Feature request: MutableIdeal

Macaulay2 / M2

The primary source code repository for Macaulay2, a system for computing in commutative algebra, algebraic geometry and related fields.

https://macaulay2.com

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Feature request: MutableIdeal #1749

Open mahrud opened 3 years ago

mahrud commented 3 years ago

I've seen a lot of cases where in each step of an iterative algorithm, an ideal is updated and the new ideal is used for some membership test. I think this is somewhat slow because:

a new ideal is allocated and the old one is garbage collected in each step
the groebner basis information of the old ideal may not survive

Would be good to add MutableIdeals that satisfy the two points above.

dylanpeifer commented 3 years ago

The new ideal is actually distinct from the old ideal, right? So the Groebner basis would be different, and what you'd really need is some way to update a Groebner basis when a new generator is added. You can perform Buchberger with only the new pairs from a new generator, but I don't think this is implemented in the engine.

mahrud commented 3 years ago

Do you mean mathematically or the pointer to the mutable object? Mathematically the ideal may be the same, if the new generator was already in the ideal, and I don't think the gb would need to be immediately recomputed after a new generator is added (i.e. addition should be O(1)), but yes, computing the new gb should definitely be incremental.