Macaulay2 / Macaulay2/M2

coefficients in iterated rings

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Macaulay2
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Description

This is not really a bug (and I understand why it happens -- kind of...), but I still find it disturbing and unpleasant:
```
i1 : R=QQ[x]; S=R[y];

i3 : coefficients(x+y,Monomials=>{x,y})

o3 = (| x y |, {0, 1} | x |)
{1, 0} | 1 |

o3 : Sequence

i4 : first oo * last oo -- not the expected result x+y !

o4 = | y+x2 |

1 1
o4 : Matrix S <--- S
```

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Research direction

Start by reproducing the issue using the Macaulay2 transcript with R=QQ[x], S=R[y], and coefficients(x+y,Monomials=>{x,y}). Investigate the iterated-ring coefficient behavior; done means the resulting matrix multiplication represents the expected expression x+y rather than y+x2.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Bug
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
25/100

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