TMS Analytics & Physics Pack is a Delphi library that provides an easy way to evaluate mathematical expressions, calculate symbolic derivatives and integration, solve nonlinear equations, perform approximation function calculations, and more. It contains special classes to work with analytical expressions in Delphi programs, including parsing expressions, calculating expression values with multiple parameters, performing expression-based derivatives and integration calculations, and various other analytical tasks. In addition, it offers approximation function calculation, solving differential and non‑linear equations, and allows using various physics concepts—such as physical quantities and units of measurement—in Delphi programs.

Features

• Analytical expression engine: Parse expressions, calculate expression values with multiple parameters, and perform expression-based derivatives and integration calculation.
• Physics concepts integration: Use physical quantities, units of measurement, and other physics-related constructs directly within Delphi programs.
• Approximation function calculation: Perform least-squares approximation of multidimensional data with arbitrary, user‑defined basis functions.
• Solving differential and non-linear equations: Use tools for solving initial value problems for systems of ordinary differential equations and for solving systems of nonlinear equations.
• Complex mathematical entities: Work with complex numbers, 3D vectors, tensors, indexed data, arrays, matrices, and higher‑dimensional datasets.
• Symbolic derivative calculation: Compute analytical (expression‑based) derivatives including support for conditional “if” functions (real, complex, fractions) and their derivative evaluation.
• Special functions extension: Support for calculating special functions (Bessel, Legendre) and their derivatives.
• Fractions extension: Use common fractions in math expressions, perform operations such as 1/2 + 1/3 = 5/6, and convert floating values to common fractions and vice versa.
• Numerical integration: Calculate definite integrals for one‑ and two‑dimensional functions.
• Function analysis tools: Find roots and extremums for univariate functions.
• Platform independence: Can be used in VCL and FMX applications for Windows, macOS, iOS, and Android.
• Strong class hierarchy and extensibility: Strongly structured class hierarchy, universal algorithms for working with formulae of any complexity, and easy introduction of new functions or physics concepts.
• Operator overloading: Easily overload operators for any argument types.
• Many predefined functions & entities: Includes many predefined mathematical functions, physical quantities, and units of measurement.

Benefits

• 100% Delphi code
• Strongly structured class hierarchy
• Universal algorithms for working with formulae of any complexity and for working with physics concepts
• Many predefined functions and physical entities (physical quantities, units of measurement)
• Easy to introduce new functions for any argument types and new physics concepts (physical quantities, units of measurement and so on)
• Easy to overload operators for any argument types
• Working with Complex numbers, 3D vectors and tensors
• Working with indexed data (arrays, matrixes and higher dimensioned data)
• Analytical (expression based) derivative calculation
• Conditional 'if' function (supporting real, complex and fractions), including derivative evaluation
• Special extension: allows calculation of special functions (Bessel, Legendre) and their derivatives
• Platform independent: can be used in VCL and FMX applications for Windows, macOS, iOS, Android
• Fractions extension: allows using common fractions in math expressions, including making operations like 1/2+1/3 = 5/6, converting floating values to common fractions and vice versa
• Approximation tool: least squares approximation of multidimensional data with arbitrary, user defined basis functions
• Numerical integration: calculating definite integral values for one- and two- dimensional functions
• ODE tool: solving initial value problems for the systems of ordinary differential equations
• Function analysis tool: finding roots and extremums for univariate functions
• Nonlinear tool: solving systems of nonlinear equations