polynomial Namespace Reference

Classes
class	DifferentialOperator
class	DifferentialOperatorTwo
class	Polynomial
class	PolynomialSum
class	RecursionRelation
class	RecursionRelationTwo

Functions
bool	operator< (const TwoPolynomial &left, const TwoPolynomial &right)
bool	operator== (const TwoPolynomial &left, const TwoPolynomial &right)

Detailed Description

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DifferentialOperator describes a differential operator in terms of
polynomial coefficients.

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Class category: AbsBeamline
Author: Martin Duy Tat

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A differential operator is a linear sum of operators in the form

\[p(x)\frac{\partial^n}{\partial x^n}\frac{\partial^m}{\partial s^m}\]

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and the polynomials p(x) are stored in a n by m list.

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DifferentialOperatorTwo describes a differential operator in terms of
polynomial coefficients. The polynomials have two variables x and S(s).

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Class category: AbsBeamline
Author: Martin Duy Tat

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A differential operator is a linear sum of operators in the form

\[p(x, S(s))\frac{\partial^n}{\partial x^n} \frac{\partial^m}{\partial s^m}\]

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and the polynomials p(x, S(s)) are stored in a n by m list.

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Polynomial describes a polynomial of one variable.

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Class category: AbsBeamline
Author: Martin Duy Tat

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The polynomial

\[p(x) = a_0 + a_1x + ... + a_nx^n \]

is stored as a
list (a_0, a_1, ..., a_n).
BUG: For large n the integer type might overflow. If you need this many
terms change all int to long int.

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PolynomialSum describes a sum of TwoPolynomial objects.

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Class category: AbsBeamline
Author: Martin Duy Tat

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The polynomial of two variables

\[p(x) = a_{00} + a_{10}x + a_{11}xS(s) + ... + a_{nm}x^nS(s)^m \]

cannot be summed with other polynomials
unless all the powers of S(s)-derivatives are identical.
Instead all terms are just stored seperately in a list.

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RecursionRelation describes the differential operator used to find the
coefficients in the expansion of the magnetic scalar potential
It contains member functions for extracting all information required to
reconstruct the differential operator and evaluate its terms.

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Class category: AbsBeamline
Author: Martin Duy Tat

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The operator of interest is

\begin{eqnarray*} { \Big(\frac{1}{\rho(1 &+& x/\rho)}\frac{\partial}{\partial x} + \frac{\partial^2}{\partial x^2} &+& \frac{1}{(1 + x/\rho)^2}\frac{\partial^2}{\partial s^2}\Big)^n \end{eqnarray*}

and it can be initialised to any power of x and up to any n.

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RecursionRelationTwo describes the differential operator used to find
the coefficients in the expansion of the magnetic scalar potential. It
contains member functions for extracting all information required to
reconstruct the differential operator and evaluate its terms.

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Class category: AbsBeamline
Author: Martin Duy Tat

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The operator of interest is

\begin{eqnarray*} { \Big(\frac{1}{\rho(s)(1 &+& x/\rho(s))}\frac{\partial}{\partial x} + \frac{\partial^2}{\partial x^2} &+& \frac{1}{1 + x/\rho(s)}\frac{\partial}{\partial s}\Big(\frac{1}{1 + x/\rho(s)}\frac{\partial}{\partial s}\Big)\Big)^n \end{eqnarray*}

and it can be initialised to any power of x and up to any n.

Function Documentation

operator<()

bool polynomial::operator<	(	const TwoPolynomial &	left,
		const TwoPolynomial &	right )

Definition at line 375 of file TwoPolynomial.cpp.

operator==()

bool polynomial::operator==	(	const TwoPolynomial &	left,
		const TwoPolynomial &	right )

Definition at line 396 of file TwoPolynomial.cpp.