Numerical & symbolic computing apps
Solve problems in MATLAB, Mathematica or Maple to verified results.
20 project-authored proposals · taxonomy v1.1 · 0 new benchmark runs. Verifiers and partial-credit rules below are designs, not executed results.
- Typical applications
- MATLAB · Mathematica · Maple
- Class GUI-need label
HY· Hybrid
Task proposals · 20
Expand to inspect the complete original wording and proposed checks. Original proposal text remains English in both interfaces.
R08.11.01.02-T01 Integrate the stiff Robertson kinetics problem in MATLAB
Original instruction
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|.
- Platforms
mac· macOSwin· Windowslin· Linux- Applications
- MATLAB
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 2 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
click· Point & clickdrag· Drag & droptype· Text & forms- Work product
WP02· Records/table- Conditions
licensed· Licensed pro app- Proposed difficulty
- 2 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
G2· GUI-essential- Interaction primitives
click· Point & clickvis· Visual judgment- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Maple
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandstype· Text & forms- Work product
WP12· Answer/decision- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
drag· Drag & dropgeom· Precise geometryclick· Point & click- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandsclick· Point & clickvis· Visual judgment- Work product
WP06· Code/engineering- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windowslin· Linux- Applications
- MATLAB
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
20% feasible point; 40% global optimum; 20% multipliers; 20% KKT residual
R08.11.01.02-T09 Find parameter values giving degenerate eigenvalues in Mathematica
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP12· Answer/decision- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
g_values set compared with gold (discriminant roots plus 2 symmetry-protected crossings) to 1e-10; missing or extra values fail per item.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Maple
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
solutions.csv real solution set matched to gold (8 solutions, 2 near-coincident) within 1e-9; residuals checked by substitution < 1e-8.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUIterm· Terminal- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandsclick· Point & click- Work product
WP06· Code/engineering- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
G2· GUI-essential- Interaction primitives
click· Point & clicktype· Text & forms- Work product
WP06· Code/engineering- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 2 / 5
Proposed verifier
Parameters within 1e-4 relative of the reference least-squares optimum, SEs within 1%, AIC within 0.01.
Proposed partial credit
60% parameters; 25% SEs; 15% AIC
R08.11.01.02-T14 Solve a rod heat equation series solution with pdsolve in Maple
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Maple
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 4 / 5
Proposed verifier
answer within 1e-8 of a reference from a converged Chebyshev spectral solve; worksheet contains pdsolve call and eigenvalue root-finding.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- MATLAB
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
G2· GUI-essential- Interaction primitives
click· Point & clicktype· Text & forms- Work product
WP02· Records/table- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 5 / 5
Proposed verifier
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.
Proposed partial credit
70% correct series terms (proportional); 30% numeric verification
R08.11.01.02-T17 Step response via symbolic Laplace transforms in MATLAB
Original instruction
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.
- Platforms
mac· macOSwin· Windowslin· Linux- Applications
- MATLAB
- Interfaces
desk· Desktop GUIterm· Terminal- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
25% partial fractions; 50% correct y(t); 25% numeric comparison
R08.11.01.02-T18 Check a paper's claimed identity symbolically and numerically
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Mathematica
- Interfaces
desk· Desktop GUI- GUI need · task setting
HY· Hybrid- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commandsmulti· Cross-app- Work product
WP12· Answer/decision- Conditions
licensed· Licensed pro app- Proposed difficulty
- 5 / 5
Proposed verifier
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.
Proposed partial credit
40% correct verdict; 30% valid counterexample; 30% corrected form
R08.11.01.02-T19 Solve an optimization word problem with Maple's Optimization Assistant
Original instruction
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.
- Platforms
mac· macOSwin· Windows- Applications
- Maple
- Interfaces
desk· Desktop GUI- GUI need · task setting
G2· GUI-essential- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
click· Point & clicktype· Text & forms- Work product
WP12· Answer/decision- Conditions
licensed· Licensed pro app- Proposed difficulty
- 3 / 5
Proposed verifier
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.
Proposed partial credit
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
Original instruction
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).
- Platforms
mac· macOSwin· Windowslin· Linux- Applications
- MATLAB
- Interfaces
term· Terminal- GUI need · task setting
CL· CLI-sufficient- GUI need · ordinary access
CL· CLI-sufficient- Interaction primitives
code· Code & commands- Work product
WP07· Simulation result- Conditions
licensed· Licensed pro app- Proposed difficulty
- 5 / 5
Proposed verifier
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).
Proposed partial credit
20% matrix assembly correct; 30% converged residual; 30% checksum; 20% time and iteration limits
Mapped research references
Existing benchmark-to-class links from the research catalog. They are not record-level annotations, executions or product endorsements.