Factorize reaches inside a product the rules already made - #1095
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#1094 asks the polynomial layer only where the rewrite rules said nothing, so that an answer the rules already gave is never replaced -- the order two factors come out in is arbitrary and theirs is the one on record. Declining a **product** outright was too broad for that goal. The rules take a numeric content out and hand back `2 * (x ^ 3 - 1)`. That is a product, so the layer declined it, and the remainder is exactly the shape #1018 is about. Every polynomial with a numeric content whose remainder needs the layer stopped one step short: `2 * x^3 - 2`, `3 * x^6 - 3`, `5 * x^7 - 5`. Each factor is asked separately now instead of the product being handed over whole. Every factor the rules found survives, and only the ones they could not split are split -- so `2 * x^4 - 10x^2 + 8`, which the rules factor in full, is unchanged, and so is `x * (1 + y)`. Found by asking of `Factorize` the property #1092 was about -- that the answer multiplies back to what it factored -- and noticing a row that *satisfied* it and was still less factored than it should be. The value check said nothing because `2 * (x ^ 3 - 1)` is perfectly equal to `2 * x ^ 3 - 2`; what was wrong was not the value but the stopping point, which is a thing a property test does not ask about unless it is told to.
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A follow-up to #1094, fixing an incompleteness that PR introduced.
#1094 asks the polynomial layer only where the rewrite rules said nothing, so that an answer
the rules already gave is never replaced — the order two factors come out in is arbitrary and
theirs is the one on record. Declining a product outright was too broad for that goal.
The rules take a numeric content out and hand back
2 * (x ^ 3 - 1). That is a product, so thelayer declined it — and the remainder is exactly the shape #1018 is about.
"2 * x3 - 2".Factorize()2 * (x ^ 3 - 1)2 * (x - 1) * (x ^ 2 + x + 1)"3 * x6 - 3".Factorize()3 * (x ^ 6 - 1)"5 * x7 - 5".Factorize()5 * (x ^ 7 - 1)5 * (x - 1) * (x ^ 6 + … + 1)"y * (x3 - 1)".Factorize()y * (x ^ 3 - 1)y * (x - 1) * (x ^ 2 + x + 1)"2 * x4 - 10 * x2 + 8".Factorize()"x * y + x".Factorize()x * (1 + y)Each factor is asked separately instead of the product being handed over whole. Every factor the
rules found survives; only the ones they could not split are split.
How it was found, which is the part worth keeping
By asking of
Factorizethe property #1092 was about — that the answer multiplies back to what itfactored — and noticing a row that satisfied it and was still wrong.
2 * (x ^ 3 - 1)is perfectly equal to2 * x ^ 3 - 2. The value check says nothing. What waswrong was not the value but the stopping point, and a property test does not ask about that
unless it is told to. The new test asserts the number of factors as well as the value, for exactly
that reason.
Full suite: 8751 passed, 0 failed.
🤖 Generated with Claude Code
https://claude.ai/code/session_01Bjumi5K7fg8yx6UK1mZTQd