Macaulay2 / Macaulay2/M2

Frobenius powers

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#662 2 comments 0 reactions 0 assignees View on GitHub

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Core
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Macaulay2
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Avg merge
4d 20h
Merged PRs (30d)
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Description

This operation on ideals is not well defined, i.e., equal ideals don't provide equal results.
We should make it mathematically sensible.

```
Ideal ^ Array := (I, e) -> (
R := ring I;
n := numgens R;
-- Error if input is not correct.
if any(e, i -> i < 0) then error "Expected nonnegative exponents.";
if #e != 1 and n != #e then error "Expected single integer array, or array with length equal to the number of variables.";
-- if only one element, then make vector the same as the length of
-- the number of variables with the same number in each entry
if #e == 1 then e = new Array from n:(e_0);
-- build a ring homomorphism that will perform this substitution for us
phi := map(R,R,matrix {apply(numgens R, i -> (R_i)^(e_i))});
-- apply the ring homomorphism and create the new ideal
ideal phi generators I
)
```

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Research direction

Start by locating the Ideal ^ Array operation described in the issue and review the proposed input checks and substitution behavior. Done means the operation is mathematically well defined: equal ideals produce equal results, while the stated exponent validation remains correct.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Bug
Difficulty
5/5
Estimated time
Over a week
Activity status
Quiet
Clarity
Needs clarification
Newbie friendliness
35/100

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