You can embed HTML

€csage.server.notebook.notebook
Notebook
q)q}q(U_Notebook__worksheetsq}qU	_scratch_q(csage.server.notebook.worksheet
Worksheet
qoq}q	(U_Worksheet__filenameq
U	_scratch_qU_Worksheet__cellsq]q((csage.server.notebook.cell
Cell
qoq}q(U	_Cell__inqU2^3qU_Cell__introspect_htmlqU!<pre class="introspection"></pre>qU_Cell__worksheetqhU_Cell__completionsq‰U_Cell__introspectq‰U_Cell__out_htmlqU U	_Cell__idqK U_before_preparseqU[os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/0")
2^3qU
_Cell__dirqU*sage_notebook/worksheets/_scratch_/cells/0qU
_Cell__outqU8Uhas_new_outputq‰U_Cell__is_htmlq ‰U_Cell__sageq!csage.interfaces.sage0
reduce_load_Sage
q")Rq#U_Cell__typeq$Uwrapq%U_Cell__timeq&‰U_Cell__interruptedq'‰ub(hoq(}q)(U	_Cell__inq*U2/3q+U_Cell__introspect_htmlq,U!<pre class="introspection"></pre>q-U_Cell__worksheetq.hU_Cell__completionsq/‰U_Cell__introspectq0‰U_Cell__out_htmlq1U U	_Cell__idq2KU_before_preparseq3U\os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/18")
2/3q4U
_Cell__dirq5U+sage_notebook/worksheets/_scratch_/cells/18q6U
_Cell__outq7U2/3q8Uhas_new_outputq9‰U_Cell__is_htmlq:‰U_Cell__sageq;h#U_Cell__typeq<h%U_Cell__timeq=‰U_Cell__interruptedq>‰ub(hoq?}q@(U	_Cell__inqAU%python

print(2^3)
print(2/3)qBU_Cell__introspect_htmlqCU!<pre class="introspection"></pre>qDU_Cell__worksheetqEhU_Cell__completionsqF‰U_Cell__introspectqG‰U_Cell__out_htmlqHU U	_Cell__idqIKU_before_preparseqJUwos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/21")
%python

print(2^3)
print(2/3)qKU
_Cell__dirqLU+sage_notebook/worksheets/_scratch_/cells/21qMU
_Cell__outqNU1
0qOUhas_new_outputqP‰U_Cell__is_htmlqQ‰U_Cell__sageqRh#U_Cell__typeqSh%U_Cell__timeqT‰U_Cell__interruptedqU‰ub(hoqV}qW(hUfactor(2007)qXhU!<pre class="introspection"></pre>qYhhh‰h‰hU hKhUdos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/1")
factor(2007)qZhU*sage_notebook/worksheets/_scratch_/cells/1q[hU	3^2 * 223q\h‰h ‰h!h#h$h%h&‰h'‰ub(hoq]}q^(hU5factor(2^997-1)    # you can hit escape and it works!q_hU!<pre class="introspection"></pre>q`hhh‰h‰hU hKhUos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/5")
factor(2^997-1)    # you can hit escape and it works!qahU*sage_notebook/worksheets/_scratch_/cells/5qbhU h‰h ‰h!Nh$h%h&‰h'ˆub(hoqc}qd(h*U3M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
Mqeh,U!<pre class="introspection"></pre>qfh.hh/‰h0‰h1U h2Kh3UŒos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/12")
M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
Mqgh5U+sage_notebook/worksheets/_scratch_/cells/12qhh7U4[   1    2    3]
[ 1/3   17 -2/3]
[   1    5   -5]qih9‰h:‰h;h#h<h%h=‰h>‰ub(hoqj}qk(hAU
M.parent()qlhCU!<pre class="introspection"></pre>qmhEhhF‰hG‰hHU hIKhJUcos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/24")
M.parent()qnhLU+sage_notebook/worksheets/_scratch_/cells/24qohNU=Full MatrixSpace of 3 by 3 dense matrices over Rational FieldqphP‰hQ‰hRh#hSh%hT‰hU‰ub(hoqq}qr(h*Uview(M)qsh,U!<pre class="introspection"></pre>qth.hh/‰h0‰h1U h2Kh3U`os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/13")
view(M)quh5U+sage_notebook/worksheets/_scratch_/cells/13qvh7Uƒ<html><span class="math">\left(\begin{array}{rrr}
1&2&3\\
\frac{1}{3}&17&-\frac{2}{3}\\
1&5&-5
\end{array}\right)</span></html>qwh9‰h:‰h;h#h<h%h=‰h>‰ub(hoqx}qy(hAUview(M.echelon_form())qzhCU!<pre class="introspection"></pre>q{hEhhF‰hG‰hHU hIKU_word_being_completedq|UM.echq}hJUoos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/20")
view(M.echelon_form())q~hLU+sage_notebook/worksheets/_scratch_/cells/20qhNUl<html><span class="math">\left(\begin{array}{rrr}
1&0&0\\
0&1&0\\
0&0&1
\end{array}\right)</span></html>q€hP‰hQ‰hRh#hSh%hT‰hU‰ub(hoq}q‚(h*UG = AlternatingGroup(5)qƒh,U!<pre class="introspection"></pre>q„h.hh/‰h0‰h1U h2KU_word_being_completedq…USymmetriq†h3Upos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/14")
G = AlternatingGroup(5)q‡h5U+sage_notebook/worksheets/_scratch_/cells/14qˆh7U h9‰h:‰h;h#h<h%h=‰h>‰ub(hoq‰}qŠ(h*U%G.conjugacy_classes_representatives()q‹h,U!<pre class="introspection"></pre>qŒh.hh/‰h0‰h1U h2Kh…UG.conjugqh3U~os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/15")
G.conjugacy_classes_representatives()qŽh5U+sage_notebook/worksheets/_scratch_/cells/15qh7U3[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]qh9‰h:‰h;h#h<h%h=‰h>‰ub(hoq‘}q’(h*UG%time 
f = x^389 + 17/3*x + 2
g = x^397 - 18*x + 15
h = f*g^10 + f^10*gq“h,U!<pre class="introspection"></pre>q”h.hh/‰h0‰h1U h2Kh3UÄos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/16")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
f = x^389 + 17/3*x + 2
g = x^397 - 18*x + 15
h = f*g^10 + f^10*gq•h5U+sage_notebook/worksheets/_scratch_/cells/16q–h7U$CPU time: 0.02 s,  Wall time: 0.02 sq—h9‰h:‰h;h#h<h%h=ˆh>‰ub(hoq˜}q™(U	_Cell__inqšUh[:50]q›U_Cell__introspect_htmlqœU!<pre class="introspection"></pre>qU_Cell__worksheetqžhU_Cell__completionsqŸ‰U_Cell__introspectq ‰U_Cell__out_htmlq¡U U	_Cell__idq¢KU_before_preparseq£U_os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/28")
h[:50]q¤U
_Cell__dirq¥U+sage_notebook/worksheets/_scratch_/cells/28q¦U
_Cell__outq§Tv  [1153300796610, -10571923411357, 35521669089060, -82207173890380/3, -1578378351911680/9, 6297739398214880/9, -107392893078774688/81, 377409713492725760/243, -287199547816076060/243, 3757883697935134460/6561, -3178137624289098691/19683, 132742369030852798/6561, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]q¨Uhas_new_outputq©‰U_Cell__is_htmlqª‰U_Cell__sageq«h#U_Cell__typeq¬h%U_Cell__timeq­‰U_Cell__interruptedq®‰ub(hoq¯}q°(h*Uview(f)q±h,U!<pre class="introspection"></pre>q²h.hh/‰h0‰h1U h2Kh3U`os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/17")
view(f)q³h5U+sage_notebook/worksheets/_scratch_/cells/17q´h7UB<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>qµh9‰h:‰h;h#h<h%h=‰h>‰ub(hoq¶}q·(U	_Cell__inq¸Ug%hide%html
<h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span>q¹U_Cell__introspect_htmlqºU!<pre class="introspection"></pre>q»U_Cell__worksheetq¼hU_Cell__completionsq½‰U_Cell__introspectq¾‰U_Cell__out_htmlq¿U U	_Cell__idqÀK	U_before_preparseqÁU¿os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/9")
%hide%html
<h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span>qÂU
_Cell__dirqÃU*sage_notebook/worksheets/_scratch_/cells/9qÄU
_Cell__outqÅUj<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>qÆUhas_new_outputqÇ‰U_Cell__is_htmlqÈˆU_Cell__sageqÉh#U_Cell__typeqÊh%U_Cell__timeqË‰U_Cell__interruptedqÌ‰ub(hoqÍ}qÎ(h¸Uu%latex
Cells can be written in latex, which can refer to SAGE objects.
For example, consider $E$ given by $\sage{E}$.qÏhºU!<pre class="introspection"></pre>qÐh¼hh½‰h¾‰h¿UE<img src="sage_notebook/worksheets/_scratch_/cells/11/sage491.png?1">qÑhÀKhÁUÎos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/11")
%latex
Cells can be written in latex, which can refer to SAGE objects.
For example, consider $E$ given by $\sage{E}$.qÒhÃU+sage_notebook/worksheets/_scratch_/cells/11qÓhÅU hÇ‰hÈ‰hÉh#hÊh%hË‰hÌ‰ub(hoqÔ}qÕ(hUtime n=factorial(10^6)qÖhU!<pre class="introspection"></pre>q×hhh‰h‰hU hKhU”os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/3")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
n=factorial(10^6)qØhU*sage_notebook/worksheets/_scratch_/cells/3qÙhU$CPU time: 3.31 s,  Wall time: 3.34 sqÚh‰h ‰h!h#h$h%h&ˆh'‰ub(hoqÛ}qÜ(hU0f = maxima('x*sin(x)*cos(x)^2')
print f, type(f)qÝhU!<pre class="introspection"></pre>qÞhhh‰h‰hU hKhUˆos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/4")
f = maxima('x*sin(x)*cos(x)^2')
print f, type(f)qßhU*sage_notebook/worksheets/_scratch_/cells/4qàhU@x*cos(x)^2*sin(x) <class 'sage.interfaces.maxima.MaximaElement'>qáh‰h ‰h!h#h$h%h&‰h'‰ub(hoqâ}qã(hAUf.integrate()qähCU!<pre class="introspection"></pre>qåhEhhF‰hG‰hHU hIKh|Uf.qæhJUfos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/22")
f.integrate()qçhLU+sage_notebook/worksheets/_scratch_/cells/22qèhNU4(sin(3*x) - 3*x*cos(3*x) + 9*sin(x) - 9*x*cos(x))/36qéhP‰hQ‰hRh#hSh%hT‰hU‰ub(hoqê}që(hAUf.name()qìhCU!<pre class="introspection"></pre>qíhEhhF‰hG‰hHU hIKhJUaos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/23")
f.name()qîhLU+sage_notebook/worksheets/_scratch_/cells/23qïhNU'sage0'qðhP‰hQ‰hRh#hSUhiddenqñhT‰hU‰ub(hoqò}qó(hTº  # Many random spheres:
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)qôhCU!<pre class="introspection"></pre>qõhhh‰hG‰hUA<img src="sage_notebook/worksheets/_scratch_/cells/6/sage.png?2">qöhKhJT  os.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/6")
# Many random spheres:
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)q÷hU*sage_notebook/worksheets/_scratch_/cells/6qøhU h‰hQ‰hRh#h$h%hT‰h'‰ub(hoqù}qú(U	_Cell__inqûUEplot3dsoya(lambda x,y: abs(zeta(x+I*y)),(1,0), side=4, res=32).show()qüU_Cell__introspect_htmlqýU!<pre class="introspection"></pre>qþU_Cell__worksheetqÿhU_Cell__completionsr   ‰U_Cell__introspectr  ‰U_Cell__out_htmlr  U U	_Cell__idr  KU_before_preparser  Užos.chdir("/home/was/talks/2006-08-17-scipy/sage_notebook/worksheets/_scratch_/cells/26")
plot3dsoya(lambda x,y: abs(zeta(x+I*y)),(1,0), side=4, res=32).show()r  U
_Cell__dirr  U+sage_notebook/worksheets/_scratch_/cells/26r  U
_Cell__outr  TR  [>                                                            ] 0%[------>                                                      ] 10%[---------------->                                            ] 27%[------------------------------>                              ] 51%[----------------------------------------------->             ] 78%[------------------------------------------------------------>] 100%
* Soya * Using 8 bits stencil buffer

* Soya * version 0.11.2
* Using OpenGL 2.0.5879 (8.26.18)
*   - renderer : ATI Mobility Radeon X1600 Generic
*   - vendor   : ATI Technologies Inc.
*   - maximum number of lights        : 8
*   - maximum number of clip planes   : 6
*   - maximum number of texture units : 8
*   - maximum texture size            : 4096 pixels

* Soya Pudding * Version: 0.1-0
* Soya * Using 16 bits stencil bufferr	  Uhas_new_outputr
  ‰U_Cell__is_htmlr  ‰U_Cell__sager  NU_Cell__typer  h%U_Cell__timer  ‰U_Cell__interruptedr  ‰ub(hor  }r  (hûU hÿhj   ‰j  U j  Kj  U+sage_notebook/worksheets/_scratch_/cells/25r  j  U j
  ‰j  hñj  ‰ubeU_Worksheet__synchror  KÒU_Worksheet__namer  U	_scratch_r  U_Worksheet__attachedr  }r  U_Worksheet__dirr  U"sage_notebook/worksheets/_scratch_r  U_Worksheet__queuer  ]r  U_Worksheet__next_idr  KU_Worksheet__comp_is_runningr  ‰U_Worksheet__notebookr  hU_Worksheet__next_block_idr  KU_Worksheet__idr   K U_Worksheet__systemr!  NubsU_Notebook__historyr"  ]r#  (U9# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: 2^3
8r$  UL# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: factor(2006)
2 * 17 * 59r%  UJ# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: factor(2007)
3^2 * 223r&  Th  # Worksheet '_scratch_' (2006-08-15 at 00:39)
sage: ModularSymbols(43).decomposition()
[
Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0 over Rational Field,
Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0 over ...r'  To  # Worksheet '_scratch_' (2006-08-15 at 00:39)
sage: ModularSymbols(43,sign=1).decomposition()
[
Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field,
Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over ...r(  Uo# Worksheet '_scratch_' (2006-08-15 at 00:39)
sage: time n=factorial(10^6)
CPU time: 3.61 s,  Wall time: 3.63 sr)  U{# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: show(factor(2007))
<html><div class="math">3^{2} \cdot 223</div></html>r*  U}# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(factor(2007))
<html><span class="math">3^{2} \cdot 223</span></html>r+  Tj  # Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('sin(x^2)').integrate())
<html><span class="math">\frac{\sqrt{\pi} \left(\left(\sqrt{2} i+\sqrt{2}\right)   \mathrm{erf}\left(\frac{\left(\sqrt{2} i+\sqrt{2}\right) x}{2}  \right)+\left(\sqrt{2} i-\sqrt{2}\right) \mathrm{erf}\left(\frac{  \left(\sqrt{2} i-\sqrt{2}\right) x}{2}\right)\right)}{8}...r,  Tj  # Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('cos(x^2)').integrate())
<html><span class="math">-\frac{\sqrt{\pi} \left(\left(\sqrt{2} i-\sqrt{2}\right)   \mathrm{erf}\left(\frac{\left(\sqrt{2} i+\sqrt{2}\right) x}{2}  \right)+\left(\sqrt{2} i+\sqrt{2}\right) \mathrm{erf}\left(\frac{  \left(\sqrt{2} i-\sqrt{2}\right) x}{2}\right)\right)}{8...r-  U•# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('tan(x^2)').integrate())
<html><span class="math">\int {\tan x^2}{\;dx}</span></html>r.  U‰# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(x)').integrate())
<html><span class="math">\log \sec x</span></html>r/  Uª# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(1/x)').integrate())
<html><span class="math">\int {\tan \left(\frac{1}{x}\right)}{\;dx}</span></html>r0  UÖ# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('sin(1/x)').integrate())
<html><span class="math">\sin \left(\frac{1}{x}\right) x+\int {\frac{\cos \left(\frac{1}{x}  \right)}{x}}{\;dx}</span></html>r1  UÙ# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('x*sin(x)*cos(x)^2').integrate())
<html><span class="math">\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x   \cos x}{36}</span></html>r2  U×# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: show(maxima('x*sin(x)*cos(x)^2').integrate())
<html><div class="math">\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x   \cos x}{36}</div></html>r3  U\# Worksheet 'interfaces' (2006-08-15 at 00:42)
sage: E = magma.EllipticCurve('[1,2,3,4,5]')
r4  UŒ# Worksheet 'interfaces' (2006-08-15 at 00:42)
sage: E
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Fieldr5  U†# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup()
Abelian Group isomorphic to Z
Defined on 1 generator (free)r6  Te  # Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup(bound = 10)
...
TypeError: Error evaluation Magma code.
IN:_sage_[18] := MordellWeilGroup(_sage_[17] : bound:=10);
OUT:
>> _sage_[18] := MordellWeilGroup(_sage_[17] : bound:=10);
                                 ^
Runtime error in 'MordellWeilGroup': Parameter 'bound' is not d...r7  U# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup(Bound = 10)
Abelian Group isomorphic to Z
Defined on 1 generator (free)r8  Ui# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: type(E)
<class 'sage.interfaces.magma.MagmaElement'>r9  UD# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: parent(E)
Magmar:  UI# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.name()
'_sage_[2]'r;  T]  # Worksheet 'coverage' (2006-08-15 at 01:05)
sage: buzzard_tpslopes(2,1,50)
[[], [], [], [], [], [], [], [], [], [], [], [], [3], [], [], [], [3], [], [4], [], [3], [], [5], [], [3, 7], [], [4], [], [3, 8], [], [6, 6], [], [3, 7], [], [4, 8], [], [3, 9, 9], [], [5, 8], [], [3, 7, 11], [], [4, 9, 12], [], [3, 8, 11], [], [6, 6, 13], [], [3, 7, 1...r<  U~# Worksheet 'coverage' (2006-08-15 at 01:06)
sage: factor(genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5).conductor)
5^4 * 2267r=  U¼# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM.factor(2007)
...
TypeError: unbound method factor() must be called with ECM instance as first argument (got Integer instance instead)r>  U€# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM().factor(next_prime(10^10)*next_prime(10^11))
[10000000019, 100000000003]r?  U“# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM().factor(next_prime(10^10)*next_prime(10^30))
[10000000019, 1000000000000000000000000000057]r@  Uà# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ecm = ECM(); print ecm
sage: ecm.factor(next_prime(10^10)*next_prime(10^30))
<sage.interfaces.ecm.ECM instance at 0xb7c29a0c>
[10000000019, 1000000000000000000000000000057]rA  U¥# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ecm = ECM(); 
sage: ecm.factor(next_prime(10^10)*next_prime(10^30))
[10000000019, 1000000000000000000000000000057]rB  Ty  # Worksheet 'coverage' (2006-08-15 at 01:08)
sage: factor(ModularSymbols(389,2,sign=1).T(2).charpoly())
(x - 3) * (x + 2) * (x^2 - 2) * (x^3 - 4*x - 2) * (x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1) * (x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 + 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 - 74752*x^7 + 1407*x^6 + 46...rC  U[# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: A.<i,j,k> = QuaternionAlgebra(QQ,-1,-1)
rD  UA# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: i^2 + j
-1 + jrE  U£# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: A.<i,j,k> = QuaternionAlgebra(QQ,-1,-1)
sage: A
Quaternion algebra with generators (i, j, k) over Rational FieldrF  Uî# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: SupersingularModule(37).T(2)
Supersingular Module -- work in progress; use at own risk. (2006-08-08)
Hecke operator T_2 on Module of supersingular points on X_0(1)/F_37 over Integer RingrG  U»# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: SupersingularModule(37).T(2).matrix()
Supersingular Module -- work in progress; use at own risk. (2006-08-08)
[1 1 1]
[1 0 2]
[1 2 0]rH  U# Worksheet '_scratch_' (2006-08-15 at 08:56)
sage: def f(x):
...    return dimension_cusp_forms(Gamma0(int(x)))
...
sage: show(plot(f,1,100))
rI  U# Worksheet '_scratch_' (2006-08-15 at 08:57)
sage: E = EllipticCurve('37a'); E
Elliptic Curve defined by y^2 + y = x^3 - x over Rational FieldrJ  U‹# Worksheet '_scratch_' (2006-08-15 at 08:58)
sage: L = E.Lseries_dokchitser(5)
sage: show(plot(L,-1,1, plot_points=50, plot_division=50))
rK  Ui# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: L = E.Lseries_dokchitser(5)
sage: show(plot(L,-1,2))
rL  Uj# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2))
rM  U€# Worksheet '_scratch_' (2006-08-15 at 09:00)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2, thickness=2, hue=0.6))
rN  U–# Worksheet '_scratch_' (2006-08-15 at 09:00)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2, thickness=2, hue=0.6, ymin=-0.25, ymax=0.5))
rO  U–# Worksheet '_scratch_' (2006-08-15 at 09:01)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2, thickness=2, hue=0.6), ymin=-0.25, ymax=0.5)
rP  U\# Worksheet 'interfaces' (2006-08-15 at 09:01)
sage: E = magma.EllipticCurve('[1,2,3,4,5]')
rQ  T  # Worksheet '_scratch_' (2006-08-15 at 09:03)
html> <h1>You can embed HTML</h1>
html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h1>You can embed HTML</h1>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>rR  UÊ# Worksheet '_scratch_' (2006-08-15 at 09:03)
html%hide> <h2>You can embed HTML</h2>
html%hide> It can even include math: <span class='math'>\prod(1-q^n)</span>
...
NameError: name 'hide' is not definedrS  T  # Worksheet '_scratch_' (2006-08-15 at 09:03)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>rT  U«# Worksheet '_scratch_' (2006-08-15 at 09:04)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
rU  UA# Worksheet 'interfaces' (2006-08-15 at 09:04)
sage: gap('2^3')
8rV  U´# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: E = magma.EllipticCurve('[1,2,3,4,5]'); E
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational FieldrW  UF# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: singular('2^3')
8rX  U@# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gp('2^3')
8rY  U×# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gap('Factorization(2007)')
...
TypeError: Gap produced error output
Function: number of arguments must be 2 (not 1)

   executing $sage1:=Factorization(2007);;rZ  UÉ# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gap('Factorize(2007)')
...
TypeError: Gap produced error output
Variable: 'Factorize' must have a value


   executing $sage2:=Factorize(2007);;r[  UÀ# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gap('Factor(2007)')
...
TypeError: Gap produced error output
Variable: 'Factor' must have a value


   executing $sage3:=Factor(2007);;r\  UA# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gap('2^3')
8r]  UÄ# Worksheet 'cnta - using other systems' (2006-08-15 at 09:08)
sage: E = magma.EllipticCurve('[1,2,3,4,5]'); E
Elliptic Curve defined by y^2 + x*y + 3*y = x^3 + 2*x^2 + 4*x + 5 over Rational Fieldr^  U # Worksheet 'cnta - using other systems' (2006-08-15 at 09:08)
sage: E.MordellWeilGroup(Bound = 10)
Abelian Group isomorphic to Z
Defined on 1 generator (free)r_  Uy# Worksheet 'cnta - using other systems' (2006-08-15 at 09:08)
sage: type(E)
<class 'sage.interfaces.magma.MagmaElement'>r`  U¾# Worksheet 'cnta - using other systems' (2006-08-15 at 09:09)
sage: mathematica('BernoulliB[100]')
-94598037819122125295227433069493721872702841533066936133385696204311395415197247711/33330ra  U9# Worksheet '_scratch_' (2006-08-16 at 00:02)
sage: 2^3
8rb  U9# Worksheet '_scratch_' (2006-08-16 at 00:02)
sage: 2^3
8rc  Un# Worksheet 'sys' (2006-08-16 at 00:02)
sage: import sys; sys.path.append('/usr/lib/python2.4/site-packages')
rd  Ua# Worksheet 'sys' (2006-08-16 at 00:02)
sage: import scipy
...
ImportError: No module named scipyre  U<# Worksheet 'sys' (2006-08-16 at 00:05)
sage: import Crypto
rf  TL  # Worksheet 'sys' (2006-08-16 at 00:05)
sage: help(Crypto)
Help on package Crypto:

NAME
    Crypto - Python Cryptography Toolkit

FILE
    /usr/lib/python2.4/site-packages/Crypto/__init__.py

DESCRIPTION
    A collection of cryptographic modules implementing various algorithms
    and protocols.
    
    Subpackage...rg  U9# Worksheet '_scratch_' (2006-08-16 at 18:58)
sage: 2^3
8rh  UJ# Worksheet '_scratch_' (2006-08-16 at 18:58)
sage: factor(2007)
3^2 * 223ri  U}# Worksheet '_scratch_' (2006-08-16 at 18:58)
sage: view(factor(2007))
<html><span class="math">3^{2} \cdot 223</span></html>rj  T  # Worksheet '_scratch_' (2006-08-16 at 18:58)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>rk  U# Worksheet '_scratch_' (2006-08-16 at 18:58)
sage: E = EllipticCurve('37a'); E
Elliptic Curve defined by y^2 + y = x^3 - x over Rational Fieldrl  U«# Worksheet '_scratch_' (2006-08-16 at 18:58)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
rm  U–# Worksheet '_scratch_' (2006-08-16 at 18:59)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2, thickness=2, hue=0.6), ymin=-0.25, ymax=0.5)
rn  UO# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: n = -2007
ro  Um# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: n = -2007
sage: factor(n)
-1 * 3^2 * 223rp  Un# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: n.factor(algorithm="kash")
-1 * 3^2 * 223rq  Ug# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: gap(n).FactorsInt()
[ -3, 3, 223 ]rr  Uk# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: pari(n).factor()
[-1, 1; 3, 2; 223, 1]rs  Ui# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: gp(n).factor()
[-1, 1; 3, 2; 223, 1]rt  U`# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: maxima(n).factor()
-3^2*223ru  U¢# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: kash(n).Factorization()
[ <3, 2>, <223, 1> ], extended by:
  ext1 := -1,
  ext2 := Unassignrv  U# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: magma(n).Factorization(nvals = 2)
([ <3, 2>, <223, 1> ], -1)rw  Uh# Worksheet 'cnta - using other systems' (2006-08-16 at 19:00)
sage: maple(n).ifactor()
-``(3)^2*``(223)rx  Un# Worksheet 'sys' (2006-08-16 at 19:01)
sage: import sys; sys.path.append('/usr/lib/python2.4/site-packages')
ry  U<# Worksheet 'sys' (2006-08-16 at 19:01)
sage: import Crypto
rz  Ua# Worksheet 'sys' (2006-08-16 at 19:01)
sage: import scipy
...
ImportError: No module named scipyr{  Tu  # Worksheet 'cnta - using other systems' (2006-08-16 at 19:01)
sage: mathematica(n).FactorInteger()
Timeout exceeded in read_nonblocking().
<pexpect.spawn instance at 0xb7c6356c>
version: 2.0 ($Revision: 1.151 $)
command: /home/was/bin/math
args: ['/home/was/bin/math']
patterns:
    In[[0-9]+]:=
buffer (last 100 chars): 
before (last 100 chars): Mathematica 5....r|  U¡# Worksheet 'cnta - using other systems' (2006-08-16 at 19:01)
magma> n := -2007;
magma> F, s := Factorization(-2007);
magma> print F, s
[ <3, 2>, <223, 1> ]
-1r}  Ud# Worksheet 'cnta - using other systems' (2006-08-16 at 19:01)
sage: magma('F')
[ <3, 2>, <223, 1> ]r~  U9# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: 2^3
8r  UJ# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: factor(2007)
3^2 * 223r€  U}# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: view(factor(2007))
<html><span class="math">3^{2} \cdot 223</span></html>r  T  # Worksheet '_scratch_' (2006-08-17 at 10:44)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>r‚  U# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: E = EllipticCurve('37a'); E
Elliptic Curve defined by y^2 + y = x^3 - x over Rational Fieldrƒ  U«# Worksheet '_scratch_' (2006-08-17 at 10:44)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
r„  Uo# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: time n=factorial(10^6)
CPU time: 3.27 s,  Wall time: 4.28 sr…  U×# Worksheet '_scratch_' (2006-08-17 at 10:44)
sage: show(maxima('x*sin(x)*cos(x)^2').integrate())
<html><div class="math">\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x   \cos x}{36}</div></html>r†  U}# Worksheet '_scratch_' (2006-08-17 at 10:54)
sage: view(factor(2007))
<html><span class="math">3^{2} \cdot 223</span></html>r‡  Uu# Worksheet '_scratch_' (2006-08-17 at 10:57)
sage: M = MatrixSpace(QQ,3)(range(9))
sage: M
[0 1 2]
[3 4 5]
[6 7 8]rˆ  U¨# Worksheet '_scratch_' (2006-08-17 at 10:57)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
0&1&2\\
3&4&5\\
6&7&8
\end{array}\right)</span></html>r‰  Un# Worksheet '_scratch_' (2006-08-17 at 10:57)
sage: view(M^(-1))
...
ZeroDivisionError: self is not invertiblerŠ  U¨# Worksheet '_scratch_' (2006-08-17 at 10:57)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
0&1&2\\
3&4&5\\
6&7&8
\end{array}\right)</span></html>r‹  Uw# Worksheet '_scratch_' (2006-08-17 at 10:59)
sage: G = PermutationGroup(5)
...
TypeError: gens must be a tuple or listrŒ  UJ# Worksheet '_scratch_' (2006-08-17 at 10:59)
sage: G = SymmetricGroup(5)
r  U # Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G.conjugacy_classes_representatives()
[(), (1,2), (1,2)(3,4), (1,2,3), (1,2,3)(4,5), (1,2,3,4), (1,2,3,4,5)]rŽ  U# Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G = AlternativeGroup(5)
...
NameError: name 'AlternativeGroup' is not definedr  UL# Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G = AlternatingGroup(5)
r  U# Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]r‘  UL# Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G = AlternatingGroup(5)
r’  U# Worksheet '_scratch_' (2006-08-17 at 11:00)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]r“  T  # Worksheet '_scratch_' (2006-08-17 at 11:00)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>r”  Ut# Worksheet '_scratch_' (2006-08-17 at 11:02)
sage: f = x^389 + 17/3*x + 2
sage: g = x^97 - 18*x + 15
sage: h = f*g
r•  U˜# Worksheet '_scratch_' (2006-08-17 at 11:02)
time> f = x^389 + 17/3*x + 2
time> g = x^97 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 sr–  U˜# Worksheet '_scratch_' (2006-08-17 at 11:03)
time> f = x^389 + 17/3*x + 2
time> g = x^97 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 sr—  U|# Worksheet '_scratch_' (2006-08-17 at 11:03)
sage: show(f)
<html><div class="math">x^{389} + \frac{17}{3}x + 2</div></html>r˜  U~# Worksheet '_scratch_' (2006-08-17 at 11:03)
sage: view(f)
<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>r™  U9# Worksheet '_scratch_' (2006-08-17 at 11:03)
sage: 2^3
8rš  U;# Worksheet '_scratch_' (2006-08-17 at 11:03)
sage: 2/3
2/3r›  UJ# Worksheet '_scratch_' (2006-08-17 at 11:03)
sage: factor(2007)
3^2 * 223rœ  U9# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: 2^3
8r  U;# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: 2/3
2/3rž  UJ# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: factor(2007)
3^2 * 223rŸ  U}# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: view(factor(2007))
<html><span class="math">3^{2} \cdot 223</span></html>r   Uu# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: M = MatrixSpace(QQ,3)(range(9))
sage: M
[0 1 2]
[3 4 5]
[6 7 8]r¡  U¨# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
0&1&2\\
3&4&5\\
6&7&8
\end{array}\right)</span></html>r¢  UL# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: G = AlternatingGroup(5)
r£  U# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]r¤  U˜# Worksheet '_scratch_' (2006-08-17 at 11:04)
time> f = x^389 + 17/3*x + 2
time> g = x^97 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 sr¥  U~# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: view(f)
<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>r¦  T  # Worksheet '_scratch_' (2006-08-17 at 11:04)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>r§  U«# Worksheet '_scratch_' (2006-08-17 at 11:04)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
r¨  Uo# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: time n=factorial(10^6)
CPU time: 3.11 s,  Wall time: 3.14 sr©  U×# Worksheet '_scratch_' (2006-08-17 at 11:04)
sage: show(maxima('x*sin(x)*cos(x)^2').integrate())
<html><div class="math">\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x   \cos x}{36}</div></html>rª  Tž  # Worksheet '_scratch_' (2006-08-17 at 11:48)
Sphere's along the twisted cubic.
        sage: t = Tachyon(xres=512,yres=512, camera_center=(3,0.3,0))
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2,diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in srange(-1,1,0.05):
        ...    k += 1
        ...    t.sphere((i,i^2-0.5,i^3), 0.1, 't%s'%(k%3))
        ...
        sage: t.save()
r«  T   # Worksheet '_scratch_' (2006-08-17 at 11:49)
# Many random spheres:
        sage: t.save()
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)
r¬  Uu# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: M = MatrixSpace(QQ,3)(range(9))
sage: M
[0 1 2]
[3 4 5]
[6 7 8]r­  U¨# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
0&1&2\\
3&4&5\\
6&7&8
\end{array}\right)</span></html>r®  Ug# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: M.echelon_form()
[ 1  0 -1]
[ 0  1  2]
[ 0  0  0]r¯  U¢# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
sage: M
[   1    2    3]
[ 1/3   17 -2/3]
[   1    5   -5]r°  U¿# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
1&2&3\\
\frac{1}{3}&17&-\frac{2}{3}\\
1&5&-5
\end{array}\right)</span></html>r±  U^# Worksheet '_scratch_' (2006-08-17 at 11:50)
sage: M.echelon_form()
[1 0 0]
[0 1 0]
[0 0 1]r²  U;# Worksheet '_scratch_' (2006-08-17 at 11:51)
python> 2/3
0r³  UX# Worksheet '_scratch_' (2006-08-17 at 11:51)
python> print(2^3)
python> print(2/3)
1
0r´  U# Worksheet '_scratch_' (2006-08-17 at 11:55)
sage: f = maxima('x*sin(x)*cos(x)^2')
sage: type(f)
<class 'sage.interfaces.maxima.MaximaElement'>rµ  U«# Worksheet '_scratch_' (2006-08-17 at 11:55)
sage: f = maxima('x*sin(x)*cos(x)^2')
sage: print f, type(f)
x*cos(x)^2*sin(x) <class 'sage.interfaces.maxima.MaximaElement'>r¶  Uv# Worksheet '_scratch_' (2006-08-17 at 11:55)
sage: f.integrate()
(sin(3*x) - 3*x*cos(3*x) + 9*sin(x) - 9*x*cos(x))/36r·  Uv# Worksheet '_scratch_' (2006-08-17 at 11:55)
sage: f.integrate()
(sin(3*x) - 3*x*cos(3*x) + 9*sin(x) - 9*x*cos(x))/36r¸  UD# Worksheet '_scratch_' (2006-08-17 at 11:56)
sage: f.name()
'sage1'r¹  T  # Worksheet '_scratch_' (2006-08-17 at 11:56)
# Many random spheres:

        sage: t.save()
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)
rº  U|# Worksheet '_scratch_' (2006-08-17 at 11:56)
sage: M.parent()
Full MatrixSpace of 3 by 3 dense matrices over Rational Fieldr»  T‚  # Worksheet '_scratch_' (2006-08-17 at 13:45)
sage: plot3dsoya(lambda x,y: sin(x^2+y^2), side=8, res=128).show()
[>                                                            ] 0%[--->                                                         ] 5%[------->                                                     ] 11%[------------>                                                ] 20%[---...r¼  U_# Worksheet '_scratch_' (2006-08-17 at 13:45)
sage: def f(x,y):
...    return abs(zeta(x+I*y))
r½  U_# Worksheet '_scratch_' (2006-08-17 at 13:45)
sage: def z(x,y):
...    return abs(zeta(x+I*y))
r¾  Tb  # Worksheet '_scratch_' (2006-08-17 at 13:46)
sage: plot3dsoya(z, (1,0) ).show()
[>                                                            ] 1%[-----------------------------------------------------------> ] 100%
* Soya * Using 8 bits stencil buffer

* Soya * version 0.11.2
* Using OpenGL 2.0.5879 (8.26.18)
*   - renderer : ATI Mobility Rade...r¿  T‹  # Worksheet '_scratch_' (2006-08-17 at 13:47)
sage: plot3dsoya(lambda x,y: abs(zeta(x+I*y)),(1,0), side=4, res=32).show()
[>                                                            ] 0%[------>                                                      ] 10%[------------>                                                ] 21%[------------------->                                         ] 32%[--...rÀ  U9# Worksheet '_scratch_' (2006-08-17 at 13:48)
sage: 2^3
8rÁ  U9# Worksheet '_scratch_' (2006-08-17 at 13:48)
sage: 2^3
8rÂ  U9# Worksheet '_scratch_' (2006-08-17 at 13:48)
sage: 2^3
8rÃ  U/# Worksheet '_scratch_' (2006-08-17 at 13:50)

rÄ  U9# Worksheet '_scratch_' (2006-08-17 at 13:50)
sage: 2^3
8rÅ  U9# Worksheet '_scratch_' (2006-08-17 at 13:50)
sage: 2^3
8rÆ  U9# Worksheet '_scratch_' (2006-08-17 at 13:50)
sage: 2^3
8rÇ  U9# Worksheet '_scratch_' (2006-08-17 at 13:50)
sage: 2^3
8rÈ  U9# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: 2^3
8rÉ  U;# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: 2/3
2/3rÊ  UX# Worksheet '_scratch_' (2006-08-17 at 15:14)
python> print(2^3)
python> print(2/3)
1
0rË  UJ# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: factor(2007)
3^2 * 223rÌ  U¢# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
sage: M
[   1    2    3]
[ 1/3   17 -2/3]
[   1    5   -5]rÍ  U|# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: M.parent()
Full MatrixSpace of 3 by 3 dense matrices over Rational FieldrÎ  U¿# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
1&2&3\\
\frac{1}{3}&17&-\frac{2}{3}\\
1&5&-5
\end{array}\right)</span></html>rÏ  U^# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: M.echelon_form()
[1 0 0]
[0 1 0]
[0 0 1]rÐ  UL# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: G = AlternatingGroup(5)
rÑ  U˜# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^97 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 srÒ  U˜# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^97 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 srÓ  U# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]rÔ  U™# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g
CPU time: 0.00 s,  Wall time: 0.00 srÕ  U~# Worksheet '_scratch_' (2006-08-17 at 15:14)
sage: view(f)
<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>rÖ  T  # Worksheet '_scratch_' (2006-08-17 at 15:14)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>r×  U«# Worksheet '_scratch_' (2006-08-17 at 15:14)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
rØ  Uœ# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10
CPU time: 0.01 s,  Wall time: 0.01 srÙ  U¢# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f*g
CPU time: 0.01 s,  Wall time: 0.01 srÚ  U¤# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f^5*g
CPU time: 0.01 s,  Wall time: 0.01 srÛ  U¥# Worksheet '_scratch_' (2006-08-17 at 15:14)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f^10*g
CPU time: 0.02 s,  Wall time: 0.02 srÜ  U¥# Worksheet '_scratch_' (2006-08-17 at 15:15)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f^10*g
CPU time: 0.01 s,  Wall time: 0.01 srÝ  TL  # Worksheet '_scratch_' (2006-08-17 at 15:15)
sage: h[:50]
[1153300796610, -10571923411357, 35521669089060, -82207173890380/3, -1578378351911680/9, 6297739398214880/9, -107392893078774688/81, 377409713492725760/243, -287199547816076060/243, 3757883697935134460/6561, -3178137624289098691/19683, 132742369030852798/6561, 0, 0, 0, ...rÞ  U9# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: 2^3
8rß  U;# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: 2/3
2/3rà  UX# Worksheet '_scratch_' (2006-08-17 at 17:00)
python> print(2^3)
python> print(2/3)
1
0rá  UJ# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: factor(2007)
3^2 * 223râ  U¢# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
sage: M
[   1    2    3]
[ 1/3   17 -2/3]
[   1    5   -5]rã  U|# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: M.parent()
Full MatrixSpace of 3 by 3 dense matrices over Rational Fieldrä  U¿# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
1&2&3\\
\frac{1}{3}&17&-\frac{2}{3}\\
1&5&-5
\end{array}\right)</span></html>rå  U^# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: M.echelon_form()
[1 0 0]
[0 1 0]
[0 0 1]ræ  UL# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: G = AlternatingGroup(5)
rç  U# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]rè  U¥# Worksheet '_scratch_' (2006-08-17 at 17:00)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f^10*g
CPU time: 0.01 s,  Wall time: 0.01 sré  TL  # Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: h[:50]
[1153300796610, -10571923411357, 35521669089060, -82207173890380/3, -1578378351911680/9, 6297739398214880/9, -107392893078774688/81, 377409713492725760/243, -287199547816076060/243, 3757883697935134460/6561, -3178137624289098691/19683, 132742369030852798/6561, 0, 0, 0, ...rê  U~# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: view(f)
<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>rë  T  # Worksheet '_scratch_' (2006-08-17 at 17:00)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>rì  U«# Worksheet '_scratch_' (2006-08-17 at 17:00)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
rí  Uo# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: time n=factorial(10^6)
CPU time: 3.25 s,  Wall time: 3.28 srî  U«# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: f = maxima('x*sin(x)*cos(x)^2')
sage: print f, type(f)
x*cos(x)^2*sin(x) <class 'sage.interfaces.maxima.MaximaElement'>rï  Uv# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: f.integrate()
(sin(3*x) - 3*x*cos(3*x) + 9*sin(x) - 9*x*cos(x))/36rð  UD# Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: f.name()
'sage0'rñ  Té  # Worksheet '_scratch_' (2006-08-17 at 17:00)
# Many random spheres:
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)
rò  T‹  # Worksheet '_scratch_' (2006-08-17 at 17:00)
sage: plot3dsoya(lambda x,y: abs(zeta(x+I*y)),(1,0), side=4, res=32).show()
[>                                                            ] 0%[---------->                                                  ] 17%[-------------------->                                        ] 34%[------------------------------------>                        ] 60%[--...ró  U9# Worksheet '_scratch_' (2006-08-17 at 17:23)
sage: 2^3
8rô  U;# Worksheet '_scratch_' (2006-08-17 at 17:23)
sage: 2/3
2/3rõ  UX# Worksheet '_scratch_' (2006-08-17 at 17:24)
python> print(2^3)
python> print(2/3)
1
0rö  UJ# Worksheet '_scratch_' (2006-08-17 at 17:24)
sage: factor(2007)
3^2 * 223r÷  U¢# Worksheet '_scratch_' (2006-08-17 at 17:25)
sage: M = MatrixSpace(QQ,3)([1,2,3,1/3,17,-2/3,1,5,-5])
sage: M
[   1    2    3]
[ 1/3   17 -2/3]
[   1    5   -5]rø  U|# Worksheet '_scratch_' (2006-08-17 at 17:25)
sage: M.parent()
Full MatrixSpace of 3 by 3 dense matrices over Rational Fieldrù  U¿# Worksheet '_scratch_' (2006-08-17 at 17:25)
sage: view(M)
<html><span class="math">\left(\begin{array}{rrr}
1&2&3\\
\frac{1}{3}&17&-\frac{2}{3}\\
1&5&-5
\end{array}\right)</span></html>rú  U^# Worksheet '_scratch_' (2006-08-17 at 17:27)
sage: M.echelon_form()
[1 0 0]
[0 1 0]
[0 0 1]rû  U·# Worksheet '_scratch_' (2006-08-17 at 17:27)
sage: view(M.echelon_form())
<html><span class="math">\left(\begin{array}{rrr}
1&0&0\\
0&1&0\\
0&0&1
\end{array}\right)</span></html>rü  UL# Worksheet '_scratch_' (2006-08-17 at 17:27)
sage: G = AlternatingGroup(5)
rý  U# Worksheet '_scratch_' (2006-08-17 at 17:27)
sage: G.conjugacy_classes_representatives()
[(), (1,2)(3,4), (1,2,3), (1,2,3,4,5), (1,2,3,5,4)]rþ  U¥# Worksheet '_scratch_' (2006-08-17 at 17:28)
time> f = x^389 + 17/3*x + 2
time> g = x^397 - 18*x + 15
time> h = f*g^10 + f^10*g
CPU time: 0.02 s,  Wall time: 0.02 srÿ  TL  # Worksheet '_scratch_' (2006-08-17 at 17:28)
sage: h[:50]
[1153300796610, -10571923411357, 35521669089060, -82207173890380/3, -1578378351911680/9, 6297739398214880/9, -107392893078774688/81, 377409713492725760/243, -287199547816076060/243, 3757883697935134460/6561, -3178137624289098691/19683, 132742369030852798/6561, 0, 0, 0, ...r   U~# Worksheet '_scratch_' (2006-08-17 at 17:28)
sage: view(f)
<html><span class="math">x^{389} + \frac{17}{3}x + 2</span></html>r  T  # Worksheet '_scratch_' (2006-08-17 at 17:28)
hide%html> <h2>You can embed HTML</h2>
hide%html> It can even include math: <span class='math'>\prod(1-q^n)</span>
<html><h2>You can embed HTML</h2>
It can even include math: <span class='math'>\prod(1-q^n)</span></html>r  U«# Worksheet '_scratch_' (2006-08-17 at 17:29)
latex> Cells can be written in latex, which can refer to SAGE objects.
latex> For example, consider $E$ given by $\sage{E}$.
r  Uo# Worksheet '_scratch_' (2006-08-17 at 17:31)
sage: time n=factorial(10^6)
CPU time: 3.31 s,  Wall time: 3.34 sr  U«# Worksheet '_scratch_' (2006-08-17 at 17:31)
sage: f = maxima('x*sin(x)*cos(x)^2')
sage: print f, type(f)
x*cos(x)^2*sin(x) <class 'sage.interfaces.maxima.MaximaElement'>r  Uv# Worksheet '_scratch_' (2006-08-17 at 17:32)
sage: f.integrate()
(sin(3*x) - 3*x*cos(3*x) + 9*sin(x) - 9*x*cos(x))/36r  Té  # Worksheet '_scratch_' (2006-08-17 at 17:32)
# Many random spheres:
        sage: t = Tachyon(xres=512,yres=512, camera_center=(2,0.5,0.5), look_at=(0.5,0.5,0.5), raydepth=4)
        sage: t.light((4,3,2), 0.2, (1,1,1))
        sage: t.texture('t0', ambient=0.1, diffuse=0.9, specular=0.5, opacity=1.0, color=(1.0,0,0))
        sage: t.texture('t1', ambient=0.1, diffuse=0.9, specular=0.3, opacity=1.0, color=(0,1.0,0))
        sage: t.texture('t2', ambient=0.2, diffuse=0.7, specular=0.5, opacity=0.7, color=(0,0,1.0))
        sage: k=0
        sage: for i in range(100):
        ...    k += 1
        ...    t.sphere((random(),random(), random()), random()/10, 't%s'%(k%3))
        ...
        sage: t.save()         # long (several seconds)
r  eU_Notebook__defaultsr  }r	  (Ucell_output_colorr
  U#0000EEr  Umax_history_lengthr  MôUcell_input_colorr  U#0000000r  Uword_wrap_colsr  KduU_Notebook__worksheet_dirr  Usage_notebook/worksheetsr  U_Notebook__filenamer  Usage_notebook/nb.sobjr  U_Notebook__default_worksheetr  hU_Notebook__next_worksheet_idr  KU_default_filenamer  U6/home/was/talks/2006-08-17-scipy/sage_notebook/nb.sobjr  U_Notebook__systemr  NU_Notebook__show_debugr  ‰U_Notebook__dirr  Usage_notebookr  U_Notebook__authr  U:U_Notebook__colorr  NU_Notebook__object_dirr  Usage_notebook/objectsr  ub.