Difference between revisions of "Package sagbi/SB.GetTruncSAGBI"
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<short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description> | <short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description> | ||
| − | <syntax>SB.GetTruncSAGBI(ref S: TAGGED( | + | <syntax>SB.GetTruncSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"), d: INT): LIST of POLY</syntax> |
<description> | <description> | ||
This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>. | This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>. | ||
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</itemize> | </itemize> | ||
| − | <example> </example> | + | <example> |
| + | Use P ::= QQ[x,y,z]; | ||
| + | S := SB.Subalgebra(P,[x^2 -z^2, x*y +z^2, y^2 -2*z^2]); | ||
| + | PrintLn SB.GetTruncSAGBI(S,3); | ||
| + | -- [y^2 -2*z^2, x*y +z^2, x^2 -z^2]</example> | ||
</description> | </description> | ||
Latest revision as of 13:21, 29 October 2020
| This article is about a function from ApCoCoA-2. |
SB.GetTruncSAGBI
This function returns a truncated SAGBI basis of a given standard-graded subalgebra.
Syntax
SB.GetTruncSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"), d: INT): LIST of POLY
Description
This function takes a subalgebra S generated by homogeneous polynomials as a reference, computes a d-truncated SAGBI basis, returns it and saves it into S if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree d, then it just returns the truncated SAGBI basis of S.
@param S A subalgebra
@param d A positive integer
@return A d-truncated SAGBI basis of S
Example
Use P ::= QQ[x,y,z]; S := SB.Subalgebra(P,[x^2 -z^2, x*y +z^2, y^2 -2*z^2]); PrintLn SB.GetTruncSAGBI(S,3); -- [y^2 -2*z^2, x*y +z^2, x^2 -z^2]
See also
