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| {{Version|2|[[ApCoCoA-1:SB.Sagbi]] and [[ApCoCoA-1:SB.ReducedSagbi]]}}
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| <command>
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| <title>SB.SAGBI</title>
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| <short_description>Computes a finite SAGBI-basis of a subalgebra if existing.</short_description>
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| <syntax>SB.SAGBI(G:LIST of POLY):LIST of POLY</syntax>
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| <description>
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| This function computes a finite SAGBI-basis of a subalgebra <tt>S</tt> generated by the polynomials of the list <tt>G</tt>, if a finite SAGBI-basis of <tt>S</tt> exists. Then a list of polynomials is returned which form a SAGBI-basis of <tt>S</tt>. Otherwise the computation runs until it is interrupted.
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| <itemize>
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| <item>@param <em>G</em> A list of polynomials which generates a subalgebra.</item>
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| <item>@return A list of polynomials which form a finite SAGBI-basis of the subalgebra generated by <tt>G</tt>.</item>
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| </itemize>
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|
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| <example>
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| Use QQ[x,y,z], DegRevLex;
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| S := SB.SAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2]);
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| indent(S);
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| -- [
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| -- y^2 -2*z^2,
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| -- x*y +z^2,
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| -- x^2 -z^2,
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| -- x^2*z^2 +x*y*z^2 +(1/2)*y^2*z^2 +(-1/2)*z^4
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| -- ]</example>
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| </description>
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| <seealso>
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| <see>Package zerodim</see>
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| <see>Package sagbi/SB.SAGBITimeout</see>
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| <see>Package sagbi/SB.IsSAGBIOf</see>
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| <see>Package sagbi/SB.GetSAGBI</see>
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| <see>Package sagbi/SB.GetTruncSAGBI</see>
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| </seealso>
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|
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| <types>
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| <type>sagbi</type>
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| <type>poly</type>
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| </types>
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|
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| <key>SAGBI</key>
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| <key>SB.SAGBI</key>
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| <key>apcocoa/sagbi.SAGBI</key>
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| <wiki-category>Package sagbi</wiki-category>
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| </command>
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