The names of functions to come are refused by name by Rafael-SOWNet · Pull Request #2184 · ASC-Community/AngouriMath

Rafael-SOWNet · 2026-10-28T15:30:14Z

An unknown name followed by a bracket is read as a product, so zeta(2) was zeta * 2 and simplified to 2 * zeta, with nothing said. #2182 registers the functions the library is to have, named by what a mathematician calls them. Reworked with Happypig375 there, it is reserved here in two kinds.

Functions to come, refused until each is implemented, as trunc already is:

zeta, riemannzeta, hurwitzzeta. All three are reserved, since zeta(s) must not stay a product whichever name A register of function names, by what a mathematician calls each #2182 settles on.
lambertw and Mathematica's productlog.
mobius and moebiusmu, divisorsigma, primenu, primeomega, primepi.
harmonicnumber, catalannumber, multinomial.
fallingfactorial and factorialpower, risingfactorial.
forwarddifference, laplacian, jacobian, hessian.

Names that will not be functions, refused with the spelling to use, as NN is refused with ZZ+ and ZZ*:

Name	Why	The refusal says
`heaviside`	its value at 0 is `0`, `1/2` or `1` by source	`iverson(x > 0)`, `iverson(x >= 0)` or `(1 + sgn(x))/2`
`unitstep`		`iverson(x >= 0)`
`isprime`	`n in PP` is the statement	`n in PP`
`fractionalpart`		`x mod 1`
`quotient`		`floor(a / b)`
`doublefactorial`, `factorial2`	the double factorial is to be the postfix `n!!`	that, and that it is not implemented yet
`pochhammer`	the rising factorial to some authors, the falling one to others	`risingfactorial` or `fallingfactorial`

Each name without a bracket is still a variable. Short names that could be somebody's variable before a bracket are not reserved: beta, norm, grad, div, curl. Docs/Usage/Syntax.md's "Refused by name" paragraph lists both kinds, and so does the MCP server's syntax document. The parser is regenerated.

Input	Was (2.6.0)	Now
`zeta(s)`	`zeta * s`	throws `UnrecognizedFunctionParseException`
`zeta(2)`, simplified	`2 * zeta`	throws `UnrecognizedFunctionParseException`
`isprime(7)`	`isprime * 7`	throws, with `n in PP`
`heaviside(x)`	`heaviside * x`	throws, with the three spellings
`divisorsigma(k, n)`	throws `UnhandledParseException`	throws `UnrecognizedFunctionParseException`

Measured, on the branch before its rebase onto #2186's merge, which shares only BREAKING-CHANGES.md with it, at a different entry, and none of its code:

Suite: 17,397 passed, 0 failed, 13 skipped. McpUnitTests 419 passed.
Intbench chain against master d44599f: identical on every family, 0 moves. Performance gate passed on all 19 gated benchmarks.
Harnesses: BoundCheck 1208 shapes with 0 disagreements, RootCheck 596/596, CasBench 120/121 with 0 wrong, SimpSweep 10463/10463, CrashCheck 0 crashed, PropCheck and RuleCheck clean, CanonCheck (2091) and Confluence (3) matching their baselines.

Part of #2182.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

codecov · 2026-10-28T15:33:28Z

Codecov Report

❌ Patch coverage is 95.74468% with 30 lines in your changes missing coverage. Please review.
✅ Project coverage is 86.53%. Comparing base (059513d) to head (2af815c).

Files with missing lines	Patch %	Lines
...ources/AngouriMath/Core/Antlr/AngouriMathParser.cs	95.74%	29 Missing and 1 partial ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2184      +/-   ##
==========================================
+ Coverage   86.47%   86.53%   +0.06%     
==========================================
  Files         297      297              
  Lines       65603    66096     +493     
  Branches    19227    19227              
==========================================
+ Hits        56730    57197     +467     
- Misses       4810     4836      +26     
  Partials     4063     4063

Flag	Coverage Δ
cpp	`37.77% <ø> (ø)`
csharp	`87.09% <95.74%> (+0.05%)`	⬆️
fsharp	`32.97% <ø> (ø)`
interactive	`40.72% <ø> (ø)`

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
Sources/AngouriMath/Core/Antlr/AngouriMathLexer.cs	`99.20% <ø> (+0.17%)`	⬆️
...ources/AngouriMath/Core/Antlr/AngouriMathParser.cs	`87.28% <95.74%> (+0.39%)`	⬆️

... and 6 files with indirect coverage changes

🚀 New features to boost your workflow:

❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

Rafael-SOWNet · 2026-10-28T15:43:00Z

Back to draft: the names it reserves wait for #2182's register to settle, which Happypig375 rightly found arbitrary. It will be redone from the settled table.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

An unknown name followed by a bracket is read as a product, so zeta(2) was zeta * 2 and simplified to 2 * zeta, silently. #2182 registers the functions the library is to have, named by what a mathematician calls them, and their long names are now refused until each is implemented, as trunc is: zeta, riemannzeta and hurwitzzeta, lambertw and productlog, mobius and moebiusmu, divisorsigma, primenu, primeomega, primepi, harmonicnumber, catalannumber, multinomial, fallingfactorial and factorialpower, risingfactorial, forwarddifference, laplacian, jacobian and hessian. Names that will not be functions are refused with the spelling to use, as NN is with ZZ+ and ZZ*. heaviside's value at 0 is 0, 1/2 or 1 by source, so it points to iverson(x > 0), iverson(x >= 0) and (1 + sgn(x))/2, and unitstep to iverson(x >= 0). isprime(n) is n in PP, fractionalpart(x) is x mod 1, quotient(a, b) is floor(a / b), the double factorial is to be the postfix n!!, and pochhammer is the rising factorial to some authors and the falling one to others. Each name without a bracket is still a variable, and short names such as beta and norm are still read as products. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

laplacian, jacobian and hessian were reserved by name in #2184 and are now computed when they are parsed, as det is. Each is made of derivative nodes and needs no node of its own. laplacian(f, [x, y, z]) is the sum of the second derivatives of a scalar f. jacobian(F, [x, y]) is the matrix of the first derivatives of F's components, with a row for each component and a column for each variable; a scalar F is one row. hessian(f, [x, y]) is the matrix of the second derivatives of a scalar f, the entry in row i and column j being the derivative in x_i of the derivative in x_j, as the definition writes it. The variables are a vector of distinct names written out, or a single name. A set is refused, having no order to give the columns, and so are a constant, a repeated name, and a vector or matrix as the function of a Laplacian or a Hessian. det(jacobian([r cos(t), r sin(t)], [r, t])) simplifies to r, and the Laplacian of 1/r vanishes in space. The syntax page and the MCP server's syntax document describe them, and the native smoke test evaluates two of them. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

fallingfactorial(x, n), also factorialpower(x, n), Mathematica's name, and risingfactorial(x, n) were reserved by name in #2184 and are now Entity.FallingFactorialf and Entity.RisingFactorialf, built by MathS.FallingFactorial and MathS.RisingFactorial. For a whole n >= 0 they are x (x - 1) ... (x - n + 1) and x (x + 1) ... (x + n - 1), x to the n falling and rising, computed exactly for any number x. For a negative whole n they are the reciprocals of (x + 1) ... (x - n) and (x - 1) ... (x + n), (2.52) in Graham, Knuth and Patashnik's Concrete Mathematics, with no value where a factor vanishes. For any other n they are Gamma(x + 1)/Gamma(x - n + 1) and Gamma(x + n)/Gamma(x), as Mathematica's FactorialPower and Pochhammer are, evaluated numerically: no value at a pole of the numerator, and 0 at one of the denominator. fallingfactorial(5, 1/2) agrees with mpmath to 1e-20. risingfactorial(x, n) is fallingfactorial(x + n - 1, n), and binomial(n, k) is fallingfactorial(n, k)/k!. They draw with Knuth's bars, x^{\underline{n}} and x^{\overline{n}}, and export to SymPy's ff and rf. A conjugate as the whole exponent of a power is drawn in brackets, x^{\left(\overline{n}\right)}, since x^{\overline{n}} is the rising factorial. pochhammer stays refused, (x)_n being the rising factorial to some authors and the falling one to others. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

multinomial(k_1, ..., k_m) was reserved by name in #2184. It is now (k_1 + ... + k_m)! / (k_1! ... k_m!), written so when it is parsed, as Happypig375 agreed on #2182. The factorial is the gamma function off the whole numbers, so the coefficient is symmetric in its arguments everywhere, and it has no value where an argument or their sum is a negative integer, a pole of the gamma function. multinomial(2, 3, 4) is 1260, multinomial(1/2, 1/2) is 4 / pi, and multinomial(1/2, 1/3) agrees with mpmath to 1e-25. It is not built as the product of binomial coefficients the multinomial theorem factors it into. binomial is 0 at a negative whole lower index, and that product depends on the order of the arguments there: multinomial(-3, 1) would be -2 and multinomial(1, -3) would be 0. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

catalannumber(n) was reserved by name in #2184 and is now Entity.CatalanNumberf, built by MathS.CatalanNumber. For a whole n >= 0 it is binomial(2n, n) / (n + 1), computed exactly up to n = 1000, so 1, 1, 2, 5, 14 from n = 0. Elsewhere it is 4^n Gamma(n + 1/2) / (sqrt(pi) Gamma(n + 2)), as Mathematica's CatalanNumber and SymPy's catalan are. That is -1/2 at -1, where the poles of the two gammas cancel, and 0 at every whole number below it, where the reciprocal of Gamma(n + 2) vanishes. A negative half-integer, a pole of Gamma(n + 1/2), has no value, and any other number is evaluated numerically: catalannumber(1/2) agrees with SymPy's 8/(3 pi) to 1e-25. The recurrence C(n + 1) = sum of C(i) C(n - i) holds. It prints as catalannumber(n), draws as \operatorname{C}_{n} and exports to SymPy's catalan. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

harmonicnumber(n) and harmonicnumber(n, m) were reserved by name in #2184 and are now Entity.HarmonicNumberf, built by MathS.HarmonicNumber. For a whole n >= 0 they are 1 + 1/2^m + ... + 1/n^m, summed exactly for a rational order: harmonicnumber(4) is 25/12 and harmonicnumber(4, 2) is 205/144. Elsewhere they are zeta(m) - zeta(m, n + 1), as Mathematica's HarmonicNumber is, which is evaluated numerically for a whole m >= 1 through the polygamma function: psi(n + 1) - psi(1) at m = 1, and (-1)^m / (m - 1)! (psi^(m - 1)(1) - psi^(m - 1)(n + 1)) above it. harmonicnumber(1/2) is 2 - 2 ln 2 and agrees with mpmath to 1e-25, as do H(5/2), H(-1/2) and H(1/2, 2). A negative integer n is a pole of the Hurwitz zeta function, and has no value but for a whole order m <= 0, where the harmonic number is a polynomial in n. What is not computed is left as the node. They print as harmonicnumber(n) and harmonicnumber(n, m), draw as \operatorname{H}_{n} and \operatorname{H}_{n}^{(m)}, and export to SymPy's harmonic. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

forwarddifference(f, k) was reserved by name in #2184. It is now f(k + 1) - f(k), the forward difference with a step of 1, as Mathematica's DifferenceDelta[f, k] is. It is written that way when parsed, as laplacian is, and needs no node: forwarddifference(k^2, k) simplifies to 1 + 2 k, and sum(forwarddifference(k^3, k), k, 1, 5) is 215, which is 6^3 - 1. A derivative in f is taken at k + 1, as #2189 lets it be, so the difference of derivative(k^3, k) is 6 k + 3. It is taken in a variable, and a number or a constant in that place is refused. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

lambertw(z) and lambertw(k, z), also productlog, Mathematica's name, were reserved by name in #2184 and are now Entity.LambertWf, built by MathS.LambertW: the solution w of w e^w = z on the branch k, a whole number, and the principal branch without one. The branches are those of Corless, Gonnet, Hare, Jeffrey and Knuth (1996), as Mathematica's ProductLog and mpmath's lambertw have them: W_0 is real on [-1/e, +oo) and W_(-1) on [-1/e, 0), both are -1 at -1/e, and a value on a cut is the one approached from above. It is exact at 0, which is 0 on the principal branch and -oo off it as ln 0 is, and where z is c e^c for a real number c the branch takes: lambertw(e) is 1, lambertw(-1/e) is -1 and lambertw(-1, -2 e^(-2)) is -2. Elsewhere it is evaluated at the working precision, in Number.LambertW. The branch is found in double precision: from the series in p = sqrt(2 (e z + 1)) about the branch point, from ln(1 + z) on the principal branch short of |z| = 3, and from ln z + 2 pi i k - ln(ln z + 2 pi i k) otherwise, each taken to a root by Halley's iteration. That root is refined by the same iteration on decimal pairs at the working precision, which triples the digits with each step and does not leave the branch. Near the branch point, where double precision cannot resolve z + 1/e, the series is evaluated at the working precision instead. Forty-five points on branches -2 to 2, and 700 random ones on -3 to 3 on and about the cuts, agree with mpmath to 1e-25. Its derivative is e^(-W(z)) / (1 + W(z)), which is 1 at 0 where W(z) / (z (1 + W(z))) is 0/0. It prints as lambertw(z) and lambertw(k, z), draws as \operatorname{W}_{k}, and exports to SymPy's LambertW. Part of #2182. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura

github-project-automation Bot added this to AngouriMath Oct 28, 2026

github-project-automation Bot moved this to Todo in AngouriMath Oct 28, 2026

Rafael-SOWNet moved this from Todo to In review in AngouriMath Oct 28, 2026

Rafael-SOWNet marked this pull request as draft October 28, 2026 15:40

Rafael-SOWNet mentioned this pull request Oct 28, 2026

A register of function names, by what a mathematician calls each #2182

Open

Rafael-SOWNet force-pushed the the-names-of-functions-to-come-are-refused branch from 97243eb to 2af815c Compare October 28, 2026 18:14

Rafael-SOWNet marked this pull request as ready for review October 28, 2026 18:14

Rafael-SOWNet merged commit 3dbb55b into master Oct 28, 2026
36 checks passed

github-project-automation Bot moved this from In review to Done in AngouriMath Oct 28, 2026

Rafael-SOWNet deleted the the-names-of-functions-to-come-are-refused branch October 28, 2026 19:21

This was referenced Oct 28, 2026

The double factorial is the postfix n!! #2187

Merged

The Möbius, divisor and prime-counting functions #2188

Merged

The Laplacian, the Jacobian and the Hessian #2190

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The falling and the rising factorial #2194

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The multinomial coefficient #2197

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The Catalan numbers #2198

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The harmonic numbers #2200

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The forward difference #2201

Merged

Rafael-SOWNet mentioned this pull request Oct 29, 2026

The Lambert W function #2202

Merged

Navigation Menu

Repository navigation

The names of functions to come are refused by name - #2184

The names of functions to come are refused by name#2184
Rafael-SOWNet merged 1 commit into
masterfrom
the-names-of-functions-to-come-are-refused

Rafael-SOWNet commented Oct 28, 2026 •

edited

Loading

Uh oh!

codecov Bot commented Oct 28, 2026 •

edited

Loading

Uh oh!

Rafael-SOWNet commented Oct 28, 2026

Uh oh!

Uh oh!

Reviewers

Uh oh!

Assignees

Labels

Projects

Milestone

Development

Uh oh!

1 participant

Conversation

Rafael-SOWNet commented Oct 28, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

codecov Bot commented Oct 28, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Codecov Report

Uh oh!

Rafael-SOWNet commented Oct 28, 2026

Uh oh!

Uh oh!

Reviewers

Uh oh!

Assignees

Labels

Projects

Milestone

Development

Uh oh!

1 participant

Rafael-SOWNet commented Oct 28, 2026 •

edited

Loading

codecov Bot commented Oct 28, 2026 •

edited

Loading