# Difference between revisions of "Numeric Quest"

## Introduction

Numeric Quest is a collection of Haskell modules written by Jan Skibinski. The modules in Numeric Quest are useful for Mathematics in general, and Quantum Mechanics in particular.

Some of the modules in Numeric Quest are hosted on haskell.org. Those are summarized below.

Other modules in Numeric Quest are currently only available via the Internet Archive. See Jan Skibinski's Haskell page via the Internet Archive for more information.

## Numeric Quest modules hosted on haskell.org

The following summaries are abstracted from the author's comments in the modules themselves.

### Rational numbers

Fraction.hs
This is a generalized Rational in disguise. Rational, as a type
synonim, could not be directly made an instance of any new class
at all.
But we would like it to be an instance of Transcendental, where
trigonometry, hyperbolics, logarithms, etc. are defined.
So here we are tiptoe-ing around, re-defining everything from
scratch, before designing the transcendental functions -- which
is the main motivation for this module.
Aside from its ability to compute transcendentals, Fraction
allows for denominators zero. Unlike Rational, Fraction does
not produce run-time errors for zero denominators, but use such
entities as indicators of invalid results -- plus or minus
infinities. Operations on fractions never fail in principle.

### Polynomials

Roots.hs
List of complex roots of a polynomial
a0 + a1*x + a2*x^2...

### General linear algebra

Eigensystem.hs
This module extends the QuantumVector module by providing functions
to calculate eigenvalues and eigenvectors of Hermitian operators.
Such toolkit is of primary importance due to pervasiveness of
eigenproblems in Quantum Mechanics.
EigensystemNum.hs

### Tensors

Tensor.lhs
This is a quick sketch of what might be a basis of a real
Tensor module.
Datatype Tensor defined here is an instance
of class Eq, Show and Num.
customized operations are defined for
variety of inner products.
Tensor components are Doubles.
The shape of tensors defined here involves two parameters:
dimension and rank. Rank is associated with the
depth of the tensor tree and corresponds to a total number
of indices by which you can access the individual components.

### Quantum mechanics

QuantumVector.lhs
This is our attempt to model the abstract Dirac's formalism
of Quantum Mechanics in Haskell.
We recognize a quantum state as an abstract vector | x >,
which can be represented in one of many possible bases -- similar
to many alternative representations of a 3D vector in rotated systems
of coordinates. A choice of a particular basis is controlled
by a generic type variable, which can be any Haskell object
-- providing that it supports a notion of equality and ordering.
A state which is composed of many quantum subsystems, not
necessarily of the same type, can be represented in a vector
space considered to be a tensor product of the subspaces.
With this abstract notion we proceed with Haskell definition of two
vector spaces: Ket and its dual Bra. We demonstrate
that both are properly defined according to the abstract
mathematical definition of vector spaces. We then introduce inner
product and show that our Bra and Ket can be indeed
considered the vector spaces with inner product.

This page contains a list of libraries and tools in a certain category. For a comprehensive list of such pages, see Applications and libraries.