View source for Package sagbi/SB.ReductionStep

{{Version|2}}
<command>
  <title>SB.ReductionStep</title>
  <short_description>This function computes a polynomial to which the given polynomial reduces in one step.</short_description>
  
  <syntax>SB.ReductionStep(f: POLY, G: LIST of POLY): POLY</syntax>
  <description>
This function takes a polynomial <tt>f</tt> and a list of polynomials <tt>G</tt> and computes a polynomial <tt>g</tt> such that <tt>f</tt> reduces to <tt>g</tt> in one step with respect to the Subalgebra rewrite relation defined by <tt>G</tt>, see [[Package sagbi]]. If there is no such polynomial <tt>g</tt>, then <tt>f</tt> is returned.
    <itemize>
      <item>@param <tt>f</tt> A polynomial </item>
      <item>@param <tt>G</tt> A list of polynomials </item>
      <item>@return see description above </item>
    </itemize>
 
    <example>
Use QQ[x,y];
f := x^4*y^2 + x^2*y^4;
G := [x^2-1, y^2-1];
SB.ReductionStep(f,G);
-- x^4*y^3 +2*x^2*y^2 +y^4 -x^2 -2*y^2 +1</example>

    <example>
Use QQ[x,y];
f := x^4*y^3 + x^2*y^3;
G := [x^2-1, y^2-1];
SB.ReductionStep(f,G);
-- x^4*y^3 +x^2*y^3</example>

  </description>

  <seealso>
    <see>Package sagbi/SB.SDA</see>
    <see>Package sagbi/SB.Interreduction</see>
    <see>Package sagbi/SB.FindLTRepr</see>
    <see>Package sagbi/SB.FindLTRepr_glpk</see>
  </seealso>

  <types>
    <type>poly</type>
    <type>poly_list</type>
  </types>

  <key>ReductionStep</key>
  <key>SB.ReductionStep</key>
  <key>apcocoa/sagbi.ReductionStep</key>

  <wiki-category>Package sagbi</wiki-category>
</command>