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kmath/docs/expressions.md
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Expressions

Expressions is a feature, which allows constructing lazily or immediately calculated parametric mathematical expressions.

The potential use-cases for it (so far) are following:

  • lazy evaluation (in general simple lambda is better, but there are some border cases);
  • automatic differentiation in single-dimension and in multiple dimensions;
  • generation of mathematical syntax trees with subsequent code generation for other languages;
  • symbolic computations, especially differentiation (and some other actions with kmath-symja integration with Symja's IExpr—integration, simplification, and more);
  • visualization with kmath-jupyter.

The workhorse of this API is Expression interface, which exposes single operator fun invoke(arguments: Map<Symbol, T>): T method. ExpressionAlgebra is used to generate expressions and introduce variables.

Currently there are two implementations:

  • Generic ExpressionField in kmath-core which allows construction of custom lazy expressions

  • Auto-differentiation expression in kmath-commons module allows using full power of DerivativeStructure from commons-math. TODO: add example