R08.11.01.02 · 任务小类

数值与符号计算应用

Numerical & symbolic computing apps

Solve problems in MATLAB, Mathematica or Maple to verified results.

20 条本项目编写的提案 · 分类 v1.1 · 新增基准运行 0 次。下方验证方式与部分得分规则是设计，不是执行结果。

典型应用: MATLAB · Mathematica · Maple
小类 GUI 需求标签: HY · 混合

任务提案 · 20

展开查看完整原文与建议检查方式；两种界面均保留提案英文原文。

R08.11.01.02-T01 Integrate the stiff Robertson kinetics problem in MATLAB

原始指令

Solve the Robertson chemical kinetics ODE system (rate constants 0.04, 1e4, 3e7; y0=[1,0,0]) in MATLAB to t=4e5 with ode15s, RelTol 1e-8, AbsTol 1e-12. Save output/robertson.mat with variables t_out=[1e-3 1 1e2 1e4 4e5] and Y (5x3) evaluated at those times, plus the mass-conservation error max|sum(y)-1|.

平台: mac · macOS win · Windows lin · Linux
应用: MATLAB
交互表面: term · 终端
GUI 需求 · 任务设定: CL · CLI 足够
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 2 / 5

建议验证方式

Checker loads the .mat: Y within 1e-6 relative of a reference computed with a high-accuracy Radau solver; conservation error <1e-9; variable names and shapes exact.

建议部分得分

20% file and shapes; 60% Y values (proportional); 20% conservation error

R08.11.01.02-T02 Import a messy spreadsheet range with the MATLAB Import Tool

原始指令

Use the MATLAB Import Tool on input/messy.xlsx (sheet 'raw'): import rows 5-200, columns B:E as a table with types datetime (format dd.MM.yyyy), categorical, double and double, replacing '-' and 'n/a' with missing. Save the table as T in output/clean.mat and the generated import function as output/importfile.m.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: click · 指向与点击 drag · 拖放 type · 文字与表单
工作产物: WP02 · 记录 / 表格
条件: licensed · 授权专业软件
提案难度: 2 / 5

建议验证方式

Checker loads T: 196 rows, variable types exact, values equal gold table (NaT/NaN in the same positions); importfile.m runs and reproduces T. Generated-code header from the Import Tool required. The VM has no shell or matlab -batch, and Command Window history (History.xml) is audited, so hand-typed readtable/writetable import code instead of the Import Tool is detected and fails.

建议部分得分

25% row/column range; 30% types; 30% missing handling; 15% import function

R08.11.01.02-T03 Fit a two-term exponential in MATLAB Curve Fitter excluding outliers

原始指令

Open input/decay.csv in the MATLAB Curve Fitter app. Fit exp2 (a*exp(b*x)+c*exp(d*x)), visually exclude the 3 points that are obvious detector spikes, use bisquare robust fitting, and save the session output/decay.sfit; export fit coefficients and R^2 to output/fit.mat.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: G2 · GUI 必要
交互原语: click · 指向与点击 vis · 视觉判断
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

Exclusion set in the .sfit equals the 3 gold spike indices; coefficients within 1e-3 relative of reference fit with those exclusions and bisquare; R^2 within 1e-4. The VM has no shell or matlab -batch, and Command Window history is audited, so fit()/fitoptions calls typed instead of using the Curve Fitter app are detected and fail.

建议部分得分

30% correct exclusions; 20% model and robust option; 40% coefficients; 10% export

R08.11.01.02-T04 Solve an ODE symbolically in Mathematica and save the notebook

原始指令

In Mathematica solve y''(x) + 2 y'(x) + 5 y(x) = x E^(-x) with y(0)=1, y'(0)=0 using DSolve, simplify to real form, plot on [0,10], and store the solution as ysol[x_] in output/ode.nb; write the solution in InputForm to output/solution.txt.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令 type · 文字与表单
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

wolframscript checker: FullSimplify[gold - parsed solution]==0 and both sides satisfy ODE and ICs; notebook contains evaluated DSolve and Plot cells; solution free of complex I.

建议部分得分

50% correct solution; 20% real form; 15% plot; 15% notebook saved

R08.11.01.02-T05 Evaluate a parametric definite integral in closed form in Maple

原始指令

In Maple evaluate the integral from 0 to infinity of x^2/(x^4 + a^4) dx with assumption a>0, simplify, and verify numerically at a=1.7 to 15 digits. Save the worksheet output/integral.mw and write the closed form in Maple syntax to output/answer.txt.

平台: mac · macOS win · Windows
应用: Maple
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令 type · 文字与表单
工作产物: WP12 · 答案 / 决策
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

SymPy checker parses answer.txt and verifies equality with Pi/(2*sqrt(2)*a) for 20 random a>0 to 1e-12; worksheet contains assumption and a numeric check.

建议部分得分

60% correct closed form; 20% assumption used; 20% numeric verification in worksheet

R08.11.01.02-T06 Solve heat conduction on an L-shaped domain in the PDE Modeler app

原始指令

In MATLAB PDE Modeler, draw the L-shaped domain from input/geometry.pdf (unit square minus [0.5,1]x[0.5,1]), set steady conduction k=1 with Dirichlet T=100 on the left edge, T=0 on the re-entrant edges, insulated elsewhere, mesh Hmax 0.05, solve, and save output/lshape.m (exported model) and output/result.json with T at (0.25,0.25) and max T gradient.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: drag · 拖放 geom · 精确几何 click · 指向与点击
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 4 / 5

建议验证方式

Exported .m reproduces the geometry (area 0.75, 6 edges) and BCs; checker re-solves on a fine mesh: T(0.25,0.25) within 1% and gradient magnitude within 5%. Writing the model without the app is detected by missing PDE Modeler export header.

建议部分得分

30% geometry correct; 30% boundary conditions; 25% point value; 15% gradient

R08.11.01.02-T07 Build a Manipulate explorer for a damped oscillator in Mathematica

原始指令

Create output/oscillator.nb in Mathematica with a Manipulate showing x(t) for a damped driven oscillator over t in [0,30], sliders gamma 0-2 (default 0.2), omega 0.5-3 (default 1.2) and a checkbox to overlay the undamped solution. Save the notebook with the dynamic output evaluated at defaults.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令 click · 指向与点击 vis · 视觉判断
工作产物: WP06 · 代码 / 工程
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

Checker parses the notebook: Manipulate with exactly these controls, ranges and defaults; evaluating the expression at defaults yields x(10) within 1e-6 of reference; overlay toggles a second curve.

建议部分得分

40% controls/ranges/defaults; 40% correct physics at defaults; 20% overlay works

R08.11.01.02-T08 Solve a constrained nonlinear program with fmincon and verify KKT

原始指令

Solve the problem in input/problem.pdf (5 variables, 2 nonlinear inequality constraints, 1 equality, bounds) in MATLAB with fmincon (interior-point, analytic gradients). Save output/opt.mat with xstar, fstar, lambda and a KKT residual you compute yourself.

平台: mac · macOS win · Windows lin · Linux
应用: MATLAB
交互表面: term · 终端
GUI 需求 · 任务设定: CL · CLI 足够
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

xstar within 1e-5 and fstar within 1e-7 of the global optimum (known); checker recomputes KKT residual from xstar and lambda < 1e-6; local-optimum trap from default start must be avoided.

建议部分得分

20% feasible point; 40% global optimum; 20% multipliers; 20% KKT residual

R08.11.01.02-T09 Find parameter values giving degenerate eigenvalues in Mathematica

原始指令

input/hamiltonian.m defines a 6x6 symbolic matrix H(g) for a coupled spin model. In Mathematica find all real g in [0,5] where two or more eigenvalues coincide, with exact forms where possible and 12-digit numerics otherwise. Save output/degeneracy.nb and output/g_values.txt.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP12 · 答案 / 决策
条件: licensed · 授权专业软件
提案难度: 4 / 5

建议验证方式

g_values set compared with gold (discriminant roots plus 2 symmetry-protected crossings) to 1e-10; missing or extra values fail per item.

建议部分得分

60% the 3 discriminant-root g-values (equal shares); 40% the 2 symmetry-protected crossings (equal shares); each spurious value deducts one-fifth of credit

R08.11.01.02-T10 Find all real solutions of a polynomial system with Groebner bases in Maple

原始指令

In Maple solve the 3-variable polynomial system in input/system.txt using a lexicographic Groebner basis, isolate all real solutions to 10 significant digits, and confirm the count with RootFinding. Save output/system.mw and output/solutions.csv.

平台: mac · macOS win · Windows
应用: Maple
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 4 / 5

建议验证方式

solutions.csv real solution set matched to gold (8 solutions, 2 near-coincident) within 1e-9; residuals checked by substitution < 1e-8.

建议部分得分

30% correct count; 50% solutions matched; 20% Groebner basis present in worksheet

R08.11.01.02-T11 Debug a MATLAB script that gives wrong simulation results

原始指令

input/heat1d.m simulates 1-D diffusion but its final profile is wrong. Use the MATLAB editor and debugger to find the bugs (there are three: index shift, matrix vs element-wise multiply, integer division in dt) and fix them minimally. Save the corrected file as output/heat1d.m; its output must match input/expected_profile.csv.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI term · 终端
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令 click · 指向与点击
工作产物: WP06 · 代码 / 工程
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

Checker runs the fixed script: profile within 1e-10 of expected; diff vs input touches only the 3 bug lines (+-1 line each); no hard-coded expected data.

建议部分得分

30% index-shift bug fixed; 30% matrix vs element-wise bug fixed; 30% integer-division dt bug fixed (each verified by targeted unit checks); 10% minimal diff

R08.11.01.02-T12 Design an equiripple FIR lowpass in MATLAB Filter Designer

原始指令

Open Filter Designer (filterDesigner) and design a minimum-order equiripple FIR lowpass for Fs=48 kHz, passband 0-4 kHz with 0.5 dB ripple, stopband from 5 kHz with 60 dB attenuation. Quantize to 16-bit fixed point and export coefficients to output/lp.mat; save the session output/lp.fda.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: G2 · GUI 必要
交互原语: click · 指向与点击 type · 文字与表单
工作产物: WP06 · 代码 / 工程
条件: licensed · 授权专业软件
提案难度: 4 / 5

建议验证方式

Checker computes freqz of exported quantized coefficients: passband ripple <=0.5 dB, stopband <=-60 dB; order <= minimum (firpmord) + 2; .fda session present with quantization 16-bit. The VM has no shell or matlab -batch, and Command Window history is audited, so firpm/designfilt calls typed instead of using Filter Designer are detected and fail.

建议部分得分

35% passband spec; 35% stopband spec; 15% order; 15% quantization and session

R08.11.01.02-T13 Nonlinear model fit with standard errors and AIC in Mathematica

原始指令

Load input/titration.csv in Mathematica and fit the Hill model y = b + (t-b) x^n/(K^n + x^n) with NonlinearModelFit (starting values of your choice). Save output/fit.nb and write b, t, K, n with standard errors and the AIC to output/params.json.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 2 / 5

建议验证方式

Parameters within 1e-4 relative of the reference least-squares optimum, SEs within 1%, AIC within 0.01.

建议部分得分

60% parameters; 25% SEs; 15% AIC

R08.11.01.02-T14 Solve a rod heat equation series solution with pdsolve in Maple

原始指令

In Maple solve u_t = 0.5 u_xx on 0<x<1 with u(0,t)=0, u_x(1,t)=-u(1,t) (Robin), u(x,0)=x(1-x). Obtain the series solution with pdsolve (eigenvalues from the transcendental equation), sum enough terms, and report u(0.3,0.1) to 8 significant digits in output/answer.txt. Save output/rod.mw.

平台: mac · macOS win · Windows
应用: Maple
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 4 / 5

建议验证方式

answer within 1e-8 of a reference from a converged Chebyshev spectral solve; worksheet contains pdsolve call and eigenvalue root-finding.

建议部分得分

30% correct eigenvalue equation; 20% series form; 50% value to 8 digits

R08.11.01.02-T15 Clean sensor data with MATLAB Live Editor tasks and export a report

原始指令

Create output/clean_sensor.mlx in MATLAB Live Editor that loads input/sensor.csv, uses the 'Clean Missing Data' task (linear interpolation), 'Clean Outlier Data' task (moving median, window 15, threshold 3) and 'Smooth Data' task (Gaussian, window 9) with code visible, and exports output/clean_sensor.pdf.

平台: mac · macOS win · Windows
应用: MATLAB
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: G2 · GUI 必要
交互原语: click · 指向与点击 type · 文字与表单
工作产物: WP02 · 记录 / 表格
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

Checker unzips the .mlx: three Live Task elements with the stated parameters; re-running yields cleaned vector within 1e-10 of reference; PDF export exists. Plain code without Live Tasks fails the task-element check. The VM has no shell or matlab -batch and Command Window history is audited, so an .mlx assembled by code rather than in the Live Editor is detected and fails.

建议部分得分

45% three Live Tasks with parameters (equal share each); 40% output values; 15% PDF

R08.11.01.02-T16 Derive an asymptotic expansion of an integral in Mathematica

原始指令

For F(x) = integral from 0 to infinity of exp(-x t) / (1 + t^2) dt, derive the asymptotic expansion as x -> infinity through O(x^-7) in Mathematica, verify it numerically at x=20 (error below the next term), and save output/asymptotic.nb and the series in InputForm to output/series.txt.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 5 / 5

建议验证方式

series.txt parsed and compared term by term with 1/x - 2/x^3 + 24/x^5 - 720/x^7; numeric check present showing error below 8!/x^9 at x=20.

建议部分得分

70% correct series terms (proportional); 30% numeric verification

R08.11.01.02-T17 Step response via symbolic Laplace transforms in MATLAB

原始指令

For G(s) = (s+3)/(s^3 + 4 s^2 + 6 s + 4) use MATLAB Symbolic Math Toolbox to compute the unit-step response y(t) via partial fractions and ilaplace, simplify to real form, and compare with step() on the tf object. Save output/step.mlx and y(t) as a string in output/y.txt.

平台: mac · macOS win · Windows lin · Linux
应用: MATLAB
交互表面: desk · 桌面 GUI term · 终端
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

y.txt parsed with SymPy: equal to the gold inverse Laplace at 50 time points to 1e-10; real-valued form required; .mlx shows step() comparison.

建议部分得分

25% partial fractions; 50% correct y(t); 25% numeric comparison

R08.11.01.02-T18 Check a paper's claimed identity symbolically and numerically

原始指令

Equation 7 of input/paper.pdf claims a closed form for a hypergeometric sum. In Mathematica, test the identity numerically at 20 random parameter points with 30-digit precision and attempt a symbolic proof. Write output/verdict.json {holds: bool, counterexample, corrected_form} and save output/check.nb.

平台: mac · macOS win · Windows
应用: Mathematica
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: HY · 混合
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令 multi · 跨应用
工作产物: WP12 · 答案 / 决策
条件: licensed · 授权专业软件
提案难度: 5 / 5

建议验证方式

Gold: the identity has a sign error for odd n. holds must be false; counterexample must violate the claimed form by >1e-20 when checked; corrected_form verified equal to gold at 50 points.

建议部分得分

40% correct verdict; 30% valid counterexample; 30% corrected form

R08.11.01.02-T19 Solve an optimization word problem with Maple's Optimization Assistant

原始指令

Using Maple's Optimization Assistant (Tools > Assistants), formulate and solve the canning problem in input/word_problem.pdf: minimize metal area of a closed cylindrical can with volume 500 cm^3 and height at least 1.2 times diameter. Save output/can.mw and report r, h and area in output/can.json.

平台: mac · macOS win · Windows
应用: Maple
交互表面: desk · 桌面 GUI
GUI 需求 · 任务设定: G2 · GUI 必要
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: click · 指向与点击 type · 文字与表单
工作产物: WP12 · 答案 / 决策
条件: licensed · 授权专业软件
提案难度: 3 / 5

建议验证方式

can.json values within 1e-4 of the constrained optimum (active constraint h=1.2*2r); worksheet contains the Assistant-generated Optimization command. The VM has no shell or command-line Maple (cmaple), so the worksheet must be built in the Maple GUI; .mw writes by any other process are caught by file-access auditing and fail.

建议部分得分

30% formulation (objective and constraints); 50% optimal values; 20% assistant used

R08.11.01.02-T20 Solve a million-unknown 3-D Poisson system with preconditioned CG

原始指令

In MATLAB assemble the 7-point Laplacian for a 100x100x100 grid with Dirichlet boundaries and right-hand side from input/rhs.mat, then solve with pcg using an incomplete Cholesky preconditioner to relative residual 1e-8 within 120 s wall time. Save output/poisson.mat with iterations, relres and the solution checksum sum(u.^2).

平台: mac · macOS win · Windows lin · Linux
应用: MATLAB
交互表面: term · 终端
GUI 需求 · 任务设定: CL · CLI 足够
GUI 需求 · 普通权限: CL · CLI 足够
交互原语: code · 代码与命令
工作产物: WP07 · 仿真结果
条件: licensed · 授权专业软件
提案难度: 5 / 5

建议验证方式

Checker reruns script with timing: relres<=1e-8, checksum within 1e-6 relative of reference, wall time <=120 s on the reference machine, iterations <=250 (unpreconditioned CG exceeds this).

建议部分得分

20% matrix assembly correct; 30% converged residual; 30% checksum; 20% time and iteration limits

已有研究映射

以下沿用研究目录中的基准与小类映射，不是逐题标注、执行记录或产品背书。

数值与符号计算应用

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建议部分得分

原始指令

建议验证方式

建议部分得分

已有研究映射

同工作流族的小类