡
︠20c8e8d5-0c71-49b5-9cfd-779841ee6586︠
plot(p) + plot(q) + plot(p-q, color='red')
︡124802b5-1b35-4e84-a25e-eeb78e3f736a︡︡
︠025b83e6-d86a-431f-8d21-70f4f55568bf︠
@interact
def _(p=input_box(default=(0,2,4)),q=input_box(default=(1,1,1))):
    show(plot(vector(p)) + plot(vector(q)) + plot(vector(p)-vector(q), color='red'))
    print html('Enter vectors p and q.  This will plot p and q in blue and p-q in red.')
︡8358f802-ab3b-4b4b-8bef-546953b64dbb︡{"html": "<!--notruncate-->\n        <div padding=6 id=\"div-interact-14\">\n          <table width=800px height=20px bgcolor=\"#c5c5c5\" cellpadding=15>\n            <tr>\n              <td bgcolor=\"#f9f9f9\" valign=top align=left>\n            <table>\n              <tr><td colspan=3><table><tr><td align=right><font color=\"black\">p&nbsp;</font></td><td><input type=\"text\" value=\"(0, 2, 4)\" size=80 onchange=\"interact(14, {variable: 'p', adapt_number: 3, value: encode64(this.value)}, 1)\"></input></td>\n</tr><tr><td align=right><font color=\"black\">q&nbsp;</font></td><td><input type=\"text\" value=\"(1, 1, 1)\" size=80 onchange=\"interact(14, {variable: 'q', adapt_number: 4, value: encode64(this.value)}, 1)\"></input></td>\n</tr></table></td></tr>\n              <tr><td></td><td style='width: 100%;'>\n        <div id=\"cell-interact-14\"><?__SAGE__START>\n          <table border=0 bgcolor=\"white\" width=100%>\n            <tr>\n              <td bgcolor=\"white\" align=left valign=top>\n                <pre><?__SAGE__TEXT></pre>\n              </td>\n            </tr>\n            <tr>\n              <td align=left valign=top><?__SAGE__HTML></td>\n            </tr>\n          </table><?__SAGE__END>\n        </div></td><td></td></tr>\n              <tr><td colspan=3></td></tr>\n            </table></td>\n            </tr>\n          </table>\n        </div>"}︡
︠245044e5-8074-4eea-b08b-ce81707aebc2i︠
%html
<p><span style="font-size: small;">Now we plot the (boundary of) the cylinder we talked about in class! &nbsp;</span></p>
<p><span style="font-size: small;">Grab it (with your mouse) to rotate it around and view it from different angles.</span></p>

︡bdd42fc9-5882-4887-9a27-6e8eaa2007d0︡{"html": "<p><span style=\"font-size: small;\">Now we plot the (boundary of) the cylinder we talked about in class! &nbsp;</span></p>\n<p><span style=\"font-size: small;\">Grab it (with your mouse) to rotate it around and view it from different angles.</span></p>"}︡
︠dd52e77a-efba-4e59-af29-12b5fdf5d774︠
var('x,y,z')
equation=x^2+z^2==9
equation
︡1e5561d8-5a80-4c20-b8c9-09a4fa42d881︡{"stdout": "x^2 + z^2 == 9"}︡
︠4239e951-bb69-462a-abdd-9f9cf9ec2e7e︠
implicit_plot3d(equation, (x,-5,5),(y,-5,5),(z,-5,5))
︡6f09c97e-3bfb-4beb-a489-37ec0d4b319d︡︡
︠acd7b990-b855-46f0-b81d-b1bfe0d2c991︠
var('x,y,z')

@interact
def _(equation=input_box(default=(x-1)^2+(y-2)^2+(z+3)^2==16), size=(5)):
    show(implicit_plot3d(equation, (x,-size,size),(y,-size,size),(z,-size,size)))
    print html('Enter implicitly defined surface in 3-d (in variables x, y and z) and size of display box.')
︡3fad75cd-57d9-4d96-bebd-12315e1a5aee︡{"html": "<!--notruncate-->\n        <div padding=6 id=\"div-interact-12\">\n          <table width=800px height=20px bgcolor=\"#c5c5c5\" cellpadding=15>\n            <tr>\n              <td bgcolor=\"#f9f9f9\" valign=top align=left>\n            <table>\n              <tr><td colspan=3><table><tr><td align=right><font color=\"black\">equation&nbsp;</font></td><td><input type=\"text\" value=\"(z + 3)^2 + (y - 2)^2 + (x - 1)^2 == 16\" size=80 onchange=\"interact(12, {variable: 'equation', adapt_number: 5, value: encode64(this.value)}, 1)\"></input></td>\n</tr><tr><td align=right><font color=\"black\">size&nbsp;</font></td><td><input type=\"text\" value=\"5\" size=80 onchange=\"interact(12, {variable: 'size', adapt_number: 6, value: encode64(this.value)}, 1)\"></input></td>\n</tr></table></td></tr>\n              <tr><td></td><td style='width: 100%;'>\n        <div id=\"cell-interact-12\"><?__SAGE__START>\n          <table border=0 bgcolor=\"white\" width=100%>\n            <tr>\n              <td bgcolor=\"white\" align=left valign=top>\n                <pre><?__SAGE__TEXT></pre>\n              </td>\n            </tr>\n            <tr>\n              <td align=left valign=top><?__SAGE__HTML></td>\n            </tr>\n          </table><?__SAGE__END>\n        </div></td><td></td></tr>\n              <tr><td colspan=3></td></tr>\n            </table></td>\n            </tr>\n          </table>\n        </div>"}︡