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Simplify does not combine fractions over a common denominator #2137
Description
Simplify leaves a sum of fractions over one denominator apart:
| Input | Simplify |
Should be |
|---|---|---|
x/(x+y) + y/(x+y) |
unchanged | 1 provided not x + y = 0 |
1/(1 - (b/a)^2) - a^2/(a^2 - b^2) |
unchanged, also by simplifyn::8 |
0 provided … |
x/c + (y*c - x*d)/(c^2*(z + d/c)) - (x*z + y)/(c*z + d) |
unchanged | 0 provided … |
With c*(c*z + d) in place of the nested c^2*(z + d/c), the last one does reach 0.
Transformation.RationalCanonicalization proves identities of this kind, but Simplify does not reach them. A reader of Modenov's Problems in Geometry (#2131) found that most of the book's complex-number proofs are rational identities in several letters, and these shapes are where they fail.
Activity
Rafael-SOWNet commentedon Oct 27, 2026
Two more shapes from the same reading:
(1+l^3)/(1+l)^3stays unchanged. Its numerator and denominator share the factor1 + l.0. The same proofs written as polynomial determinants, in homogeneous or barycentric coordinates, reach0in about a second.Rafael-SOWNet commentedon Oct 27, 2026
The library can already prove these.
Transformation.RationalCanonicalizationis public and decides every row above. It was written for #1251.RationalCanonicalizationx/(x+y) + y/(x+y)1 provided not x + y = 01/(1 - (b/a)^2) - a^2/(a^2 - b^2)0 provided not a ^ 3 - a * b ^ 2 = 00 provided not c ^ 2 * z + c * d = 0(1+l^3)/(1+l)^3(l ^ 2 - l + 1) / (l ^ 2 + 2 * l + 1)Entity.AsSingleFraction(#1239) writes the first as(x + y) / (x + y).So the defect is that
Simplifydoes not reach the canonical form, not that the form is missing. #2146 asked fortogetherandcancel. Those areAsSingleFractionand this transformation, which already exist;AGENTS.mdrecords thatTogetherwas turned down as a name. I'm closing #2146 as a duplicate of this one.Whether
Simplifyshould try the canonical form as one of its candidates is a cost question. It probably fits 2.8 as a candidate tried only on rational expressions, measured against theSimplifybenchmarks. Making it the default canonical form is v3's.Simplify does not add a condition the input does not have (#2171)
A sum of fractions that is a constant over one denominator simplifies…