[was@descent was]$ [was@descent was]$ Magma V2.7-1      Tue Jul  4 2000 20:49:39 on descent  [Seed = 3118648700]
Type ? for help.  Type <Ctrl>-D to quit.

Loading startup file "/home/was/modsym/init-magma.m"

C               IndexGamma0     R               factormod       padiccharpoly
CS              MS              Tn              fcp             qexp
DC              ND              Z               fn              x
ES              NS              charpoly        idxG0
F               Q               ellap           modcharpoly
> M:=ModularSymbols(9,4);
> M;
Full Modular symbols space of level 9, weight 4, and dimension 6
> A:=CS(M);
> A;
Modular symbols space of level 9, weight 4, and dimension 2
> Periods(A,50);
[
(0.1047477693755510168878537506 + 0.06047615284598721747189642123*i),
(0.1047477693755510168878537506 - 0.06047615284598721747189642123*i)
]
> EllipticInvariants(A,50);
-0.000008545806165793494726244039305 + 0.00001480177046680886373605378910*i -56626421681.55843066 - 4.336808688938617706 E-19*i -2.6906338494440222415129152749036827420 E-33 - 9.4002327278681342691728250862648041580 E-43*i
> EllipticInvariants;
Intrinsic 'EllipticInvariants'

Signatures:

(<ModSym> A) -> FldPrElt, FldPrElt, FldPrElt
(<ModSym> A, <RngIntElt> n) -> FldPrElt, FldPrElt, FldPrElt

The invariants c4, c6, and j, computed to precision n.


> P:=Periods(A,97);
> P;
[
(0.1047477693755510168878523836 + 0.06047615284598721747189198005*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> C<i>:=ComplexField();
> i*P[1];
(-0.06047615284598721747189198005 + 0.1047477693755510168878523836*i)
> v:=i*P[1];
> v;
(-0.06047615284598721747189198005 + 0.1047477693755510168878523836*i)
> P[1]+P[2];
(0.2094955387511020337757047673 +  0.E-30*i)
> 3*v;
(-0.1814284585379616524156759401 + 0.3142433081266530506635571509*i)
> 4*v;
(-0.2419046113839488698875679202 + 0.4189910775022040675514095346*i)
> omega:=(1+Sqrt(-3))/2;
> omega;
1/2 + 0.8660254037844386467637231707*i
> omega*P[1];
(1.262177448254078626000000000 E-29 + 0.1209523056919744349437839601*i)
> P;
[
(0.1047477693755510168878523836 + 0.06047615284598721747189198005*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> P[1]-P[2];
( 0.E-30 + 0.1209523056919744349437839601*i)
> P;
[
(0.1047477693755510168878523836 + 0.06047615284598721747189198005*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> P[1]+P[2];
(0.2094955387511020337757047673 +  0.E-30*i)
> EM:=MS("27A");
> EM;
Modular symbols space of level 27, weight 2, and dimension 2
> Periods(EM,97);
[
(1.766638750285479428628084783),
(-0.8833193751427397143140423916 + 1.529954037057257284034757869*i)
]
> jInvariant(EllipticCurve(EM));
0
> P;
[
(0.1047477693755510168878523836 + 0.06047615284598721747189198005*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> [P[1]+P[2], P[2]];
[
(0.2094955387511020337757047673 +  0.E-30*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> PE:=Periods(EM,97);
> PE[1][1]/PE[2][1];PE[1][1]/PE[2][1];
-0.4999999999999809375574334612 - 0.8660254037844276410573759675*i
> omega;
1/2 + 0.8660254037844386467637231707*i
> P[1][1]/P[2][1];
0.5000000000000000000000000001 + 0.8660254037844386467637231706*i
> Periods(EM,97)[1][1]/(P[1]+P[2])[1];
8.432822774256743799544616666 +  0.E-28*i
> a:=8.432822774256743799544616666;
a:=8.432822774256743799544616666;
> a;
8.432822774256743799544616665
> ContinuedFraction(a);
8.432822774256743799544616665
> ContinuedFraction(a);
[ 8, 2, 3, 4, 1, 1, 16, 1, 1, 10, 1, 1, 1, 9, 1, 16, 2, 2, 3, 1, 1, 5, 121, 1, 4 ]
> 22/7.0;
3.142857142857142857142857142
> ContinuedFraction(3.142857142857142857142857142);
[ 3, 7 ]
> ContinuedFraction(3.142857142857142857142857143);
[ 3, 7 ]
> ContinuedFraction(3.1428571428571428571422948);
[ 3, 7 ]
> ContinuedFraction(3.142857142857142857129808235598);
[ 3, 7, 1563974887706165852 ]
> ContinuedFraction(a);
[ 8, 2, 3, 4, 1, 1, 16, 1, 1, 10, 1, 1, 1, 9, 1, 16, 2, 2, 3, 1, 1, 5, 121, 1, 4 ]
> ContinuedFraction(234.32423423515371578548);
> ContinuedFraction(234.32423423515371578548);

>> ContinuedFraction(234.32423423515371578548);
   ^
User error: bad syntax
> User error: bad syntax

>> User error: bad syntax
        ^
User error: bad syntax
> ContinuedFraction(234.32423423515371578548);
[ 234, 3, 11, 1, 7, 5, 3, 1, 1, 8, 3, 1, 5, 1, 33, 5, 1, 7, 2, 3, 2, 11, 6 ]
> E;

>> E;
   ^
User error: Identifier 'E' has not been declared or assigned
> P;
[
(0.1047477693755510168878523836 + 0.06047615284598721747189198005*i),
(0.1047477693755510168878523836 - 0.06047615284598721747189198005*i)
]
> PE;
[
(1.766638750285479428628084783),
(-0.8833193751427397143140423916 + 1.529954037057257284034757869*i)
]
> [P[1]*a, P[2]*a];
[
(0.8833193751427397143140423915 + 0.5099846790190727992733811351*i),
(0.8833193751427397143140423915 - 0.5099846790190727992733811351*i)
]
> PE;
[
(1.766638750285479428628084783),
(-0.8833193751427397143140423916 + 1.529954037057257284034757869*i)
]
> a;
8.432822774256743799544616665
> LSeries(A,1,97);
-0.4189910775022040675514095346
> LSeries(A,2,97);
-0.7599657499933076359136227472 +  0.E-29*i
> LSeries(A,3,97);
-0.9189502627850946258433477704
>