Difference between revisions of "ApCoCoA-1:LinSyz.BettyNumber"
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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> | + | <short_description>Computes the <tt>N</tt>-th Betty number of a module generated by linear forms.</short_description> |
<syntax> | <syntax> | ||
LinSyz.BettyNumber(M:MODULE,N:INT):INT | LinSyz.BettyNumber(M:MODULE,N:INT):INT | ||
| Line 8: | Line 9: | ||
<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. | <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/> | <par/> | ||
| − | 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 | + | 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. |
<itemize> | <itemize> | ||
| − | <item>@param <em>M</em> A module for which the N-th Betty number is computed.</item> | + | <item>@param <em>M</em> A module for which the <tt>N</tt>-th Betty number is computed.</item> |
<item>@param <em>N</em> Declares which Betty number will be computed.</item> | <item>@param <em>N</em> Declares which Betty number will be computed.</item> | ||
</itemize> | </itemize> | ||
| + | |||
| + | <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 | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>LinSyz.BettyNumbers</see> | + | <see>ApCoCoA-1:LinSyz.BettyNumbers|LinSyz.BettyNumbers</see> |
| − | <see>LinSyz.Resolution | + | <see>ApCoCoA-1:LinSyz.Resolution|LinSyz.Resolution</see> |
| − | + | <see>ApCoCoA-1:Introduction to Modules|Introduction to Modules</see> | |
| − | <see>Introduction to Modules</see> | ||
</seealso> | </seealso> | ||
<types> | <types> | ||
| − | <type> | + | <type>apcocoaserver</type> |
<type>module</type> | <type>module</type> | ||
</types> | </types> | ||
| Line 30: | Line 62: | ||
<key>BettyNumber</key> | <key>BettyNumber</key> | ||
<key>linsyz.BettyNumber</key> | <key>linsyz.BettyNumber</key> | ||
| − | <wiki-category>Package_linsyz</wiki-category> | + | <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
