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Common tasks by domain

This index is for someone who knows the problem they want to solve but does not yet know the Pascal identifier. Every entry point below is documented in the linked guide and, where one exists, demonstrated by a runnable example in examples/. The beginner recipes (RECIPES.md) provide the same route in a shorter task-first form.

If a task is not supported by a documented entry point, it is marked gap — roadmap candidate; the capability inventory (CAPABILITIES.md) and the post-2.0 capability programme in ROADMAP.md track those families.

MathBase

Task	Unit	Entry point	Runnable example
Share numeric samples across units	`MathBase.SharedTypes`	`TDoubleArray`; `ToDoubleArray(Data)`	`00_getting_started.pas`
Convert angles and compute trigonometry	`MathBase.Trigonometry`	`TTrigKit.DegToRad`, `TTrigKit.Hypotenuse`	`00_getting_started.pas`
Evaluate low-level special functions	`MathBase.Precision`	`NormalCDF(X)`, `Erf(X)`, `GammaLn(X)`	`00_getting_started.pas`
Portable complex scalar arithmetic	`MathBase.Complex`	`TComplex.Create`, `CSqrt`	`14_complex_vectors.pas`
Reproducible seeded random numbers	`MathBase.Random`	`TLocalRandom.Seeded`, `TLocalRandom.GetState`	`20_interchange_replay.pas`

AlgebraLib

Task	Unit	Entry point	Runnable example
Solve a square dense system `A*X = B`	`AlgebraLib.DenseSolvers`	`Solve(A, B)`	`15_typed_dense_solve.pas`
Fit a tall model by least squares	`AlgebraLib.DenseDecompositions`	`LeastSquares(A, B, Info)`	`16_dense_solver_selection.pas`
Compute all eigenpairs of a symmetric matrix	`AlgebraLib.DenseDecompositions`	`FactorSymmetricEigen(A)`	`16_dense_solver_selection.pas`
Solve a sparse positive-definite system with CG	`AlgebraLib.IterativeSolvers`	`TDoubleIterativeSolver.ConjugateGradient(Op, B, Options)`	`22_sparse_end_to_end.pas`
Compatibility `IMatrix` arithmetic and LU	`AlgebraLib.Matrices`	`TMatrixKit.CreateFromArray`, `Multiply`, `LU`, `Determinant`	`03_matrix_operations.pas`

FinanceLib

Task	Unit	Entry point	Runnable example
Net present value of a cash-flow series	`FinanceLib.NPV`	`TNPVKit.NetPresentValue(Investment, CashFlows, Rate)`	`04_finance_npv_irr.pas`
Internal rate of return	`FinanceLib.NPV`	`TNPVKit.InternalRateOfReturn(Investment, CashFlows)`	`04_finance_npv_irr.pas`
Periodic payment on a loan	`FinanceLib.Interest`	`TFinanceKit.Payment(PV, Rate, Periods)`	`04_finance_npv_irr.pas`
Full loan amortisation schedule	`FinanceLib.Bonds`	`TBondKit.AmortizationSchedule(Loan, Rate, Periods)`	`04_finance_npv_irr.pas`
European call or put price	`FinanceLib.Interest`	`TFinanceKit.BlackScholes(Spot, Strike, Rate, Vol, T, OptionType)`	option pricing section

StatsLib

Task	Unit	Entry point	Runnable example
Summarise a numeric sample in one call	`StatsLib.Stats`	`TStatsKit.Describe(Data)`	`01_stats_basics.pas`
Two-sample pooled t-test with p-value	`StatsLib.Stats`	`TStatsKit.TTest(X, Y, TPValue)`	`02_hypothesis_test.pas`
Seeded bootstrap confidence interval	`StatsLib.Stats`	`TStatsKit.BootstrapConfidenceInterval(Data, Alpha, Iterations, Seed)`	`01_stats_basics.pas`
Streaming mean/variance in constant memory	`StatsLib.Streaming`	`TOnlineStatistics.Create`; `Add`; `Merge`	`19_applied_data_pipeline.pas`
OLS regression with diagnostics	`StatsLib.Inference`	`TInferenceKit.FitOLS(Design, Response)`	`26_probability_finance.pas`

EngineeringLib

Task	Unit	Entry point	Runnable example
Convert a physical quantity between units	`EngineeringLib.UnitConversion`	`TUnitConversionKit.ConvertLength(Value, From, To)`	`05_unit_conversion.pas`
Classify pipe flow with Reynolds number	`EngineeringLib.FluidDynamics`	`TFluidDynamicsKit.ReynoldsNumber(...)`	`06_fluid_dynamics.pas`
Carnot efficiency of an ideal heat engine	`EngineeringLib.Thermodynamics`	`TThermodynamicsKit.CarnotEfficiency(HotK, ColdK)`	quick-start program
Windowed-sinc FIR low-pass filter	`EngineeringLib.Signal`	`TSignalKit.DesignFIRLowPass(Cutoff, Order, Window)`; `ApplyFIRFilter`	`24_sensor_pipeline.pas`
Block convolution with a finite impulse response	`EngineeringLib.DSP`	`TOverlapAddConvolver.ProcessBlock` then `Flush`	`21_release_1_8_workflows.pas`

NumericsLib

Task	Unit	Entry point	Runnable example
Find a bracketed scalar root	`NumericsLib.Numerics`	`TNumericsKit.Brent(F, A, B)` or `BrentResult`	`13_numerical_methods.pas`
Approximate a definite integral	`NumericsLib.Numerics`	`TNumericsKit.SimpsonRule(F, A, B)`	`13_numerical_methods.pas`
Integrate an initial-value scalar ODE	`NumericsLib.Numerics`	`TNumericsKit.RK4Solve(F, T0, Y0, T1, N)`	`13_numerical_methods.pas`
Interpolate knots with a cubic spline	`NumericsLib.Numerics`	`TNumericsKit.CubicSplineBuild`; `CubicSplineEval`	`13_numerical_methods.pas`
Fit a nonlinear model with diagnostics	`NumericsLib.Modelling`	`TModellingKit.FitNonlinear(@Residual, nil, Initial, Options)`	`17_numerical_modelling.pas`

ProbabilityLib

Task	Unit	Entry point	Runnable example
Upper-tail normal probability `P(X > x)`	`ProbabilityLib.Distributions`	`TProbabilityKit.NormalSurvival(X, Mu, Sigma)`	`07_probability.pas`
Two-tailed t-test p-value	`ProbabilityLib.Distributions`	`TProbabilityKit.StudentTTwoTail(X, DF)`	`07_probability.pas`
P-value from a chi-squared statistic	`ProbabilityLib.Distributions`	`TProbabilityKit.ChiSquaredSurvival(X, DF)`	`07_probability.pas`
Binomial probability `P(X <= K)`	`ProbabilityLib.Distributions`	`TProbabilityKit.BinomialCDF(K, N, P)`	`07_probability.pas`
Weibull reliability (survival)	`ProbabilityLib.Distributions`	`TProbabilityKit.WeibullSurvival(X, K, Lambda)`	`07_probability.pas`

CombinatoricsLib

Task	Unit	Entry point	Runnable example
Count unordered selections `C(n, k)`	`CombinatoricsLib.Combinatorics`	`TCombinatoricsKit.Combination(N, K)`	`08_combinatorics.pas`
Count ordered arrangements `P(n, k)`	`CombinatoricsLib.Combinatorics`	`TCombinatoricsKit.Permutation(N, K)`	`08_combinatorics.pas`
Overflow-safe large counts in log space	`CombinatoricsLib.Combinatorics`	`TCombinatoricsKit.LogFactorial(N)`, `LogCombination(N, K)`	`08_combinatorics.pas`
Enumerate permutations and combinations	`CombinatoricsLib.Combinatorics`	`TCombinatoricsKit.Permutations(Items)`, `Combinations(N, K)`, `NextPermutation`	`08_combinatorics.pas`
Modular arithmetic and primality	`CombinatoricsLib.Combinatorics`	`TCombinatoricsKit.ModPow(A, B, M)`, `ModInverse`, `IsPrime`	`08_combinatorics.pas`

OptimizationLib

Task	Unit	Entry point	Runnable example
Minimise a bounded single-variable function	`OptimizationLib.Optimization`	`TOptimizationKit.GoldenSection(F, A, B)`	`09_optimization.pas`
Minimise a smooth multivariate function	`OptimizationLib.Optimization`	`TOptimizationKit.LBFGS(F, Grad, X0)`	`09_optimization.pas`
Minimise a derivative-free function	`OptimizationLib.Optimization`	`TOptimizationKit.NelderMead(F, X0)`	`09_optimization.pas`
Solve a small linear program	`OptimizationLib.Optimization`	`TOptimizationKit.SimplexLP(C, A, B)`	`09_optimization.pas`
Solve a dense convex quadratic program	`OptimizationLib.Convex`	`TConvexOptimizationKit.SolveQuadraticProgram(Model, Options)`	`18_convex_optimization.pas`

TimeSeriesLib

Task	Unit	Entry point	Runnable example
Smooth a series with a centred moving average	`TimeSeriesLib.TimeSeries`	`TTimeSeriesKit.SimpleMovingAverage(Y, Window)`	`10_timeseries.pas`
Decompose trend/seasonal/residual	`TimeSeriesLib.TimeSeries`	`TTimeSeriesKit.Decompose(Y, Period)`	`10_timeseries.pas`
Fit ARIMA and forecast on the original scale	`TimeSeriesLib.TimeSeries`	`TTimeSeriesKit.ARIMAFit(Y, P, D, Q)`; `ARIMAForecast`	`10_timeseries.pas`
Detect z-score anomalies	`TimeSeriesLib.TimeSeries`	`TTimeSeriesKit.ZScoreAnomalies(Y, Threshold)`	`10_timeseries.pas`
Scalar Kalman filtering	`TimeSeriesLib.StateSpace`	`TScalarKalmanFilter.Create(Config, InitialState, InitialCov)`; `Process`	`19_applied_data_pipeline.pas`

MLLib

Task	Unit	Entry point	Runnable example
Fit a linear regression model	`MLLib.MachineLearning`	`TMLKit.LinearRegression(X, Y)`	`11_machinelearning.pas`
Fit a logistic-regression classifier	`MLLib.MachineLearning`	`TMLKit.LogisticRegression(TrainX, TrainY)`; `LogisticPredict`	`11_machinelearning.pas`
Reproducible train/test split	`MLLib.MachineLearning`	`TMLKit.TrainTestSplit(X, Y, Fraction, Seed, TrainX, ...)`	`11_machinelearning.pas`
Cluster data with k-means	`MLLib.MachineLearning`	`TMLKit.KMeans(X, K)`	`11_machinelearning.pas`
Reduce dimensionality with PCA	`MLLib.MachineLearning`	`TMLKit.PCA(X, NComponents)`; `PCATransform`	`11_machinelearning.pas`

GeometryLib

Task	Unit	Entry point	Runnable example
Construct a 2-D vector and read its length	`GeometryLib.Geometry`	`TVector2D.Create(AX, AY)`; `Magnitude`	`12_geometry.pas`
Distance from a point to a segment or line	`GeometryLib.Geometry`	`TGeometryKit.PointToSegment2D(P, A, B, T)`; `PointToLine2D`	`12_geometry.pas`
Test whether two segments intersect	`GeometryLib.Geometry`	`TGeometryKit.SegmentIntersect2D(A1, A2, B1, B2, Pt, T)`	`12_geometry.pas`
Polygon area, perimeter, centroid, containment	`GeometryLib.Geometry`	`TGeometryKit.PolygonArea(Poly)`, `PolygonCentroid`, `PointInPolygon`	`12_geometry.pas`
Translate, scale, or rotate a polygon	`GeometryLib.Geometry`	`TGeometryKit.Translate2D(Poly, DX, DY)`, `Scale2D`, `Rotate2D`	`12_geometry.pas`

Interchange

Task	Unit	Entry point	Runnable example
Exact binary round trip of a dense matrix	`MathBase.Interchange`	`SaveBinary(Stream, A)`; `LoadDoubleMatrixBinary(Stream)`	`20_interchange_replay.pas`
Save and replay local RNG state	`MathBase.Interchange`	`SaveRandomStateBinary(Stream, State)`; `LoadRandomStateBinary`	`20_interchange_replay.pas`
Sparse Matrix Market exchange	`MathBase.Interchange`	`WriteSparseMatrixMarket`; `ReadSparseMatrixMarketDouble`	`22_sparse_end_to_end.pas`
Persist a selected fitted/stateful model	`InterchangeLib.Models`	`SaveCubicSpline`/`LoadCubicSpline` and sibling adapters	`21_release_1_8_workflows.pas`
Evaluate a bounded mathematical expression	`MathBase.Expressions`	`TExpressionEvaluator.Evaluate(Text, Symbols, Limits)`	`21_release_1_8_workflows.pas`