Ziele Untersuchung
mit Columbo Integrität von
Datenbanken Interaktion und
Portierbarkeit Ergonomie der
Schnittstellen

Angebot Produkte Projekt Beratung

Mittel Analytik Modellierung Sprachen Algebra Logik Hardware Denken Kreativität

Zusammenhänge Gesellschaft Wirtschaft Branche Firma


products/sources/formale Sprachen/GAP/pkg/4ti2interface/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 23.10.2024 mit Größe 2 kB

Quelle _Chunks.xml Sprache: XML

<#GAPDoc Label="Groebner1">
We want to compute the groebner basis of the ideal
defining the affine toric variety associated to the cone
generated by the inequalities [ [ 7, -1 ], [ 0, 1 ] ],
i.e. a rational normal curve.
<Example><![CDATA[
gap> cone := [ [ 7, -1 ], [ 0, 1 ] ];
[ [ 7, -1 ], [ 0, 1 ] ]
gap> basis := 4ti2Interface_hilbert_inequalities( cone );;
gap> Sort( basis );
gap> basis;
[ [ 1, 0 ], [ 1, 1 ], [ 1, 2 ], [ 1, 3 ],
  [ 1, 4 ], [ 1, 5 ], [ 1, 6 ], [ 1, 7 ] ]
gap> groebner := 4ti2Interface_groebner_matrix( basis );;
gap> Sort( groebner );
gap> groebner;
[ [ -1, 0, 0, 1, 1, 0, 0, -1 ], [ -1, 0, 0, 2, 0, 0, -1, 0 ],
  [ -1, 0, 1, 0, 0, 1, 0, -1 ], [ -1, 0, 1, 0, 1, 0, -1, 0 ],
  [ -1, 0, 1, 1, 0, -1, 0, 0 ], [ -1, 0, 2, 0, -1, 0, 0, 0 ],
  [ -1, 1, 0, 0, 0, 0, 1, -1 ], [ -1, 1, 0, 0, 0, 1, -1, 0 ],
  [ -1, 1, 0, 0, 1, -1, 0, 0 ], [ -1, 1, 0, 1, -1, 0, 0, 0 ],
  [ -1, 1, 1, -1, 0, 0, 0, 0 ], [ -1, 2, -1, 0, 0, 0, 0, 0 ],
  [ 0, -1, 0, 0, 2, 0, 0, -1 ], [ 0, -1, 0, 1, 0, 1, 0, -1 ],
  [ 0, -1, 1, 0, 0, 0, 1, -1 ], [ 0, 0, -1, 0, 1, 1, 0, -1 ],
  [ 0, 0, -1, 1, 0, 0, 1, -1 ], [ 0, 0, 0, -1, 0, 2, 0, -1 ],
  [ 0, 0, 0, -1, 1, 0, 1, -1 ], [ 0, 0, 0, 0, -1, 1, 1, -1 ],
  [ 0, 0, 0, 0, 0, -1, 2, -1 ] ]
gap> Length( groebner );
21
]]></Example>

<#/GAPDoc>
<#GAPDoc Label="HilbertBasis">
We want to compute the Hilbert basis of the cone obtained
by intersecting the positive orthant with the hyperplane
given by the equation below.
<Example><![CDATA[
gap> gens := [ 23, 25, 37, 49 ];
[ 23, 25, 37, 49 ]
gap> equation := [ Concatenation( gens, -gens ) ];
[ [ 23, 25, 37, 49, -23, -25, -37, -49 ] ]
gap> basis := 4ti2Interface_hilbert_equalities_in_positive_orthant( equation );;
gap> Length( basis );
436
]]></Example>

<#/GAPDoc>
<#GAPDoc Label="HilbertBasis2">
We want to compute the Hilbert basis of the cone which faces
are represented by the inequalities below. This example is
taken from the toric and the ToricVarieties package manual.
In both packages it is very slow with the internal algorithms.
<Example><![CDATA[
gap> inequalities := [ [1,2,3,4], [0,1,0,7], [3,1,0,2], [0,0,1,0] ];
[ [ 1, 2, 3, 4 ], [ 0, 1, 0, 7 ], [ 3, 1, 0, 2 ], [ 0, 0, 1, 0 ] ]
gap> basis := 4ti2Interface_hilbert_inequalities( inequalities );;
gap> Length( basis );
29
]]></Example>

<#/GAPDoc>

quality93%

¤ Dauer der Verarbeitung: 0.19 Sekunden (vorverarbeitet) ¤

Wurzel

Suchen

Beweissystem der NASA

Beweissystem Isabelle

NIST Cobol Testsuite

Cephes Mathematical Library

Wiener Entwicklungsmethode

Haftungshinweis

Die Informationen auf dieser Webseite wurden nach bestem Wissen sorgfältig zusammengestellt. Es wird jedoch weder Vollständigkeit, noch Richtigkeit, noch Qualität der bereit gestellten Informationen zugesichert.