Difference between revisions of "ApCoCoA-1:LinSyz.BettyNumber"

From ApCoCoAWiki
(Added ApCoCoAServer note)
m (replaced <quotes> tag by real quotes)
 
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{{Version|1}}
 
<command>  
 
<command>  
 
   <title>LinSyz.BettyNumber</title>
 
   <title>LinSyz.BettyNumber</title>
     <short_description>computing a Betty Number for a Module, generated by linear forms</short_description>
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     <short_description>Computes the <tt>N</tt>-th Betty number of a module generated by linear forms.</short_description>
 
<syntax>
 
<syntax>
$linsyz.BettyNumber(Module,Int):Int
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LinSyz.BettyNumber(M:MODULE,N:INT):INT
 
</syntax>
 
</syntax>
 
     <description>
 
     <description>
{{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.
 +
<par/>
 +
This command computes the <tt>N</tt>-th Betty number of a given module which is generated by vectors consisting of linear forms. Be aware of the fact that this is not well tested and may contain bugs! Also the linear forms may not have any constant component, so if your system has some, you have to homogenize the system first via introducing a new indeterminate.
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 +
<itemize>
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<item>@param <em>M</em> A module for which the <tt>N</tt>-th Betty number is computed.</item>
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<item>@param <em>N</em> Declares which Betty number will be computed.</item>
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</itemize>
 +
 
 +
<example>
 +
Use P::=QQ[x,y,z];
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M:=Module([[x+y+z,x+y+z,x-y+z],[x-y,y-4z,x+2z],[x,y,z]]);
 +
BettiDiagram(M);
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        0
 +
----------
 +
1:    3
 +
----------
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Tot:    3
 +
-------------------------------
 +
LinSyz.BettyNumber(M,0);
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ERROR: BettyNumber: Second parameter must be positive!
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CONTEXT: Error("BettyNumber: Second parameter must be positive!")
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-------------------------------
 +
LinSyz.BettyNumber(M,1);
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-- CoCoAServer: computing Cpu Time = 0
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-------------------------------
 +
3
 +
-------------------------------
 +
LinSyz.BettyNumber(M,2);
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-- CoCoAServer: computing Cpu Time = 0
 +
-------------------------------
 +
0
 +
-------------------------------
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LinSyz.BettyNumber(M,3);
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-- CoCoAServer: computing Cpu Time = 0
 +
-------------------------------
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0
 +
-------------------------------
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</example>
  
This command computes a the i-th Betty number of a given module, which is generated by vectors consisting of linear forms. Be aware of the fact that this is very new and may contain bugs! Also the linear forms may not have any constant component, so if your system has some, you have to make the system homogeneous first via introducing a new indeterminate.
 
 
     </description>
 
     </description>
 +
 
     <seealso>
 
     <seealso>
       <see>LinSyz.BettyNumbers</see>
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       <see>ApCoCoA-1:LinSyz.BettyNumbers|LinSyz.BettyNumbers</see>
     <see>LinSyz.Resolution</see>
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     <see>ApCoCoA-1:LinSyz.Resolution|LinSyz.Resolution</see>
   <see>LinSyz.SyzModule</see>  
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   <see>ApCoCoA-1:Introduction to Modules|Introduction to Modules</see>
 
   </seealso>
 
   </seealso>
     <key>heldt</key>
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 +
<types>
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<type>apcocoaserver</type>
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<type>module</type>
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</types>
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 +
     <key>BettyNumber</key>
 
     <key>linsyz.BettyNumber</key>
 
     <key>linsyz.BettyNumber</key>
     <wiki-category>Package_linsyz</wiki-category>
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     <wiki-category>ApCoCoA-1:Package_linsyz</wiki-category>
 
   </command>
 
   </command>

Latest revision as of 13:33, 29 October 2020

This article is about a function from ApCoCoA-1.

LinSyz.BettyNumber

Computes the N-th Betty number of a module generated by linear forms.

Syntax

LinSyz.BettyNumber(M:MODULE,N:INT):INT

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.

This command computes the N-th Betty number of a given module which is generated by vectors consisting of linear forms. Be aware of the fact that this is not well tested and may contain bugs! Also the linear forms may not have any constant component, so if your system has some, you have to homogenize the system first via introducing a new indeterminate.

  • @param M A module for which the N-th Betty number is computed.

  • @param N Declares which Betty number will be computed.

Example

Use P::=QQ[x,y,z];
M:=Module([[x+y+z,x+y+z,x-y+z],[x-y,y-4z,x+2z],[x,y,z]]);
BettiDiagram(M);
        0
----------
 1:     3
----------
Tot:    3
-------------------------------
LinSyz.BettyNumber(M,0);
ERROR: BettyNumber: Second parameter must be positive!
CONTEXT: Error("BettyNumber: Second parameter must be positive!")
-------------------------------
LinSyz.BettyNumber(M,1);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
3
-------------------------------
LinSyz.BettyNumber(M,2);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
0
-------------------------------
LinSyz.BettyNumber(M,3);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
0
-------------------------------


See also

LinSyz.BettyNumbers

LinSyz.Resolution

Introduction to Modules