comparison of ideals

[DanGrayson]

For ideals I==J it might be faster to compare gb's rather than to perform all the reductions performed by isSubset(I,J) and isSubset(J,I).

Why is the code here commented out?:

i41 : code (symbol ==, Ideal, Ideal)

o41 = -- code for method: Ideal == Ideal
      /Applications/Macaulay2-1.10/share/Macaulay2/Core/matrix1.m2:547:25-554:40: --source code:
      Ideal == Ideal := (I,J) -> (
           samering(I,J);
           ( generators I == generators J or 
                -- if isHomogeneous I and isHomogeneous J  -- can be removed later
                -- then gb I == gb J 
                -- else
                isSubset(I,J) and isSubset(J,I)         -- can be removed later
                ))

It's been that way since 1998.

[eisenbud]

and why wouldn't gens gb I == gens gb J work for inhomogeneous ideals too?

David

David Eisenbud Director, Mathematical Sciences Research Institute; and Professor of Mathematics,University of California, Berkeley www.msri.org/~de

On Jul 27, 2017, at 5:00 PM, Daniel R. Grayson notifications@github.com wrote:

For ideals I==J it might be faster to compare gb's rather than to perform all the reductions performed by isSubset(I,J) and isSubset(J,I).

Why is the code here commented out?:

i41 : code (symbol ==, Ideal, Ideal)

o41 = -- code for method: Ideal == Ideal /Applications/Macaulay2-1.10/share/Macaulay2/Core/matrix1.m2:547:25-554:40: --source code: Ideal == Ideal := (I,J) -> ( samering(I,J); ( generators I == generators J or -- if isHomogeneous I and isHomogeneous J -- can be removed later -- then gb I == gb J -- else isSubset(I,J) and isSubset(J,I) -- can be removed later )) It's been that way since 1998.

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[DanGrayson]

Indeed.

But we should make sure it's not a "local" ordering.