New in 10.0: Symbolic & Numeric Computation

Geometric Computation »

Geometric computation framework for modeling and computing with geometric regions.

Plane Geometry »

SSSTriangle  ▪  ArcLength  ▪  Area  ▪  ...

Solid Geometry »

Tetrahedron  ▪  Volume  ▪  RegionMember  ▪  ...

Properties and Measures »

RegionNearest find the nearest point in a region

RegionMeasure  ▪  RegionCentroid  ▪  RegionDistance  ▪  ...

Solvers over Regions »

Integrate, NIntegrate integrate over regions

NDSolve solve partial differential equations over regions

Solve  ▪  NSolve  ▪  Minimize  ▪  NMinimize  ▪  ...

Special Regions »

Ball a ball given by center and radius

Simplex  ▪  Hexahedron  ▪  InfiniteLine  ▪  ...

Formula Regions

ImplicitRegion a region given by combinations of inequalities and equalities

ParametricRegion a region given by parametric functions

Mesh Regions »

MeshRegion a region specified by a collection of mesh cells

BoundaryMeshRegion a region boundary specified by a collection of mesh cells

HighlightMesh  ▪  MeshCellStyle  ▪  MeshCellLabel  ▪  ...

Data Regions »

DelaunayMesh a Delaunay triangulation mesh constructed from points

VoronoiMesh  ▪  ConvexHullMesh  ▪  ...

Region Converters »

DiscretizeGraphics, BoundaryDiscretizeGraphics discretize 2D or 3D graphics

DiscretizeRegion, BoundaryDiscretizeRegion discretize a region

Derived Regions »

RegionUnion the union of regions

TransformedRegion a region as the image of a transformation

RegionIntersection  ▪  BooleanRegion  ▪  RegionBoundary  ▪  ...

Inactive Operators

Inactive new inactive operator for working with formal operations

Inactivate inactivate parts of expressions

Activate  ▪  IgnoringInactive

Enhanced Calculus

DSolveValue, RSolveValue new functions that can directly return functions of solutions

DSolve now solves delay differential and hybrid differential equations

Sum new algorithms for functional telescoping, multiple sums, and special functions

Product new algorithms for functional telescoping

DifferenceDelta new results for differences of special functions

DiscreteRatio new results for ratios of special functions

Enhanced Algebraic Computation

NSolve new homotopy-based algorithm for fast solution of polynomial systems

Reduce, Solve, FindInstance new fast solving over the reals

Function Properties

FunctionPeriod find the period of functions over the reals, integers, and complexes

FunctionDomain find the domain of a function

FunctionRange find the range of a function

Vector Analysis

ArcLength length

ArcCurvature curvature

FrenetSerretSystem generalized curvatures and associated basis

Linear Algebra »

PositiveSemidefiniteMatrixQ new and improved matrix predicates

NormalMatrixQ  ▪  OrthogonalMatrixQ  ▪  SquareMatrixQ  ▪  ...

New Special Functions

LogisticSigmoid the logistic function

CantorStaircase the Cantor ternary function

MinkowskiQuestionMark  ▪  ScorerHi  ▪  ScorerGi  ▪  FresnelF  ▪  FresnelG  ▪  RiemannXi  ▪  DirichletBeta  ▪  DirichletEta  ▪  DirichletLambda  ▪  Fibonorial  ▪  AlternatingFactorial  ▪  FareySequence

Nonlinear Control Systems »

AffineStateSpaceModel affine model and

FeedbackLinearize linearization through nonlinear feedback and state transformation

AsymptoticOutputTracker tracker with state feedback

NonlinearStateSpaceModel  ▪  FullInformationOutputRegulator  ▪  ...

Probability & Statistics

AutocorrelationTest test for autocorrelation in data

Time Series Processes »

TimeSeriesModelFit automatic fitting, diagnostics, and forecasting for time series

ARCHProcess, GARCHProcess new classes of time series processes

ARProcess, ARMAProcess full support for vector processes

MAProcess  ▪  SARMAProcess  ▪  FARIMAProcess

Markov Processes

HiddenMarkovProcess hidden Markov process with discrete or continuous emissions

FindHiddenMarkovStates hidden state decoding (Viterbi decoding etc.)

Parametric Processes »

TransformedProcess transformations of random processes

WhiteNoiseProcess new and improved capabilities for parametric processes

PoissonProcess  ▪  WienerProcess  ▪  GeometricBrownianMotionProcess  ▪  ...