View source for Package invarFC0/InvFC0.SAGBI

{{Version|2}}
<command>
  <title>InvFC0.SAGBI</title>
  <short_description>This function computes a SAGBI basis of an invariant ring.</short_description>
  
  <syntax>InvFC0.SAGBI(G:LIST of MAT, opt d:INT):LIST of POLY</syntax>
  <description>
This function computes a (<tt>d</tt>-truncated) SAGBI basis of the invariant ring <tt>P^G</tt>.
WARNING: May not terminate if <tt>P^G</tt> does not have a finite SAGBI basis.
    <itemize>
      <item>@param <tt>G</tt> A list of matrices of size <tt>n</tt> over a ring <tt>P</tt> with <tt>n</tt> indeterminates.</item>
      <item>@param <tt>d</tt> (optional) An integer describing the truncation degree.</item>
      <item>@return A list of polynomials that form a (<tt>d</tt>)-truncated SAGBI basis.</item>
    </itemize>
 
    <!-- Examples here (also only one or more than two possible) -->
    <!-- It is important to omit any indentation inside the example environment -->
    <!-- may also go over more lines, but the </example>-tag should not be in a new line -->
    <example>
Use P ::= QQ[x,y,z];
T := matrix(P, [[0,1,0],
                [1,0,0],
                [0,0,1]]);
C := matrix(P, [[0,1,0],
                [0,0,1],
                [1,0,0]]);
S3 := [T*T,T,C,T*C,T*C*C,T*C*T];
InvFC0.SAGBI(S3);</example>
    <example>
A := Mat(P, [[0,1,0],
             [0,0,1],
             [1,0,0]]);
G := [A,A^2,A^3]; // cyclic group generated by A
TruncG := InvFC0.SAGBI(G,7); // has no finite DegRevLex-SAGBI basis</example>
  </description>

  <!-- Add related pages (also more or none possible) -->
  <seealso>
    <see>Package invarFC0</see>
    <see>Package invarFC0/InvFC0.MinGens</see>
  </seealso>

  <!-- Add all data types used in the signature of your function (also more or none possible) -->
  <types>
    <type>list</type>
    <type>poly</type>
    <type>int</type>
    <type>mat</type>
    <type>sagbi</type>
  </types>

  <!-- Add keys here (first three are mandatory, other ones are optional) -->
  <key>SAGBI</key>
  <key>InvFC0.SAGBI</key>
  <key>apcocoa/invFC0.SAGBI</key>

  <wiki-category>Package invarFC0</wiki-category>

</command>