# Difference between revisions of "ApCoCoA:LinSyz.BettyNumbers"

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 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>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> | ||

## Latest revision as of 14:03, 13 July 2009

## 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 ApCoCoA: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

ApCoCoA:Introduction to Modules