Multiply-Connected Conformal Mapping to a Normalized Slit-Like Canonical Domain¶
- Task ID:
math.multiply_connected_conformal_mapping - Domain:
math - Subdomain:
computational_complex_analysis - Status:
test - Tags:
conformal_mapping,multiply_connected_domains,slit_domain,slit_like_obstacles,boundary_integral_equations,complex_analysis,nystrom,canonical_domain
Public Summary¶
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Example B1 Prompt Excerpt¶
You are given a smooth multiply-connected planar domain with one outer boundary and three interior obstacles. The input provides Fourier boundary data, dense source-boundary samples, and interior probe points.
Your goal is to compute a normalized conformal map from the source domain to a **slit-like canonical domain**:
- the outer boundary maps to the unit circle,
- each interior component maps to a thin oriented slit-like obstacle from a fixed template family,
- the component order must be preserved,
- the normalization rules encoded in `data/file_00.json` must remove the remaining gauge freedom.
This task is designed to test whether you can recover a single holomorphic map that explains both the boundary traces and the interior probes, not just produce a visually plausible boundary fit.
## Input
Notes¶
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