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Simplify's condition can be missing, or stricter than the input #2134
Description
The condition Simplify attaches can be missing, and it can be stricter than the input:
| Input | Simplify |
Should be |
|---|---|---|
x*(1 - 1/x) |
x - 1 |
x - 1 provided not x = 0, as (x^2 - x)/x gives |
-(t*x+y)/(1-y*x) + (t*x+y)/(1-y*x) |
0 provided not 1 - x * y = 0 and not x = 0 |
0 provided not 1 - x * y = 0. At x = 0 the input is -y + y, which is defined |
The first answer is defined where the input is not. The second leaves out points where the input is defined.
Found while reading Modenov's Problems in Geometry for #2131.
Activity
Rafael-SOWNet commentedon Oct 27, 2026
The first row,
x*(1 - 1/x)→x - 1with no condition, is the same question as #1648 (1/(1/x)isx): whether an answer keeps the point its input excluded. Whatever is decided there decides this row too. The second row, a condition stricter than the input, is a defect either way.Simplify does not add a condition the input does not have (#2171)
Rafael-SOWNet commentedon Oct 27, 2026
The second row is fixed by #2171. A polynomial division with the variables replaced divided by the symbolic leading coefficient
-x, which is the source ofnot x = 0. That attempt now declines it, as the first attempt already did, and-(t*x + y)/(1 - y*x) + (t*x + y)/(1 - y*x)simplifies to0 provided not 1 - x * y = 0. The first row, a condition left out, waits on what #1648 decides.