Two perturbation calculations in fluid mechanics using large-expression management
Journal of Symbolic Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Generating power of lazy semantics
Theoretical Computer Science - Special volume on computer algebra
Functional differentiation of computer programs
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
Quantum Mechanics on the Personal Computer
Quantum Mechanics on the Personal Computer
Functional Programming and Mathematical Objects
FPLE '95 Proceedings of the First International Symposium on Functional Programming Languages in Education
Structure and interpretation of quantum mechanics: a functional framework
Haskell '03 Proceedings of the 2003 ACM SIGPLAN workshop on Haskell
Towards an Implementation of a Computer Algebra System in a Functional Language
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
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Modern functional programming languages and lazy functional techniques are useful for describing and implementing abstract mathematical objects in quantum mechanics. Scientists can use them both for pedagogical purposes and for real, not too computationally intensive, but conceptually and algorithmically difficult applications. This article will show how to perform simple abstract computations on state vectors and will discuss the construction of lazy algorithms that enormously simplify manipulation of potentially infinite data structures or iterative processes. Lazy functional techniques can often replace the use of symbolic computer algebra packages, while also offering an interesting algorithmic complement to the manipulation of mathematical data. These techniques are more efficient than blindly used symbolic algebra and are easy to integrate with the numerical code.