Defer Evaluating RootSums - #1430
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SeriesCoefficient[(a+b*x)^p, {x, 0, n}] with a symbolic index n emitted an
opaque DifferenceRoot for finite binomial powers, and returned unevaluated
for fractional exponents such as Sqrt(1+x).
Add a binomialPowerSeriesCoefficient fast-path (run after the rational path
and before the holonomic/DifferenceRoot path) that emits the closed form
Piecewise({{b^n*a^(p-n)*Binomial(p,n), cond}}, 0), with cond = 0<=n<=p for a
non-negative integer p and n>=0 otherwise. Matches Mathematica/WOXI. Guarded
to symbolic index, x0==0, nonzero constant term, and non-negative/non-integer
exponents (negative integers stay on the rational path for a cleaner form).
Add testSeriesCoefficientBinomialWoxi to SeriesTest.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Mine the Apache-licensed WOXI test suite for Symja calculus gaps, fix the
stragglers found, and add WOXI-derived JUnit tests throughout.
ZTransform/InverseZTransform: fix the n^k infinite recursion (guard the
ExpandAll branch, route pure powers through the (-z d/dz)^k operator),
combine polynomial results via Together, add a robust single-linear-pole
inverse handler covering every sign/scaling variant and symbolic poles,
and support UnitStep.
PadeApproximant: when the Series is flagged Puiseux but expands into
integer powers of x (e.g. Sqrt(1+x)), compute the approximant from the
Normal Taylor polynomial instead of returning unevaluated.
DifferenceDelta: canonicalize the generic forward difference (Factor for a
numeric step, Expand for a symbolic step), leaving symbolic-function
differences such as f(x+1)-f(x) untouched.
DiscreteShift: for integer shifts, combine rational summands over a common
denominator and expand top-level Plus results.
DiscreteRatio: support the {k, order, step} spec and reduce the ratio via
Together(FunctionExpand(...)).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
RationalIntegration.integrate() ran before the Rubi rules in the Integrate
cascade. That is form-safe for its polynomial, Horowitz-Ostrogradsky and
degree-1/2 log/arctan parts, but its RootSum branch (irreducible denominator
factors of degree >= 5) pre-empted Rubi's frequently simpler closed form and
produced RootSum antiderivatives the downstream check often cannot verify.
Add a RootSumMode {DEFER, EMIT} parameter to RationalIntegration.integrate():
- Pre-Rubi, Integrate now calls it with DEFER. When the antiderivative is
essentially a bare RootSum, DEFER returns F.NIL so Rubi gets first crack
(like the existing degree-3/4 deferral). A mixed Log(..)+RootSum(..) is a
Plus and is still emitted pre-Rubi, preserving form-safety and avoiding a
DerivativeDivides/cancelGCD ClassCastException seen when such integrands
are routed into Rubi.
- Post-Rubi, a new first stage calls it with EMIT, so a pure degree->=5
rational denominator that Rubi leaves unevaluated re-emits the identical
RootSum. Output is unchanged except where Rubi has a simpler closed form.
The 3-arg integrate() wrapper delegates with EMIT, so existing callers
(RadicalSubstitution, IntegrateAlgorithmsTest) are unaffected. Full
matheclipse-core suite green (3509 tests, 0 failures/errors).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Description
Before producing
RootSumexpressions in the Integrate tool chain, let the Rubi integration engine search fo simplerIntegratesolutions.