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Factorize factors a polynomial in a subexpression of its variable, through the replacement the equation solver already makes - #1422
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…rough the replacement the equation solver already makes sin(x)^2 + 2 sin(x) + 1 was left as written while x^2 + 2 x + 1 is (x + 1)^2, because the polynomial layer factors with respect to a variable and sin(x) is not one. The smallest subtree that holds every occurrence of the variable -- TreeAnalyzer.GetMinimumSubtree, which is how the solver reads sin(x)^2 + sin(x) + 1 = 0 as t^2 + t + 1 = 0 -- stands in for it, the polynomial in the placeholder is factored, and the factors are read back through it: (sin(x) + 1)^2, sin(x) * (sin(x)^2 + 1), (sin(2x) - 1) * (sin(2x) + 1). Tried after the variables themselves, so nothing that factored before factors differently. Recorded in BREAKING-CHANGES.md against a v2.5.0 build. Closes #203. Part of #185. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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The one open case of #203, per the comment there: all three original cases factor on master (
1 + sqrt(2x) + x/2→(sqrt(x/2) + 1)^2,x^2 + 2x + 1→(x + 1)^2,4x^2 - 4y^2→4 (x - y)(x + y)), and what did not was a polynomial in something other than a variable —sin(x)^2 + 2 sin(x) + 1stayed as written.Now the smallest subtree that holds every occurrence of the variable (
TreeAnalyzer.GetMinimumSubtree, the replacement the equation solver already makes) stands in for it, the polynomial in the placeholder is handed to the polynomial layer, and the factors are read back through it. Tried after the variables themselves, so every answerFactorizegave is unchanged and this only adds.sin(x)^2 + 2 sin(x) + 1(sin(x) + 1) ^ 2sin(x) + sin(x)^3sin(x) * (sin(x) ^ 2 + 1)sin(2x)^2 - 1(sin(2 * x) - 1) * (sin(2 * x) + 1)ln(x)^2 - 4,cos(x)^2 - sin(x)^2Not covered: a polynomial in two subtrees (
sin(x)^2 + 2 sin(x) cos(x) + cos(x)^2), ande^x + e^(2x), whose minimal subtree isxrather thane^x.Factorizeis not on theSimplifypath, so the benchmark gate is not concerned; the factorization tests and the doc examples are green locally.Closes #203. Part of #185.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura