Difference between revisions of "ApCoCoA-1:BB.LiftASViaServer"

From ApCoCoAWiki
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{{Version|1}}
 
<command>
 
<command>
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    <title>BB.LiftASViaServer</title>
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  <title>BB.LiftASViaServer</title>
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    <short_description>Compute the border basis scheme ideal generators obtained from lifting of AS neighbors.</short_description>
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  <short_description>Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.</short_description>
 +
 
 
<syntax>
 
<syntax>
 
BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST
 
BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST
 
</syntax>
 
</syntax>
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    <description>
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  <description>
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{{ApCoCoAServer}}
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
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<par/>
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If <tt>HomogeneousLift</tt> is set to <tt>False</tt>, the generators of the border basis scheme ideal <formula>I(\mathbb{B}_\mathcal{O})</formula> that result from the lifting of across-the-street neighbors will computed by using the ApCoCoAServer. The input is a list of terms <tt>OO</tt> representing an order ideal and a list of terms <tt>Border</tt> representing the border of the order ideal. If <tt>HomogeneousLift</tt> is set to <tt>True</tt>, generators of <formula>I(\mathbb{B}^{\textrm{hom}}_\mathcal{O})</formula> will be computed instead. The output is a list of polynomials in the ring <formula>BBS=K[c_{ij}]</formula>.
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If <tt>HomogeneousLift</tt> is set to <tt>FALSE</tt>, the generators of the border basis scheme ideal <tt>I(B_O)</tt> that result from the lifting of across-the-street neighbors will be computed by using the ApCoCoAServer. If <tt>HomogeneousLift</tt> is set to <tt>TRUE</tt>, generators of <tt>I(B^hom_O)</tt> will be computed instead.
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<itemize>
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  <item>@param <em>OO</em> A list of terms representing an order ideal.</item>
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  <item>@param <em>Border</em> A list of terms representing the border of order ideal.</item>
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  <item>@param <em>Homogeneous</em> Set to <em>TRUE</em> if you want to compute the generators of the homogeneous border basis scheme.</item>
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  <item>@return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].</item>
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</itemize>
 
<example>
 
<example>
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Use Q[x,y], DegRevLex;
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Use QQ[x,y], DegRevLex;
 
BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False);
 
BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False);
  
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-------------------------------
 
-------------------------------
 
</example>
 
</example>
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    </description>
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  </description>
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     <key>kaspar</key>
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  <types>
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     <key>bb.liftasviaserver</key>
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     <type>borderbasis</type>
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     <key>borderbasis.liftasviaserver</key>
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     <type>ideal</type>
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    <see>BB.LiftAS</see>
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     <type>apcocoaserver</type>
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    <see>BB.LiftHomAS</see>
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  </types>
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    <see>BB.LiftND</see>
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    <see>BB.LiftNDViaServer</see>
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  <see>Introduction to CoCoAServer</see>
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    <see>BB.LiftHomND</see>
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  <see>ApCoCoA-1:BB.LiftAS|BB.LiftAS</see>
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    <wiki-category>Package_borderbasis</wiki-category>
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  <see>ApCoCoA-1:BB.LiftHomAS|BB.LiftHomAS</see>
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  <see>ApCoCoA-1:BB.LiftND|BB.LiftND</see>
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  <see>ApCoCoA-1:BB.LiftNDViaServer|BB.LiftNDViaServer</see>
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  <see>ApCoCoA-1:BB.LiftHomND|BB.LiftHomND</see>
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 +
  <key>LiftASViaServer</key>
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  <key>BB.LiftASViaServer</key>
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  <key>borderbasis.LiftASViaServer</key>
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  <wiki-category>ApCoCoA-1:Package_borderbasis</wiki-category>
 
</command>
 
</command>

Latest revision as of 09:41, 7 October 2020

This article is about a function from ApCoCoA-1.

BB.LiftASViaServer

Computes the border basis scheme ideal generators obtained from lifting of AS neighbours.

Syntax

BB.LiftASViaServer(OO:LIST,Border:LIST,HomogeneousLift:BOOL):LIST

Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

If HomogeneousLift is set to FALSE, the generators of the border basis scheme ideal I(B_O) that result from the lifting of across-the-street neighbors will be computed by using the ApCoCoAServer. If HomogeneousLift is set to TRUE, generators of I(B^hom_O) will be computed instead.

  • @param OO A list of terms representing an order ideal.

  • @param Border A list of terms representing the border of order ideal.

  • @param Homogeneous Set to TRUE if you want to compute the generators of the homogeneous border basis scheme.

  • @return A list of generators of the border basis scheme ideal. The polynomials will belong to the ring BBS=K[c_{ij}].

Example

Use QQ[x,y], DegRevLex;
BB.LiftASViaServer([Poly(1), x, y, xy], [y^2, x^2, xy^2, x^2y], False);

-------------------------------
[BBS :: c[3,4]c[4,1] - c[2,3]c[4,2] + c[2,4] - c[3,3],
 BBS :: -c[2,2]c[2,3] + c[2,1]c[3,4] - c[2,4]c[4,3] + c[2,3]c[4,4] - c[1,3],
 BBS :: -c[2,3]c[3,2] + c[3,1]c[3,4] - c[3,4]c[4,3] + c[3,3]c[4,4] + c[1,4],
 BBS :: -c[1,2]c[2,3] + c[1,1]c[3,4] - c[1,4]c[4,3] + c[1,3]c[4,4]]
-------------------------------


Introduction to CoCoAServer

BB.LiftAS

BB.LiftHomAS

BB.LiftND

BB.LiftNDViaServer

BB.LiftHomND




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