astronomy-physics
9
analyze-magnetic-field
使用毕奥-萨伐尔定律、安培定律和磁偶极子近似来计算和可视化电流分布产生的磁场。 适用于计算任意电流几何结构的 B 场、利用安培定律的对称性、分析多源叠加， 或通过磁导率、B-H 曲线和磁滞行为来表征磁性材料时。
pjt222
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astronomy-physics
9
solve-trigonometric-problem
系统求解三角学问题：三角方程、三角形求解（正弦定理、余弦定理）、 恒等式证明和实际应用。涵盖角度转换、周期性分析、多解处理 和结果验证。
pjt222
research
astronomy-physics
9
analyze-magnetic-field
Calculate and visualize magnetic fields produced by current distributions using the Biot-Savart law, Ampere's law, and magnetic dipole approximations. Use when computing B-fields from arbitrary current geometries, exploiting symmetry with Ampere's law, analyzing superposition of multiple sources, or characterizing magnetic materials through permeability, B-H curves, and hysteresis behavior.
pjt222
research
astronomy-physics
9
analyze-magnetic-field
Calcular y visualizar campos magnéticos producidos por distribuciones de corriente usando la ley de Biot-Savart, la ley de Ampère y aproximaciones de dipolo magnético. Usar al calcular campos B de geometrías de corriente arbitrarias, al explotar simetría con la ley de Ampère, al analizar superposición de múltiples fuentes, o al caracterizar materiales magnéticos mediante permeabilidad, curvas B-H y comportamiento de histéresis.
pjt222
research
astronomy-physics
9
formulate-maxwell-equations
積分形式と微分形式のマクスウェル方程式の完全なセットを使用して電磁場、波動、 エネルギー輸送を解析する。ガウスの法則、ファラデーの法則、またはアンペール- マクスウェルの法則を境界値問題に適用する時、電磁波動方程式を導出する時、 ポインティングベクトルと放射圧を計算する時、材料界面での場を求める時、または 静電気学と静磁気学を統一電磁気学的枠組みに接続する時に使用する。
pjt222
research
astronomy-physics
9
apply-gematria
Gematria (hebraeische Zahlenwerte) mit Standard-, Ordinal- und reduzierten Methoden berechnen und analysieren. Umfasst Wort-zu-Zahl-Umwandlung, Isopsephie-Vergleiche und interpretative Rahmenwerke. Verwenden beim Berechnen des Zahlenwerts eines hebraeischen Wortes oder Satzes, beim Vergleichen zweier Woerter auf gemeinsame Gematria-Werte, beim Studieren eines Bibelverses oder Gottesnamens auf numerische Entsprechungen oder beim Verbinden eines numerischen Ergebnisses mit seiner Position am Lebensbaum.
pjt222
research
astronomy-physics
9
construct-geometric-figure
Eine Zirkel-und-Lineal-Konstruktion einer euklidischen geometrischen Figur durchführen, indem die gewünschte Figur identifiziert, primitive Operationen (Kreisschlag, Gerade) aufgelistet, jeder Konstruktionsschritt explizit ausgeführt und das Ergebnis durch Überprüfung von Abständen, Winkeln und Kollinearität verifiziert wird.
pjt222
research
astronomy-physics
9
analyze-magnetic-field
Berechnen and visualize magnetic fields produced by current distributions using the Biot-Savart law, Ampere's law, and magnetic dipole approximations. Verwenden wenn computing B-fields from arbitrary current geometries, exploiting symmetry with Ampere's law, analyzing superposition of multiple sources, or characterizing magnetic materials durch permeability, B-H curves, and hysteresis behavior.
pjt222
research
astronomy-physics
9
prove-geometric-theorem
Geometrische Sätze formal beweisen mit euklidisch-axiomatischen Methoden, Koordinatenbeweisen und Vektorbeweisen. Verwenden zum Beweis von Kongruenz- und Ähnlichkeitssätzen, Kreiseigenschaften, Kollinearität und Konzyklität sowie zur Validierung geometrischer Konstruktionen.
pjt222
research
astronomy-physics
9
r-duckspatial
Use when code loads or uses duckspatial (library(duckspatial), duckspatial::), performing spatial joins or areal interpolation on large vector datasets in R, or needing faster spatial operations than sf
arthurgailes
research
astronomy-physics
9
solve-modular-arithmetic
Modulare Arithmetik-Probleme loesen einschliesslich Kongruenzen, Systeme ueber den Chinesischen Restsatz, modulare Inverse und Anwendungen des Satzes von Euler. Umfasst sowohl manuelle als auch rechnerische Ansaetze. Verwenden beim Loesen linearer Kongruenzen, Berechnen modularer Inverser, Auswerten grosser modularer Potenzen, Arbeiten mit simultanen Kongruenzen (CRT) oder Operieren in zyklischen Gruppen und Kontexten diskreter Logarithmen.
pjt222
research
astronomy-physics
9
geo
Geographic data validator for aviation and travel applications. Use when user says "geo audit", "check airports", "validate routes", "geo skill", "check geographic data", "verify iata codes", "check distances", or when reviewing any code/data that involves airport codes (IATA/ICAO), city-to-airport mappings, country codes (ISO 3166), flight distances, flight time estimates, flag URLs, or route feasibility. Also use for timezone validation, coordinate checks, and geopolitical accuracy (country names, disputed territories, naming conventions).
buildingopen
research
astronomy-physics
9
scientific-calculator
Expert in scientific computation. Use for complex floating-point math, orbital mechanics, and physics equations to avoid hallucination. Supports variable assignment and stateful memory.
BrianV1981
research
astronomy-physics
9
geo-infer
Geospatial Active Inference framework with 44 modules for ecological, civic, and commercial spatial analysis. Use when working with geospatial data, Active Inference, Bayesian modeling, H3 hexagonal indexing, spatial statistics, or any domain-specific geographic analysis (agriculture, health, economics, risk, climate, energy, transport, marine, forestry, water).
ActiveInferenceInstitute
research
astronomy-physics
9
geo-infer-time
Time series analysis and temporal modeling for geospatial data. Use when analyzing temporal patterns, forecasting spatial time series, detecting change points, or working with spatio-temporal datasets.
ActiveInferenceInstitute
research
astronomy-physics
9
solve-trigonometric-problem
三角関数の方程式と不等式を系統的に解き、三角形の辺と角を求める。正弦定理・ 余弦定理の適用、三角関数の恒等式の活用、一般解の導出、および実世界の 測量・ナビゲーション問題への応用を含む。
pjt222
research
astronomy-physics
9
geo-infer-space
H3 hexagonal spatial indexing and multi-backend spatial operations. Use when working with H3 cells, spatial indexing, coordinate systems, raster/vector operations, or any spatial backend dispatch (H3, SRAI, PostGIS).
ActiveInferenceInstitute
research
astronomy-physics
9
geo-infer-spm
Statistical Parametric Mapping for geospatial data. Use when performing GLM-based spatial analysis, random field theory corrections, cluster-level inference, or neuroimaging-style statistical mapping on geographic datasets.
ActiveInferenceInstitute
research
astronomy-physics
9
geo-infer-sec
Security and threat detection for geospatial systems. Use when implementing spatial access control, anomaly detection on access patterns, geospatial threat assessment, security auditing, or spatial data anonymization.
ActiveInferenceInstitute
research
astronomy-physics
9
weather-forecast
Get weather forecasts - temperature, precipitation, wind, and conditions
orthogonal-sh
research
astronomy-physics
9
geo-infer-org
Organizational modeling for geospatial entities. Use when modeling organizational structures, spatial resource allocation, inter-organizational network analysis, or institutional spatial analysis for governance.
ActiveInferenceInstitute
research
astronomy-physics
9
geo-infer-ops
Operations, monitoring, and observability for geospatial infrastructure. Use when setting up monitoring dashboards, configuring alerts, tracking system health, or managing deployment of spatial services.
ActiveInferenceInstitute
research
astronomy-physics
9
geo-infer-math
Spatial statistics, topology, and graph theory for geospatial analysis. Use when computing Moran's I, spatial autocorrelation, geodesic distances, graph connectivity, kernel density estimation, or any mathematical operation on geographic data.
ActiveInferenceInstitute
research