[tranleduy2000]

The bug

Two Factor calls with the same argument on one EvalEngine give different answers, and so does a
Factor after a Simplify of the same expression:

{Factor(6/(2-x)), Factor(6/(2-x))}                    {-6/(-2+x),6/(2-x)}
{Factor((-a+b)^3), Factor((-a+b)^3)}                  {-(a-b)^3,(-a+b)^3}
{Simplify(Cos(y)^2/(2-x)), Factor(Cos(y)^2/(2-x))}    {Cos(y)^2/(2-x),Cos(y)^2/(2-x)}
{Simplify(6/(2-x)+Cos(y)), Factor(6/(2-x)+Cos(y))}    {-6/(-2+x)+Cos(y),6/(2-x)+Cos(y)}

Factor(e) alone gives -6/(-2+x), -(a-b)^3, -Cos(y)^2/(-2+x) and
(-6-2*Cos(y)+x*Cos(y))/(-2+x). The engine cache under the key Factor(e) holds something else
than what Factor(e) returns:

• AlgebraUtil.factor(IAST ast, ...) puts its result into the cache before Factor.evaluate
  applies factorSigns to it (0d84662), so a cache hit returns the form before factorSigns.
• AlgebraUtil.factor(IExpr, EvalEngine) (withHomogenization=false, called by
  TrigSimplifyFu.tr0, which Simplify and FullSimplify run) and togetherPlus (trig=true)
  pass F.Factor(e) as that ast, and so write the same key with results computed with other
  settings. After Simplify(6/(2-x)+Cos(y)) the entry is F.NIL, and Factor returns its
  argument.

More inputs and the history are in #1570.

The fix

Factor.evaluate caches the result it returns, after factorSigns, and
AlgebraUtil.factor(IAST ast, ...) writes nothing to the cache. Factor.evaluate is the only
reader of that cache, so the other callers lose nothing. A first call returns what it returned
before; only cache hits change. With the Factor.evaluate change alone, a Factor after
TrigSimplifyFu, Simplify or FullSimplify still returns the result they cached.

Tests

AlgebraTest#testFactorIssue1570 checks the first two inputs above, the equation
Factor((x+2)/(x-5)+3==6/(2-x)) twice, and Factor(e) after TrigSimplifyFu(e), Simplify(e) and
FullSimplify(e) for four inputs.

	With fix	Without fix
AlgebraTest#testFactorIssue1570	pass	expected: <{-6/(-2+x),-6/(-2+x)}> but was: <{-6/(-2+x),6/(2-x)}> at the first check
the other 7769 tests of the fast tier	7767 pass, 2 skipped	7767 pass, 2 skipped

The fast tier is mvn test -pl matheclipse-core -am; compared test by test, none of the other 7769
changed its result. Verified on 9a50f18, against a build with the fix and a build without it.

Fixes #1570

🤖 Generated with Claude Code