Quelle gradedmodules26.tst Sprache: unbekannt

# GradedModules, single 26
#
# DO NOT EDIT THIS FILE - EDIT EXAMPLES IN THE SOURCE INSTEAD!
#
# This file has been generated by AutoDoc. It contains examples extracted from
# the package documentation. Each example is preceded by a comment which gives
# the name of a GAPDoc XML file and a line range from which the example were
# taken. Note that the XML file in turn may have been generated by AutoDoc
# from some other input.
#
gap> START_TEST("gradedmodules26.tst");

# doc/../examples/HorrocksMumford.g:5-78
gap> LoadPackage( "GradedRingForHomalg" );;
gap> R := HomalgFieldOfRationalsInDefaultCAS( ) * "x0..x4";;
gap> S := GradedRing( R );;
gap> A := KoszulDualRing( S, "e0..e4" );;
gap> LoadPackage( "GradedModules" );;
gap> mat := HomalgMatrix( "[ \
> e1*e4, e2*e0, e3*e1, e4*e2, e0*e3, \
> e2*e3, e3*e4, e4*e0, e0*e1, e1*e2  \
> ]",
> 2, 5, A );
<A 2 x 5 matrix over a graded ring>
gap> phi := GradedMap( mat, "free", "free", "left", A );;
gap> IsMorphism( phi );
true
gap> M := GuessModuleOfGlobalSectionsFromATateMap( 2, phi );
#I  GuessModuleOfGlobalSectionsFromATateMap uses a heuristic for efficiency;
please check the correctness of the following result

<A graded left module presented by yet unknown relations for 19 generators>
gap> IsPure( M );
true
gap> Rank( M );
2
gap> Display( BettiTable( Resolution( M ) ) );
total:  19 35 20  2
--------------------
     3:   4  .  .  .
     4:  15 35 20  .
     5:   .  .  .  2
--------------------
degree:   0  1  2  3
gap> Display( BettiTable( TateResolution( M, -5, 5 ) ) );
total:  100  37  14  10   5   2   5  10  14  37 100   ?   ?   ?   ?
----------|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
    4:  100  35   4   .   .   .   .   .   .   .   .   0   0   0   0
    3:    *   .   2  10  10   5   .   .   .   .   .   .   0   0   0
    2:    *   *   .   .   .   .   .   2   .   .   .   .   .   0   0
    1:    *   *   *   .   .   .   .   .   .   5  10  10   2   .   0
    0:    *   *   *   *   .   .   .   .   .   .   .   .   4  35 100
----------|---|---|---|---|---|---|---|---|---|---|---|---|---|---S
twist:   -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5
-------------------------------------------------------------------
Euler:  100  35   2 -10 -10  -5   0   2   0  -5 -10 -10   2  35 100
gap> M;
<A graded reflexive non-projective rank 2 left module presented by 99 \
relations for 19 generators>
gap> P := ElementOfGrothendieckGroup( M );
( 2*O_{P^4} - 1*O_{P^3} - 4*O_{P^2} - 2*O_{P^1} ) -> P^4
gap> P!.DisplayTwistedCoefficients := true;
true
gap> P;
( 2*O(-3) - 10*O(-2) + 15*O(-1) - 5*O(0) ) -> P^4
gap> chi := HilbertPolynomial( M );
1/12*t^4+2/3*t^3-1/12*t^2-17/3*t-5
gap> c := ChernPolynomial( M );
( 2 | 1-h+4*h^2 ) -> P^4
gap> ChernPolynomial( M * S^3 );
( 2 | 1+5*h+10*h^2 ) -> P^4
gap> ch := ChernCharacter( M );
[ 2-u-7*u^2/2!+11*u^3/3!+17*u^4/4! ] -> P^4
gap> HilbertPolynomial( ch );
1/12*t^4+2/3*t^3-1/12*t^2-17/3*t-5
gap> List( [ -8 .. 7 ], i -> Value( chi, i ) );
[ 35, 2, -10, -10, -5, 0, 2, 0, -5, -10, -10, 2, 35, 100, 210, 380 ]
gap> HF := HilbertFunction( M );
function( t ) ... end
gap> List( [ 0 .. 7 ], HF );
[ 0, 0, 0, 4, 35, 100, 210, 380 ]
gap> IndexOfRegularity( M );
4
gap> DataOfHilbertFunction( M );
[ [ [ 4 ], [ 3 ] ], 1/12*t^4+2/3*t^3-1/12*t^2-17/3*t-5 ]

#
gap> STOP_TEST("gradedmodules26.tst", 1);

Quelle gradedmodules26.tst Sprache: unbekannt

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