Difference between revisions of "ApCoCoA-1:LinSyz.BettyNumbers"
From ApCoCoAWiki
m (insert version info) |
|||
| (7 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
| + | {{Version|1}} | ||
<command> | <command> | ||
<title>LinSyz.BettyNumbers</title> | <title>LinSyz.BettyNumbers</title> | ||
| − | <short_description>Computes Betty numbers of module generated by linear forms.</short_description> | + | <short_description>Computes all Betty numbers of a module generated by linear forms.</short_description> |
<syntax> | <syntax> | ||
LinSyz.BettyNumbers(M:MODULE):LIST | LinSyz.BettyNumbers(M:MODULE):LIST | ||
| 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 all Betty numbers of a given module which is generated by vectors consisting of linear forms. Be aware of the fact that this is | + | This command computes all Betty numbers 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 all Betty numbers will be computed.</item> | <item>@param <em>M</em> A module for which all Betty numbers will be computed.</item> | ||
| − | <item>@return A list of all Betty numbers of M. The first indeterminate returned contains the number of generators, such that this command does not produce conflicts with LinSyz.Resolution, which returns the interreduced generators first.</item> | + | <item>@return A list of all Betty numbers of <tt>M</tt>. The first indeterminate returned contains the number of generators, such that this command does not produce conflicts with <ref>ApCoCoA-1:LinSyz.Resolution|LinSyz.Resolution</ref>, which returns the interreduced generators first.</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.BettyNumbers(M); | ||
| + | -- CoCoAServer: computing Cpu Time = 0 | ||
| + | ------------------------------- | ||
| + | [3] | ||
| + | ------------------------------- | ||
| + | </example> | ||
| + | |||
</description> | </description> | ||
<seealso> | <seealso> | ||
| − | <see>LinSyz.BettyNumber</see> | + | <see>ApCoCoA-1:LinSyz.BettyNumber|LinSyz.BettyNumber</see> |
| − | <see>LinSyz.Resolution</see> | + | <see>ApCoCoA-1:LinSyz.Resolution|LinSyz.Resolution</see> |
| − | <see> | + | <see>ApCoCoA-1:Introduction to Modules|Introduction to Modules</see> |
</seealso> | </seealso> | ||
| + | |||
| + | <types> | ||
| + | <type>apcocoaserver</type> | ||
| + | <type>module</type> | ||
| + | </types> | ||
<key>BettyNumbers</key> | <key>BettyNumbers</key> | ||
<key>linsyz.BettyNumbers</key> | <key>linsyz.BettyNumbers</key> | ||
| − | <wiki-category>Package_linsyz</wiki-category> | + | <wiki-category>ApCoCoA-1:Package_linsyz</wiki-category> |
</command> | </command> | ||
Latest revision as of 10:12, 7 October 2020
| This article is about a function from ApCoCoA-1. |
LinSyz.BettyNumbers
Computes all Betty numbers of a module generated by linear forms.
Syntax
LinSyz.BettyNumbers(M:MODULE):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.
This command computes all Betty numbers 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 all Betty numbers will be computed.
@return A list of all Betty numbers of M. The first indeterminate returned contains the number of generators, such that this command does not produce conflicts with LinSyz.Resolution, which returns the interreduced generators first.
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.BettyNumbers(M);
-- CoCoAServer: computing Cpu Time = 0
-------------------------------
[3]
-------------------------------
See also
