Difference between revisions of "ApCoCoA-1:LinSyz.BettyNumber"
From ApCoCoAWiki
| Line 1: | Line 1: | ||
<command> | <command> | ||
<title>LinSyz.BettyNumber</title> | <title>LinSyz.BettyNumber</title> | ||
| − | <short_description>Computes the N-th Betty number of a module generated by linear forms.</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 8: | ||
<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> | ||
Revision as of 11:58, 13 July 2009
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
