View source for Package sagbi/SB.IsInToricRing

{{Version|2}}
<command>
  <title>SB.IsInToricRing</title>
  <short_description>This function checks whether a given polynomial is in a toric subalgebra.</short_description>
  
  <syntax>SB.IsInToricRing(f: RINGELEM, S: TAGGED(<quotes>$apcocoa/sagbi.Subalgebra</quotes>)): BOOL</syntax>
  <description>
This function takes a polynomial <tt>f</tt> and a subalgebra <tt>S</tt> generated by a set of terms and checks whether <tt>f</tt> is a toric ring.
    <itemize>
      <item>@param <tt>f</tt> A polynomial </item>
      <item>@param <tt>S</tt> A subalgebra of <tt>RingOf(f)</tt> </item>
      <item>@return <tt>true</tt> if f is an element of S and <tt>false</tt> otherwise. </item>
    </itemize>
 
    <example>
Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,x*y,y*z]);
f := x^5*y^3*z^2 + x^4*y^2*z^2;
SB.IsInToricRing(f,S);
-- true</example>
  </description>

  <seealso>
    <see>Package sagbi/SB.IsInSubalgebra</see>
    <see>Package sagbi/SB.IsInSubalgebra_SAGBI</see>
    <see>Package sagbi/SB.IsInSA</see>
    <see>Package sagbi/SB.IsInSA_SAGBI</see>
  </seealso>

  <types>
    <type>subalgebra</type>
    <type>poly</type>
    <type>bool</type>
  </types>

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

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

</command>