This is a MAGMA GUI

€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UFactorization(902384029384)q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Unos.chdir("/home/was/talks/2006-08-14-ccr-sage/magma/worksheets/_scratch_/cells/0")
Factorization(902384029384)qU
_Cell__dirqU"magma/worksheets/_scratch_/cells/0qU
_Cell__outqU[ <2, 3>, <112798003673, 1> ]qUhas_new_outputq ‰U_Cell__sageq!csage.interfaces.sage0
reduce_load_Sage
q")Rq#U_Cell__is_htmlq$‰U_Cell__typeq%Uwrapq&U_Cell__timeq'‰U_Cell__interruptedq(‰ub(hoq)}q*(hU+R<x,y> := PolynomialRing(RationalField(),2)q+hU!<pre class="introspection"></pre>q,hhh‰h‰hU hKhU~os.chdir("/home/was/talks/2006-08-14-ccr-sage/magma/worksheets/_scratch_/cells/1")
R<x,y> := PolynomialRing(RationalField(),2)q-hU"magma/worksheets/_scratch_/cells/1q.hU h ‰h!h#h$‰h%h&h'‰h(‰ub(hoq/}q0(hUf := (x-y)^7; fq1hU!<pre class="introspection"></pre>q2hhh‰h‰hU hKhUbos.chdir("/home/was/talks/2006-08-14-ccr-sage/magma/worksheets/_scratch_/cells/2")
f := (x-y)^7; fq3hU"magma/worksheets/_scratch_/cells/2q4hUQx^7 - 7*x^6*y + 21*x^5*y^2 - 35*x^4*y^3 + 35*x^3*y^4 - 21*x^2*y^5 + 7*x*y^6 - y^7q5h ‰h!h#h$‰h%h&h'‰h(‰ub(hoq6}q7(hU#E := EllipticCurve([0,0,1,-1,0]); Eq8hU!<pre class="introspection"></pre>q9hhh‰h‰hU hKhUvos.chdir("/home/was/talks/2006-08-14-ccr-sage/magma/worksheets/_scratch_/cells/3")
E := EllipticCurve([0,0,1,-1,0]); Eq:hU"magma/worksheets/_scratch_/cells/3q;hU?Elliptic Curve defined by y^2 + y = x^3 - x over Rational Fieldq<h ‰h!h#h$‰h%h&h'‰h(‰ub(hoq=}q>(hUGenerators(MordellWeilGroup(E))q?hU!<pre class="introspection"></pre>q@hhh‰h‰hU hKU_word_being_completedqAUmagma.TorsionSuqBhUros.chdir("/home/was/talks/2006-08-14-ccr-sage/magma/worksheets/_scratch_/cells/4")
Generators(MordellWeilGroup(E))qChU"magma/worksheets/_scratch_/cells/4qDhU	{
$.1
}qEh ‰h!h#h$‰h%h&h'‰h(‰ub(hoqF}qG(hU hhh‰hU hKhU"magma/worksheets/_scratch_/cells/5qHhU h ‰h%h&h(‰ubeU_Worksheet__synchroqIKU_Worksheet__comp_is_runningqJ‰U_Worksheet__dirqKUmagma/worksheets/_scratch_qLU_Worksheet__variablesqM]qNU_Worksheet__attachedqO}qPU_Worksheet__queueqQ]qRU_Worksheet__next_idqSKU_Worksheet__nameqTU	_scratch_qUU_Worksheet__next_block_idqVKU_Worksheet__notebookqWhU_Worksheet__idqXK U_Worksheet__sageqYh#U_Worksheet__systemqZUmagmaq[ubsU_Notebook__historyq\]q](Um# Worksheet '_scratch_' (2006-08-15 at 08:54)
sage: Factorization(902384029384)
[ <2, 3>, <112798003673, 1> ]q^T  # Worksheet '_scratch_' (2006-08-15 at 08:54)
sage: R<x,y> = PolynomialRing(RationalField(),2)
...
RuntimeError: Error evaluation Magma code.
IN:R<x,y> = PolynomialRing(RationalField(),2);
OUT:
>> R<x,y> = PolynomialRing(RationalField(),2);
          ^
User error: bad syntaxq_U`# Worksheet '_scratch_' (2006-08-15 at 08:54)
sage: R<x,y> := PolynomialRing(RationalField(),2)
q`U•# Worksheet '_scratch_' (2006-08-15 at 08:54)
sage: f := (x-y)^7; f
x^7 - 7*x^6*y + 21*x^5*y^2 - 35*x^4*y^3 + 35*x^3*y^4 - 21*x^2*y^5 + 7*x*y^6 - y^7qaTr  # Worksheet '_scratch_' (2006-08-15 at 08:55)
sage: E := EllipticCurve(CremonaDatabase(), "37A")
...
RuntimeError: Error evaluation Magma code.
IN:E := EllipticCurve(CremonaDatabase(), "37A");
OUT:
>> E := EllipticCurve(CremonaDatabase(), "37A");
                                     ^
Runtime error in 'CremonaDatabase': The file GetLibraryRoot()/data/ECTable.d...qbU™# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: E := EllipticCurve([0,1,0,-1,0]); E
Elliptic Curve defined by y^2 = x^3 + x^2 - x over Rational FieldqcU—# Worksheet '_scratch_' (2006-08-15 at 08:59)
sage: E := EllipticCurve([0,0,1,-1,0]); E
Elliptic Curve defined by y^2 + y = x^3 - x over Rational FieldqdU_# Worksheet '_scratch_' (2006-08-15 at 09:01)
sage: TorsionSubgroup(E)
Abelian Group of order 1qeU„# Worksheet '_scratch_' (2006-08-15 at 09:02)
sage: MordellWeilGroup(E)
Abelian Group isomorphic to Z
Defined on 1 generator (free)qfU]# Worksheet '_scratch_' (2006-08-15 at 09:02)
sage: Generators(MordellWeilGroup(E))
{
$.1
}qgT  # Worksheet '_scratch_' (2006-08-15 at 09:02)
html> <h1>This is a MAGMA GUI</h1>
...
RuntimeError: Error evaluation Magma code.
IN:%html
<h1>This is a MAGMA GUI</h1>;
OUT:%: bad command

>> <h1>This is a MAGMA GUI</h1>;
       ^
User error: bad syntaxqheU_Notebook__defaultsqi}qj(Ucell_output_colorqkU#0000EEqlUmax_history_lengthqmMôUcell_input_colorqnU#0000000qoUword_wrap_colsqpKduU_Notebook__worksheet_dirqqUmagma/worksheetsqrU_Notebook__filenameqsUmagma/nb.sobjqtU_Notebook__default_worksheetquhU_Notebook__next_worksheet_idqvKU_default_filenameqwU1/home/was/talks/2006-08-14-ccr-sage/magma/nb.sobjqxU_Notebook__systemqyh[U_Notebook__show_debugqz‰U_Notebook__dirq{h[U_Notebook__authq|U:U_Notebook__colorq}NU_Notebook__object_dirq~Umagma/objectsqub.