'math' 검색 결과

Decode a 401k or workplace retirement plan — the real cost of its funds, the match's fine print, vesting math, and the plan features worth using or avoiding. Use when someone asks 'is my 401k any good', 'decode my 401k plan', 'which funds should I look at', or 'what fees am I paying'. Produces a fee decode in dollars-over-time, match and vesting math, a fund-lineup triage by cost, and the questions for HR or the plan administrator.

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Trigger when: (1) User mentions "manim" or "Manim Community" or "ManimCE", (2) Code contains `from manim import *`, (3) User runs `manim` CLI commands, (4) Working with Scene, MathTex, Create(), or ManimCE-specific classes. Best practices for Manim Community Edition - the community-maintained Python animation engine. Covers Scene structure, animations, LaTeX/MathTex, 3D with ThreeDScene, camera control, styling, and CLI usage. NOT for ManimGL/3b1b version (which uses `manimlib` imports and `manimgl` CLI).

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Generate correct MATLAB code using the Symbolic Math Toolbox. Use when the user asks for symbolic computations, analytical solutions, symbolic differentiation/integration, equation solving, or converting symbolic results to numeric MATLAB functions. Also use when converting differential equations to transfer functions or state-space form, extracting PDE coefficients (pdeCoefficients), symbolic-to-C code generation (matlabFunction + codegen), symbolic matrix variables (symmatrix), physical units and constants (symunit, newUnit), or rewriting/combining algebraic expressions (rewrite, combine).

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Deploy AI models to embedded hardware using MathWorks tools (MATLAB, Simulink, Embedded Coder). Covers two workflow patterns: (1) MathWorks-native or imported models rebuilt as dlnetwork for lean hardware, (2) direct C/C++ code generation from PyTorch and LiteRT models. Both patterns support all targets (Cortex-M/A/R, x86, GPU). Trigger when: user wants to deploy AI to embedded targets; generate C/CUDA from neural networks; compress AI models for MCU; integrate AI in Simulink for system-level simulation; import PyTorch/ONNX/TensorFlow models for embedded deployment; optimize AI for resource-constrained hardware; or use loadPyTorchExportedProgram, loadLiteRTModel, importNetworkFromPyTorch, importNetworkFromONNX, importNetworkFromTensorFlow, importNetworkFromKeras, dlquantizer, exportNetworkToSimulink, or Embedded Coder with AI models.

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Classify each parsed mathematical-modeling subquestion by required output and structure, surface ambiguous framing trade-offs for human choice, and record primary/secondary task types without selecting algorithms.

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Manage and verify references for mathematical modeling contest papers, generating BibTeX entries, checking citation completeness, and ensuring all references are traceable to actual sources.

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Polish mathematical modeling paper drafts for grammar, clarity, formula consistency, hedging calibration, overclaim detection, and contest formatting compliance. Use after paper-section-writer has drafted sections.

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Design and run risk-targeted robustness, sensitivity, error, and baseline checks for an approved mathematical model, emitting compact machine evidence in lean mode and a final report in submission mode.

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Inspect a mathematical-modeling workspace, evaluate lean or submission gates per subquestion, update machine-readable manifests, classify change impact, and route one next action without duplicating downstream work.

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Package a G6-approved mathematical-modeling paper and its exact supporting code, data, results, and figures without changing their behavior or the workspace.

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Build and maintain one global mathematical symbol and unit table from the problem frame and active method cards, resolving cross-subquestion conflicts before code or paper work.

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Build one compact choice card at a genuine mathematical-modeling judgment point. Use before method screening, after a meaningful experiment, or before final claim/freeze approval so the human chooses the trade-off while AI handles mechanical consequences.

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Parse a mathematical-modeling problem into goals, objects, data, constraints, outputs, subquestions, dependencies, variables, relationships, and human-confirmed success criteria before any method selection.

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Build and risk-screen a compact role-based method shortlist for a mathematical-modeling subquestion. Use after problem framing and data profiling, before model code generation, to propose a main candidate, a usable baseline, and at most one conditional fallback without padding the pool.

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Perform the final submission-level audit of mathematical-modeling workflow integrity, evidence quality, anti-fabrication, paper coherence, figures, references, and contest readiness after consistency and completeness audits pass.

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Extract and maintain global and method-specific mathematical-model assumptions from the problem frame, active method cards, data profile, and risk probes, while leaving necessity and impact judgments to the human modeler.

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Run scoped or final cross-media consistency checks for mathematical-modeling artifacts, comparing canonical numbers, symbols, parameters, decisions, files, and paper claims without performing full-workspace audits for low-risk changes.

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Plan the smallest set of diagnostic, comparison, paper, and appendix figures or tables needed to support verified mathematical-modeling decisions and claims.

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Draft submission-ready mathematical-modeling paper sections from the approved solution package, frozen numbers, human decision ledger, and verified figures without searching scattered exploratory outputs or inventing interpretation.

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When you want to model personal financial scenarios — house purchase + rental income (ADU, bedroom rentals, house-hacking), renovation budgets, monthly cash flow, big-purchase decisions, savings/investment what-ifs for a household. Ships with a house scenario template; other scenarios (refi, car, education, retirement, side income) slot in as templates. Outputs markdown scenario comparison tables. Saves scenarios to ~/Documents/personal-cfo/ with an index in ~/.config/makerskills/personal-cfo/archive/. Composes with decide, deep-research (rental comps, rates), business-brainstorm, second-brain. Triggers on "/personal-cfo," "model this scenario," "house math," "rental forecast," "monthly cash flow," "what if I rent out the ADU," "compare these housing scenarios," "should we buy this house," "house-hack math," "renovation budget."

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Use when implementing game math — vectors, transforms, interpolation, curves, random number generation, and common geometric recipes

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Use when a price has to be set or changed — value-based pricing, anchoring, charm pricing, decoy tiers, good-better-best packaging, discount policy, and margin math, with currency psychology for US, EU, SEA, and LATAM plus dropshipping markup and BE-ROAS. Trigger on 'pricing strategy', 'how much should I charge', 'should I raise prices', 'price tiers', 'customers say it is too expensive', 'dropshipping markup'. Also use when the product is not selling and the user suspects price is the reason. Not for — bonuses, guarantee, and value stack around the price, see `31-offer-design-global`; persuasion beyond price, see `16-marketing-psychology-global`; ad budget math, see `10-reverse-kpi-global`.

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使用 GLM 库实现 Vector3TransformNormal 和 Vector3TransformCoord 函数，模拟 DirectXMath 的行为，并使用 const T& 模板参数以支持多种向量类型。

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Develops mathematical understanding through examples, visualization, and analogy

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