dsh-complex ➗➕

Complex-number math toolbox for DeepSeek Harness (dsh). Five pure-math tools that do complex arithmetic correctly on the principal branch, so the agent never has to hand-track i² = -1 bookkeeping, Euler formulas, or polar conversions.

中文简介：dsh-complex 是 DeepSeek Harness 的复数数学工具箱插件，提供 5 个纯计算工具（复数解析、四则运算与整数幂、极坐标↔直角坐标互转、初等复函数主值、n 次方根全集），零运行时依赖、纯本地算术。适合让 Agent 直接完成「复数乘除、极坐标转换、欧拉公式、n 次方根、主值分支」等手算极易出错的计算。

Why

LLMs reliably botch complex arithmetic: (3+4i)(1-2i), exp(iπ), log(-1), √-4, the four fourth roots of 1, i^i. This plugin computes them exactly (IEEE double, output rounded to 10 decimals by default) with deterministic closed-form formulas, anchored by the Python stdlib cmath reference implementation in tests.

Tools

Tool	What it does
complex_parse	Parse "3+4i", "-2i", "1e3+2e-1j" (i or j, implicit coefficient 1 accepted) or polar "5∠53.13°" (degrees) into a full identity: rectangular/polar/exponential forms, modulus, argument (rad + deg), conjugate.
complex_calc	One operation: add, subtract, multiply, divide, conjugate, reciprocal, or integer power (De Moivre, exponent −1000..1000). Result in all three forms.
complex_convert	to_polar (any input → modulus, argument rad/deg, polar + exponential strings) and to_rect (polar input → a+bi).
complex_functions	Principal values of exp, log, sin, cos, tan, sinh, cosh, sqrt. Branch conventions are reported in the result note.
complex_roots	All n n-th roots (n = 1..64): r^(1/n)·(cos((θ+2πk)/n) + i·sin((θ+2πk)/n)), k = 0..n−1, listed from the principal root.

Every value is deterministic: computations keep raw IEEE doubles and round/snap floating-point dust only at the output boundary (10 decimal places by default, configurable via plugins.complex.roundPlaces).

Install

dsh plugin --profile web add github:TYEclipse/dsh-complex

Pin a specific version:

dsh plugin --profile web add github:TYEclipse/dsh-complex#v0.1.0

Or install through the DSH web GUI plugin browser / any dsh plugin marketplace by searching dsh-complex (topic dsh-plugin).

Requires Node ≥ 20. Zero runtime dependencies.

Usage

Parse and convert

complex_parse("3+4i")
→ 3+4i  (rectangular; |z| = 5, arg = 53.1301023542°, conjugate 3-4i)

complex_convert(input="3+4i", operation="to_polar")
→ |z| = 5, arg = 0.927295218 rad = 53.1301023542°  (5∠53.1301023542°; exponential 5·e^(i·0.927295218))

complex_convert(input="2∠270°", operation="to_rect")
→ -2i

Arithmetic

complex_calc(a="3+4i", b="1-2i", operation="multiply")   → 11-2i
complex_calc(a="3+4i", b="1-2i", operation="divide")     → -1+2i
complex_calc(a="1+i", exponent=8, operation="power")     → 16

Principal values and roots

complex_functions(input="3.141592653589793i", operation="exp")  → -1        (Euler identity)
complex_functions(input="-1", operation="log")                   → 3.1415926536i  (iπ, principal branch)
complex_functions(input="-4", operation="sqrt")                  → 2i
complex_functions(input="i", operation="sqrt")                   → 0.7071067812+0.7071067812i

complex_roots(input="1", n=4)   → 1, i, -1, -i
complex_roots(input="-8", n=3)  → 1+1.7320508076i, -2, 1-1.7320508076i

Conventions

• Input grammar: a+bi (or a-bi, bi, a, bare i; j also accepted; whitespace around the operator and the suffix is tolerated; scientific notation works; the imaginary coefficient may be omitted — 1+i is 1+1i).
• Polar input: r∠θ° with θ in degrees (the ° or deg suffix is optional; negative angles accepted; r must be ≥ 0).
• Principal branch: arg ∈ (-π, π]; log and sqrt report their branch convention in the result note.
• log(0) and division by zero return an honest valid: false with an explanation instead of guessing.

Configuration

plugins:
  complex:
    roundPlaces: 10   # decimal places for every output number (1–15)

Development

pnpm install
pnpm build
pnpm test
pnpm lint

123 tests, all anchored by an independent Python cmath oracle (/tmp/dsh-scan/anchors-complex.py — the reference implementation), plus schema-level enum rejection and recursive no-undefined (lossless-JSON) assertions on every tool result.

License

MIT