UPSTREAM.md

What belongs in AngouriMath, not here

Archived. The server is part of AngouriMath now, and what this file asked of the library is filed there: #1673, #1674, #1675 and #1676.

This server is an adapter. Anything that is a genuine computer-algebra feature belongs in the library, where AngouriMathCLI, AngouriMath.Terminal and the Jupyter integration get it too. This file records where the line was drawn, so the adapter does not quietly grow a second, worse copy of the library.

Deliberately NOT built here

A LaTeX input parser. AngouriMath emits LaTeX via Latexize() and cannot read it back. That asymmetry is a library gap, and a parser is a grammar change — it belongs next to the existing ANTLR grammar, not in a regex shim here. It is the most likely first-contact failure for an LLM caller, since models emit LaTeX constantly, so it is worth requesting upstream.

A C / C99 code emitter. MathS.ToSympyCode already establishes the pattern and the place (Functions/Output/). A C emitter is the same category of feature and would serve the embedded use case — derive a Jacobian symbolically, emit it as code. Writing it here would duplicate a facility the library has a slot for.

Built here as a workaround — should move upstream

Eigenvalues. am_eigenvalues computes det(A - lambda*I) and hands it to the solver. That is a general Matrix.Eigenvalues feature, not an agent concern. GenericTensor has no eigen support and, since there is no closed form beyond 4x4 (Abel-Ruffini), the characteristic-polynomial route is the correct design for a symbolic library rather than a compromise. It only lives here because the library does not offer it.

Tolerance-based numeric equality. MathS.UnsafeAndInternal.AreEqualNumerically compares with != and no tolerance, so any transcendental computed two mathematically equivalent ways disagrees in the last digit. A correct antiderivative of x*ln(x) fails it. Numeric.cs reimplements the comparison with a relative tolerance over positive sample points; the library should offer this itself.

Division-free determinant for symbolic entries. Entity.Matrix.Determinant calls DeterminantGaussianSafeDivision, which divides by pivots and leaves a provided guard per pivot. Those guards are wrong as mathematics: det([[a,b],[c,d]]) is a*d - b*c for every a, and [[0,J],[J,0]] has eigenvalues +/-J including at J = 0. GenericTensor already ships DeterminantLaplace, which is division-free and emits none of them. Selecting it when the entries are non-numeric is a small upstream change; this server strips the guards and reports them under dropped_guards in the meantime.

Defects worth reporting upstream

Re-verified against AngouriMath 2.5.0 — a claim measured on an older build is not worth reporting. --selftest re-checks each row on every run; three entries were dropped at the 2.0.0 upgrade because the release fixed them, which is the whole reason that check exists.

Two were dropped at 2.5.0, measured against the published 2.5.0 package rather than the sibling checkout: the integral of x^4*(1-x)^4/(1+x^2) and the determinant's pivot guards, both under "Fixed upstream" below. Nothing was dropped at 2.1.0. All identities hold, the integral is now one of them, and the four rows below still reproduce.

Observed	Note
Simplify(sqrt(x^2)) is left as written, not reduced to abs(x)	No longer the soundness bug it was — 2.0.0 stopped answering x, which was wrong for every negative. What remains is a gap: writing abs needs to know the expression is real, which the codomain of #719 can now say and the simplifier does not yet read.
MathS.Equations(...) throws on an equality	It wants each equation in = 0 form; passing an Equalsf raises NotSufficientlySupportedException rather than normalising a = b to a - b, which is a rewrite it could do itself. This server does it instead. Re-checked on 2.0.0 by --selftest; the exception type changed with the release, the behaviour did not.
Entity.DefiniteIntegral is a first-order rule	New in 2.0.0, and it is a rectangle rule: the error halves per doubling of the step count, so 4000 steps buy about four digits of ∫[0,1] e^(x^2) at ~150 ms. Simpson's rule is the same amount of code and would give roughly eight. It also samples both endpoints, so a convergent integral with a singular endpoint — ∫[0,1] sin(x)/x, ∫[0,1] ln(x) — returns NaN rather than a value. Both are worth raising; this server runs it twice and reports only the agreed digits in the meantime.
An unknown identifier still becomes implicit multiplication silently	2.0.0 closed most of this: exp, log10, log2, pow, floor, ceil, round, min, max and gcd became real functions, and eleven names the library does not have are now refused by name. The general case remains — im(z) is im * z — and cannot be closed without refusing a(b + c), so a warning or a strict default is still the only answer. This server warns.

Fixed upstream, kept here as a record

Each of these was on the list above and reproduced no longer at an upgrade. Listed so that nobody re-reports them, and so the cost of not re-measuring is visible.

• Integrate declining x^4*(1-x)^4/(1+x^2) (at 2.5.0). It divides the rational function out itself now, and the integral over [0, 1] is exactly 22/7 - pi, which --selftest checks as an identity.

• The determinant's pivot guards (at 2.5.0). det([[a,b],[c,d]]) was a*d - b*c provided not a = 0; it is a*d - b*c.

• Factorize(x^2 - 1) emitting sqrt(1). Dropped before 2.0.0: true of 1.4.0, false of the branch, and it went stale unnoticed. This is why --selftest exists.

• exp(x) parsing as exp * x. exp is the exponential as of 2.0.0.

• e^(pi*sqrt(163)) accurate to only ~23 significant digits. Ramanujan's constant now evaluates to 262537412640768743.999999999999250072597..., correct to 60 digits and on the right side of the integer, so the near-miss the number is famous for reproduces.

• Simplify leaving a multivariate rational function uncancelled. (x^2+2xy+y^2)/(x^2-y^2) now reduces to (x + y)/(x - y) provided not x + y = 0.

• Limits needing factorial asymptotics. lim x→∞ (x!/x^x)^(1/x) is 1/e, by Stirling.

Correctly belongs here

Adapter concerns, which a library should not carry:

• Parse echoing and the implicit-power / unknown-function warnings — presentation for a caller that cannot see the tree.
• The status taxonomy (solved / unchanged / declined / suspect / timeout) and decline detection before simplification.
• Per-call cancellation and the 64 MB-stack worker. The library correctly offers the cancellation token; deciding a budget and surviving a stack overflow is the host's job.
• The NaN screen, and verifying integrals by differentiating them back.
• am_check_steps, am_domain_check, am_classify — agent-facing framing, not algebra.
• The angourimath:// resources.