‰h?UB
qah@KU_word_being_completedqbU E.Lseries_doqchAU¶os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/7")
L = E.Lseries_dokchitser(20)
show(plot(L,-1,2, thickness=2, hue=0.6), ymin=-0.25, ymax=0.5)qdhCU*sage_notebook/worksheets/_scratch_/cells/7qehEU hG‰hHhIhJ‰hKhLhM‰hN‰ub(hoqf}qg(hU)ModularSymbols(43,sign=1).decomposition()qhhU!qihhh‰h‰hU hKhU„os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/2")
ModularSymbols(43,sign=1).decomposition()qjh U*sage_notebook/worksheets/_scratch_/cells/2qkh 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
]qlh ‰h ‰h!h#h$h%h&‰h'‰ub(hoqm}qn(hUtime n=factorial(10^6)qohU!qphhh‰h‰hU hKhU—os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/3")
__SAGE_t__=cputime()
__SAGE_w__=walltime()
n=factorial(10^6)qqh U*sage_notebook/worksheets/_scratch_/cells/3qrh U$CPU time: 3.61 s, Wall time: 3.63 sqsh ‰h ‰h!h#h$h%h&ˆh'‰ub(hoqt}qu(hU-show(maxima('x*sin(x)*cos(x)^2').integrate())qvhU!qwhhh‰h‰hU hKhUˆos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/_scratch_/cells/4")
show(maxima('x*sin(x)*cos(x)^2').integrate())qxh U*sage_notebook/worksheets/_scratch_/cells/4qyh Uu\frac{\sin \left(3 x\right)-3 x \cos \left(3 x\right)+9 \sin x-9 x \cos x}{36}
qzh ‰h ‰h!h#h$h%h&‰h'‰ub(hoq{}q|(hU hhh‰hU hKh U*sage_notebook/worksheets/_scratch_/cells/6q}h U h ‰h$h%h'‰ubeU_Worksheet__synchroq~K"U_Worksheet__nameqU _scratch_q€U_Worksheet__attachedq}q‚U_Worksheet__dirqƒU"sage_notebook/worksheets/_scratch_q„U_Worksheet__queueq…]q†U_Worksheet__next_idq‡K U_Worksheet__comp_is_runningqˆ‰U_Worksheet__notebookq‰hU_Worksheet__idqŠK U_Worksheet__next_block_idq‹KU_Worksheet__systemqŒNubUcnta - using other systemsq(hoqŽ}q(U_Worksheet__filenameqUcnta___using_other_systemsq‘U_Worksheet__cellsq’]q“((hoq”}q•(h8U)E = magma.EllipticCurve('[1,2,3,4,5]'); Eq–h:U!q—h‰h?U h@M°hAU–os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/cnta___using_other_systems/cells/14")
E = magma.EllipticCurve('[1,2,3,4,5]'); Eq˜hCUq h‰h?U h@M°hAU‹os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/cnta___using_other_systems/cells/15")
E.MordellWeilGroup(Bound = 10)q¡hCUq§h‰h?U h@M°hAUtos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/cnta___using_other_systems/cells/16")
type(E)q¨hCUqªhG‰hHh›hJ‰hKhLhM‰hN‰ub(hoq«}q¬(h8U mathematica('BernoulliB[100]')qh:U!q®h‰h?U h@M°hAU‹os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/cnta___using_other_systems/cells/17")
mathematica('BernoulliB[100]')q¯hCUq·U_Cell__worksheetq¸hŽU_Cell__completionsq¹‰U_Cell__introspectqº‰U_Cell__out_htmlq»U U _Cell__idq¼M °U_before_preparseq½U’os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/0")
n = -2007
print n.factor()
print factor(n)q¾U
_Cell__dirq¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/0qÀU
_Cell__outqÁU -1 * 3^2 * 223
-1 * 3^2 * 223qÂUhas_new_outputqÉU_Cell__is_htmlqĉU _Cell__sageqÅh#U _Cell__typeqÆUwrapqÇU _Cell__timeqȉU_Cell__interruptedqɉub(hoqÊ}qË(h´Un.factor(algorithm="kash")qÌh¶U!qÍh¸hŽh¹‰hº‰h»U h¼M°h½U‚os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/1")
n.factor(algorithm="kash")qÎh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/1qÏhÁU-1 * 3^2 * 223qÐhÉhĉhÅh#hÆUwrapqÑhȉhɉub(hoqÒ}qÓ(h´Ugap(n).FactorsInt()qÔh¶U!qÕh¸hŽh¹‰hº‰h»U h¼M°h½U{os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/2")
gap(n).FactorsInt()qÖh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/2q×hÁU[ -3, 3, 223 ]qØhÉhĉhÅh#hÆhÇhȉhɉub(hoqÙ}qÚ(h´Upari(n).factor()qÛh¶U!qÜh¸hŽh¹‰hº‰h»U h¼M°h½Uxos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/3")
pari(n).factor()qÝh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/3qÞhÁU[-1, 1; 3, 2; 223, 1]qßhÉhĉhÅh#hÆhÇhȉhɉub(hoqà}qá(h´Ugp(n).factor()qâh¶U!qãh¸hŽh¹‰hº‰h»U h¼M
°h½Uwos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/10")
gp(n).factor()qäh¿Uqêh¸hŽh¹‰hº‰h»U h¼M°h½Uzos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/4")
maxima(n).factor()qëh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/4qìhÁU-3^2*223qíhÉhĉhÅh#hÆhÇhȉhɉub(hoqî}qï(h´Ukash(n).Factorization()qðh¶U!qñh¸hŽh¹‰hº‰h»U h¼M°h½Uos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/5")
kash(n).Factorization()qòh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/5qóhÁUE[ <3, 2>, <223, 1> ], extended by:
ext1 := -1,
ext2 := UnassignqôhÉhĉhÅh#hÆhÇhȉhɉub(hoqõ}qö(h´U!magma(n).Factorization(nvals = 2)q÷h¶U!qøh¸hŽh¹‰hº‰h»U h¼M°h½U‰os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/6")
magma(n).Factorization(nvals = 2)qùh¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/6qúhÁU([ <3, 2>, <223, 1> ], -1)qûhÉhĉhÅh#hÆhÇhȉhɉub(hoqü}qý(h´Umaple(n).ifactor()qþh¶U!qÿh¸hŽh¹‰hº‰h»U h¼M°h½Uzos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/7")
maple(n).ifactor()r h¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/7r hÁU-``(3)^2*``(223)r hÉhĉhÅh#hÆhÇhȉhɉub(hor }r (h´U mathematica(n).FactorInteger()r h¶U!r h¸hŽh¹‰hº‰h»U h¼M°h½U†os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/8")
mathematica(n).FactorInteger()r h¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/8r hÁU{{-1, 1}, {3, 2}, {223, 1}}r hÉhĉhÅh#hÆhÇhȉhɉub(hor
}r (h´U<%magma
n := -2007;
F, s := Factorization(-2007);
print F, sr h¶U!r
h¸hŽh¹‰hº‰h»U h¼M °h½U¤os.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/9")
%magma
n := -2007;
F, s := Factorization(-2007);
print F, sr h¿U;sage_notebook/worksheets/cnta___using_other_systems/cells/9r hÁU[ <3, 2>, <223, 1> ]
-1r hÉhĉhÅh#hÆhÇhȉhɉub(hor }r (h´U
magma('F')r h¶U!r h¸hŽh¹‰hº‰h»U h¼M °h½Usos.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/11")
magma('F')r h¿U, <223, 1> ]r hÉhĉhÅh#hÆhÇhȉhɉub(hor }r (h´U U_Cell__introspect_htmlr U!r h¸hŽh¹‰U_Cell__introspectr ‰h»U h¼M °U_before_preparser Uios.chdir("/home/was/talks/2006-07-09-cnta/sage_notebook/worksheets/cnta___using_other_systems/cells/12")
r h¿U NU_Worksheet__idr? K ubUcoverager@ (horA }rB (h
UcoveragerC h ]rD ((horE }rF (hUbuzzard_tpslopes(2,1,50)rG hU!rH hjA h‰h‰hU hM U_word_being_completedrI Ubuzzard_rJ hUros.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/0")
buzzard_tpslopes(2,1,50)rK h U)sage_notebook/worksheets/coverage/cells/0rL h 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]]rM h ‰h ‰h!h#h$h%h&‰h'‰ub(horN }rO (hU@factor(genus2reduction(x^3 - 2*x^2 - 2*x + 1, -5*x^5).conductor)rP hU!rQ hjA h‰h‰hU hM jI UgenurR hUšos.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)rS h U)sage_notebook/worksheets/coverage/cells/1rT h U
5^4 * 2267rU h ‰h ‰h!h#h$h%h&‰h'‰ub(horV }rW (hU=ecm = ECM();
ecm.factor(next_prime(10^10)*next_prime(10^30))rX hU!rY hjA h‰h‰hU hM jI UECM.rZ hU—os.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/2")
ecm = ECM();
ecm.factor(next_prime(10^10)*next_prime(10^30))r[ h U)sage_notebook/worksheets/coverage/cells/2r\ h U.[10000000019, 1000000000000000000000000000057]r] h ‰h ‰h!h#h$h%h&‰h'‰ub(hor^ }r_ (hU4factor(ModularSymbols(389,2,sign=1).T(2).charpoly())r` hU!ra hjA h‰h‰hU hM hUŽos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/3")
factor(ModularSymbols(389,2,sign=1).T(2).charpoly())rb h U)sage_notebook/worksheets/coverage/cells/3rc h 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)rd h ‰h ‰h!h#h$h%h&‰h'‰ub(hore }rf (hU)A. = QuaternionAlgebra(QQ,-1,-1)
Arg hU!rh hjA h‰h‰hU hM jI U
QuaternionAlgri hUƒos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/4")
A. = QuaternionAlgebra(QQ,-1,-1)
Arj h U)sage_notebook/worksheets/coverage/cells/4rk h U@Quaternion algebra with generators (i, j, k) over Rational Fieldrl h ‰h ‰h!h#h$h%h&‰h'‰ub(horm }rn (hUi^2 + jro hU!rp hjA h‰h‰hU hM hUaos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/5")
i^2 + jrq h U)sage_notebook/worksheets/coverage/cells/5rr h U-1 + jrs h ‰h ‰h!h#h$h%h&‰h'‰ub(hort }ru (hU%SupersingularModule(37).T(2).matrix()rv hU!rw hjA h‰h‰hU hM hUos.chdir("/home/was/talks/2006-08-14-ccr-sage/sage_notebook/worksheets/coverage/cells/6")
SupersingularModule(37).T(2).matrix()rx h U)sage_notebook/worksheets/coverage/cells/6ry h UbSupersingular Module -- work in progress; use at own risk. (2006-08-08)
[1 1 1]
[1 0 2]
[1 2 0]rz h ‰h ‰h!h#h$h%h&‰h'‰ub(hor{ }r| (hU hjA h‰hU hM h U)sage_notebook/worksheets/coverage/cells/7r} h U h ‰h$h%h'‰ubeh~KhUcoverager~ h}r hƒU!sage_notebook/worksheets/coverager€ h…]r h‡M hˆ‰h‰hhŠKh‹KhŒNubuU_Notebook__historyr‚ ]rƒ (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 ...rˆ 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))
3^{2} \cdot 223
rŠ U}# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(factor(2007))
3^{2} \cdot 223r‹ Tj # 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}...rΠTj # 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...r U•# Worksheet '_scratch_' (2006-08-15 at 00:40)
sage: view(maxima('tan(x^2)').integrate())
\int {\tan x^2}{\;dx}rŽ U‰# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(x)').integrate())
\log \sec xr Uª# Worksheet '_scratch_' (2006-08-15 at 00:41)
sage: view(maxima('tan(1/x)').integrate())
\int {\tan \left(\frac{1}{x}\right)}{\;dx}r UÖ# 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}r‘ UÙ# 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}r’ U×# 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}
r“ U\# Worksheet 'interfaces' (2006-08-15 at 00:42)
sage: E = magma.EllipticCurve('[1,2,3,4,5]')
r” 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 Fieldr• U†# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup()
Abelian Group isomorphic to Z
Defined on 1 generator (free)r– 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...r— U# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: E.MordellWeilGroup(Bound = 10)
Abelian Group isomorphic to Z
Defined on 1 generator (free)r˜ Ui# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: type(E)
r™ UD# Worksheet 'interfaces' (2006-08-15 at 00:43)
sage: parent(E)
Magmarš 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...rœ 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)rž U€# Worksheet 'coverage' (2006-08-15 at 01:07)
sage: ECM().factor(next_prime(10^10)*next_prime(10^11))
[10000000019, 100000000003]rŸ 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))
[10000000019, 1000000000000000000000000000057]r¡ 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]r¢ 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...r£ U[# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: A. = QuaternionAlgebra(QQ,-1,-1)
r¤ UA# Worksheet 'coverage' (2006-08-15 at 01:09)
sage: i^2 + j
-1 + jr¥ U£# 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 Fieldr¦ 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 Ringr§ 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]r¨ 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))
r© 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 Fieldrª 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))
r« Ui# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: L = E.Lseries_dokchitser(5)
sage: show(plot(L,-1,2))
r¬ Uj# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: L = E.Lseries_dokchitser(20)
sage: show(plot(L,-1,2))
r 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))
r® 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))
r¯ 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)
r° U\# Worksheet 'interfaces' (2006-08-15 at 09:01)
sage: E = magma.EllipticCurve('[1,2,3,4,5]')
r± T # Worksheet '_scratch_' (2006-08-15 at 09:03)
html> You can embed HTML
html> It can even include math: \prod(1-q^n)
You can embed HTML
It can even include math: \prod(1-q^n)r² UÊ# Worksheet '_scratch_' (2006-08-15 at 09:03)
html%hide> You can embed HTML
html%hide> It can even include math: \prod(1-q^n)
...
NameError: name 'hide' is not definedr³ T # Worksheet '_scratch_' (2006-08-15 at 09:03)
hide%html> You can embed HTML
hide%html> It can even include math: \prod(1-q^n)
You can embed HTML
It can even include math: \prod(1-q^n)r´ 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 $\sage{E}$.
rµ UA# Worksheet 'interfaces' (2006-08-15 at 09:04)
sage: gap('2^3')
8r¶ 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 Fieldr· UF# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: singular('2^3')
8r¸ U@# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gp('2^3')
8r¹ 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);;rº 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);;r¼ UA# Worksheet 'interfaces' (2006-08-15 at 09:05)
sage: gap('2^3')
8r½ 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 Fieldr¾ 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)
rÀ U¾# Worksheet 'cnta - using other systems' (2006-08-15 at 09:09)
sage: mathematica('BernoulliB[100]')
-94598037819122125295227433069493721872702841533066936133385696204311395415197247711/33330rÁ eU_Notebook__defaultsr }rà (Ucell_output_colorrÄ U#0000EErÅ Umax_history_lengthrÆ MôUcell_input_colorrÇ U#0000000rÈ Uword_wrap_colsrÉ KduU_Notebook__worksheet_dirrÊ Usage_notebook/worksheetsrË U_Notebook__filenamerÌ Usage_notebook/nb.sobjrÍ U _Notebook__default_worksheetrÎ hU _Notebook__next_worksheet_idrÏ KU_default_filenamerÐ U9/home/was/talks/2006-08-14-ccr-sage/sage_notebook/nb.sobjrÑ U_Notebook__systemrÒ NU_Notebook__show_debugrÓ ‰U_Notebook__dirrÔ U
sage_notebookrÕ U_Notebook__authrÖ U:U_Notebook__colorr× NU_Notebook__object_dirrØ Usage_notebook/objectsrÙ ub.
qZh@K hAUÑos.chdir("/home/was/talks/2006-08-14-ccr-sage/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 $\sage{E}$.q[hCU+sage_notebook/worksheets/_scratch_/cells/11q\hEU hG‰hHhIhJ‰hKhLhM‰hN‰ub(hoq]}q^(h8U[L = E.Lseries_dokchitser(20)
show(plot(L,-1,2, thickness=2, hue=0.6), ymin=-0.25, ymax=0.5)q_h:U!q`h