q=h h h!h#h$h%h&h'ub(hoq>}q?(hU parent(E)q@hU!qAhhhhhU hMhUeos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/interfaces/cells/4")
parent(E)qBh U+sage_notebook/worksheets/interfaces/cells/4qCh UMagmaqDh h h!h#h$h%h&h'ub(hoqE}qF(hUE.name()qGhU!qHhhhhhU hMhUdos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/interfaces/cells/5")
E.name()qIh U+sage_notebook/worksheets/interfaces/cells/5qJh U '_sage_[2]'qKh h h!h#h$h%h&h'ub(hoqL}qM(hU hhhhU hMh U+sage_notebook/worksheets/interfaces/cells/6qNh U h h$h%h'ubeU_Worksheet__synchroqOK U_Worksheet__nameqPU
interfacesqQU_Worksheet__attachedqR}qSU_Worksheet__dirqTU#sage_notebook/worksheets/interfacesqUU_Worksheet__queueqV]qWU_Worksheet__next_idqXMU_Worksheet__comp_is_runningqYU_Worksheet__notebookqZhU_Worksheet__idq[KU_Worksheet__next_block_idq\K U_Worksheet__systemq]NubU _scratch_q^(hoq_}q`(h
U _scratch_qah ]qb((hoqc}qd(hU2^3qehU!qfhh_hhhU hK hU^os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/0")
2^3qgh U*sage_notebook/worksheets/_scratch_/cells/0qhh U8h h h!h#h$h%h&h'ub(hoqi}qj(hU factor(2007)qkhU!qlhh_hhhU hKhUgos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/1")
factor(2007)qmh U*sage_notebook/worksheets/_scratch_/cells/1qnh U 3^2 * 223qoh h h!h#h$h%h&h'ub(hoqp}qq(hUview(factor(2007))qrhU!qshh_hhhU hKhUmos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/5")
view(factor(2007))qth U*sage_notebook/worksheets/_scratch_/cells/5quh U63^{2} \cdot 223qvh h h!h#h$h%h&h'ub(hoqw}qx(hU)ModularSymbols(43,sign=1).decomposition()qyhU!qzhh_hhhU hKhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/2")
ModularSymbols(43,sign=1).decomposition()q{h U*sage_notebook/worksheets/_scratch_/cells/2q|h T [
Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field,
Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field,
Modular Symbols subspace of dimension 2 of Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 over Rational Field
]q}h h h!h#h$h%h&h'ub(hoq~}q(hUtime n=factorial(10^6)qhU!qhh_hhhU hKhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/3")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
n=factorial(10^6)qh U*sage_notebook/worksheets/_scratch_/cells/3qh U$CPU time: 3.61 s, Wall time: 3.63 sqh h h!h#h$h%h&h'ub(hoq}q(hU-show(maxima('x*sin(x)*cos(x)^2').integrate())qhU!qhh_hhhU hKhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/4")
show(maxima('x*sin(x)*cos(x)^2').integrate())qh U*sage_notebook/worksheets/_scratch_/cells/4qh Uu\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x \cos x}{36}
qh h h!h#h$h%h&h'ub(hoq}q(hU hh_hhU hKh U*sage_notebook/worksheets/_scratch_/cells/6qh U h h$h%h'ubehOKhPU _scratch_qhR}qhTU"sage_notebook/worksheets/_scratch_qhV]qhXKhYhZhh[K h\Kh]NubUcoverageq(hoq}q(h
Ucoverageqh ]q((hoq}q(hUbuzzard_tpslopes(2,1,50)qhU!qhhhhhU hM h2Ubuzzard_qhUros.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/0")
buzzard_tpslopes(2,1,50)qh U)sage_notebook/worksheets/coverage/cells/0qh T% [[], [], [], [], [], [], [], [], [], [], [], [], [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, 12, 15], [], [4, 8, 13]]qh h h!h#h$h%h&h'ub(hoq}q(hU@factor(genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5).conductor)qhU!qhhhhhU hM h2UgenuqhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/1")
factor(genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5).conductor)qh U)sage_notebook/worksheets/coverage/cells/1qh U
5^4 * 2267qh h h!h#h$h%h&h'ub(hoq}q(hU=ecm = ECM();
ecm.factor(next_prime(10^10)*next_prime(10^30))qhU!qhhhhhU hM h2UECM.qhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/2")
ecm = ECM();
ecm.factor(next_prime(10^10)*next_prime(10^30))qh U)sage_notebook/worksheets/coverage/cells/2qh U.[10000000019, 1000000000000000000000000000057]qh h h!h#h$h%h&h'ub(hoq}q(hU4factor(ModularSymbols(389,2,sign=1).T(2).charpoly())qhU!qhhhhhU hM hUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/3")
factor(ModularSymbols(389,2,sign=1).T(2).charpoly())qh U)sage_notebook/worksheets/coverage/cells/3qh TE (x - 3) * (x + 2) * (x^2 - 2) * (x^3 - 4*x - 2) * (x^6 + 3*x^5 - 2*x^4 - 8*x^3 + 2*x^2 + 4*x - 1) * (x^20 - 3*x^19 - 29*x^18 + 91*x^17 + 338*x^16 - 1130*x^15 - 2023*x^14 + 7432*x^13 + 6558*x^12 - 28021*x^11 - 10909*x^10 + 61267*x^9 + 6954*x^8 - 74752*x^7 + 1407*x^6 + 46330*x^5 - 1087*x^4 - 12558*x^3 - 942*x^2 + 960*x + 148)qh h h!h#h$h%h&h'ub(hoq}q(hU)A. = QuaternionAlgebra(QQ,-1,-1)
AqhU!qhhhhhU hM h2U
QuaternionAlgqhUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/4")
A. = QuaternionAlgebra(QQ,-1,-1)
Aqh U)sage_notebook/worksheets/coverage/cells/4qh U@Quaternion algebra with generators (i, j, k) over Rational Fieldqh h h!h#h$h%h&h'ub(hoq}q(hUi^2 + jqhU!qhhhhhU hM hUaos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/5")
i^2 + jqh U)sage_notebook/worksheets/coverage/cells/5qh U-1 + jqh h h!h#h$h%h&h'ub(hoq}q(hU%SupersingularModule(37).T(2).matrix()qhU!qhhhhhU hM hUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/6")
SupersingularModule(37).T(2).matrix()qh U)sage_notebook/worksheets/coverage/cells/6qh UbSupersingular Module -- work in progress; use at own risk. (2006-08-08)
[1 1 1]
[1 0 2]
[1 2 0]qh h h!h#h$h%h&h'ub(hoq}q(hU hhhhU hM h U)sage_notebook/worksheets/coverage/cells/7qh U h h$h%h'ubehOKhPUcoverageqhR}qhTU!sage_notebook/worksheets/coverageqhV]qhXM hYhZhh[Kh\Kh]NubuU_Notebook__historyq]q(U9# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: 2^3
8qUL# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: factor(2006)
2 * 17 * 59qUJ# Worksheet '_scratch_' (2006-08-15 at 00:38)
sage: factor(2007)
3^2 * 223qTh # 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 ...qTo # 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 ...qUo# Worksheet '_scratch_' (2006-08-15 at 00:39)
sage: time n=factorial(10^6)
CPU time: 3.61 s, Wall time: 3.63 sqU{# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: show(factor(2007))
3^{2} \cdot 223
qU}# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(factor(2007))
3^{2} \cdot 223qTj # Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('sin(x^2)').integrate())
\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}...qTj # Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('cos(x^2)').integrate())
-\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...qU# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('tan(x^2)').integrate())
\int {\tan x^2}{\;dx}qU# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(x)').integrate())
\log \sec xqU# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(1/x)').integrate())
\int {\tan \left(\frac{1}{x}\right)}{\;dx}qU# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('sin(1/x)').integrate())
\sin \left(\frac{1}{x}\right) x+\int {\frac{\cos \left(\frac{1}{x} \right)}{x}}{\;dx}qU# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('x*sin(x)*cos(x)^2').integrate())
\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x \cos x}{36}qU# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: show(maxima('x*sin(x)*cos(x)^2').integrate())
\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x \cos x}{36}
qU\# Worksheet 'interfaces' (2006-08-15 at 00:42)
sage: E = magma.EllipticCurve('[1,2,3,4,5]')
qU# 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 FieldqU# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup()
Abelian Group isomorphic to Z
Defined on 1 generator (free)qTe # 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...qU# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup(Bound = 10)
Abelian Group isomorphic to Z
Defined on 1 generator (free)qUi# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: type(E)
qUD# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: parent(E)
MagmaqUI# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.name()
'_sage_[2]'qT] # 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...qU~# 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 * 2267qU# 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)qU# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM().factor(next_prime(10^10)*next_prime(10^11))
[10000000019, 100000000003]qU# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM().factor(next_prime(10^10)*next_prime(10^30))
[10000000019, 1000000000000000000000000000057]qU# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ecm = ECM(); print ecm
sage: ecm.factor(next_prime(10^10)*next_prime(10^30))
[10000000019, 1000000000000000000000000000057]qU# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ecm = ECM();
sage: ecm.factor(next_prime(10^10)*next_prime(10^30))
[10000000019, 1000000000000000000000000000057]qTy # 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...qU[# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: A. = QuaternionAlgebra(QQ,-1,-1)
qUA# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: i^2 + j
-1 + jqU# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: A. = QuaternionAlgebra(QQ,-1,-1)
sage: A
Quaternion algebra with generators (i, j, k) over Rational FieldqU# 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 RingqU# 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]qeU_Notebook__defaultsq}q(Ucell_output_colorqU#0000EEqUmax_history_lengthqMUcell_input_colorr U#0000000r Uword_wrap_colsr KduU_Notebook__worksheet_dirr Usage_notebook/worksheetsr U_Notebook__filenamer Usage_notebook/nb.sobjr U _Notebook__default_worksheetr h_U _Notebook__next_worksheet_idr KU_default_filenamer U9/home/was/talks/2006-08-14-ccr-sage/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 Usage_notebook/objectsr ub.