Algebraic Structures

Various algebraic structures. More...

Classes
class	regina::AbelianGroup
	Represents a finitely generated abelian group. More...
struct	regina::GroupExpressionTerm
	Represents a power of a generator in a group presentation. More...
class	regina::GroupExpression
	Represents an expression involving generators from a group presentation or a free group. More...
class	regina::GroupPresentation
	Represents a finite presentation of a group. More...
class	regina::HomGroupPresentation
	Represents a homomorphism between groups which are described via finite presentations. More...
class	regina::IntersectionForm
	Represents a symmetric bilinear integral form, which for Regina is typically the intersection form of a 4-manifold. More...
class	regina::MarkedAbelianGroup
	Represents a finitely generated abelian group given by a chain complex. More...
class	regina::HomMarkedAbelianGroup
	Represents a homomorphism of finitely generated abelian groups. More...

Functions
void	regina::swap (AbelianGroup &lhs, AbelianGroup &rhs) noexcept
	Swaps the contents of the two given abelian groups. More...
std::ostream &	regina::operator<< (std::ostream &out, const GroupExpressionTerm &term)
	Writes the given term to the given output stream. More...
void	regina::swap (GroupExpression &lhs, GroupExpression &rhs) noexcept
	Swaps the contents of the two given expressions. More...
void	regina::swap (GroupPresentation &lhs, GroupPresentation &rhs) noexcept
	Swaps the contents of the two given group presentations. More...
void	regina::swap (HomGroupPresentation &lhs, HomGroupPresentation &rhs) noexcept
	Swaps the contents of the two given homomorphisms. More...
void	regina::swap (IntersectionForm &lhs, IntersectionForm &rhs) noexcept
	Swaps the contents of the two given intersection forms. More...
void	regina::swap (MarkedAbelianGroup &lhs, MarkedAbelianGroup &rhs) noexcept
	Swaps the contents of the two given abelian groups. More...
void	regina::swap (HomMarkedAbelianGroup &lhs, HomMarkedAbelianGroup &rhs) noexcept
	Swaps the contents of the two given homomorphisms. More...

Detailed Description

Various algebraic structures.

Function Documentation

operator<<()

std::ostream & regina::operator<<	(	std::ostream &	out,
		const GroupExpressionTerm &	term
	)

Writes the given term to the given output stream.

The term will be written in the format g3^-7, where in this example the term represents generator number 3 raised to the -7th power.

Note that generators are indexed start from 0 (so g3 is in fact the fourth generator in the group presentation, not the third).

If the term has exponent 0 or 1, the output format will be appropriately simplified.

Parameters

out	the output stream to which to write.
term	the term to write.

Returns

a reference to the given output stream.

swap() [1/7]

void regina::swap ( AbelianGroup &  lhs, AbelianGroup &  rhs  )

inlinenoexcept

Swaps the contents of the two given abelian groups.

This global routine simply calls AbelianGroup::swap(); it is provided so that AbelianGroup meets the C++ Swappable requirements.

Parameters

lhs	the group whose contents should be swapped with rhs.
rhs	the group whose contents should be swapped with lhs.

swap() [2/7]

void regina::swap ( GroupExpression &  lhs, GroupExpression &  rhs  )

inlinenoexcept

Swaps the contents of the two given expressions.

This global routine simply calls GroupExpression::swap(); it is provided so that GroupExpression meets the C++ Swappable requirements.

Parameters

lhs	the expression whose contents should be swapped with rhs.
rhs	the expression whose contents should be swapped with lhs.

swap() [3/7]

void regina::swap ( GroupPresentation &  lhs, GroupPresentation &  rhs  )

inlinenoexcept

Swaps the contents of the two given group presentations.

This global routine simply calls GroupPresentation::swap(); it is provided so that GroupPresentation meets the C++ Swappable requirements.

Parameters

lhs	the presentation whose contents should be swapped with rhs.
rhs	the presentation whose contents should be swapped with lhs.

swap() [4/7]

void regina::swap ( HomGroupPresentation &  lhs, HomGroupPresentation &  rhs  )

inlinenoexcept

Swaps the contents of the two given homomorphisms.

This global routine simply calls HomGroupPresentation::swap(); it is provided so that HomGroupPresentation meets the C++ Swappable requirements.

Parameters

lhs	the homomorphism whose contents should be swapped with rhs.
rhs	the homomorphism whose contents should be swapped with lhs.

swap() [5/7]

void regina::swap ( HomMarkedAbelianGroup &  lhs, HomMarkedAbelianGroup &  rhs  )

inlinenoexcept

Swaps the contents of the two given homomorphisms.

This global routine simply calls HomMarkedAbelianGroup::swap(); it is provided so that HomMarkedAbelianGroup meets the C++ Swappable requirements.

Parameters

lhs	the homomorphism whose contents should be swapped with rhs.
rhs	the homomorphism whose contents should be swapped with lhs.

swap() [6/7]

void regina::swap ( IntersectionForm &  lhs, IntersectionForm &  rhs  )

inlinenoexcept

Swaps the contents of the two given intersection forms.

This global routine simply calls IntersectionForm::swap(); it is provided so that IntersectionForm meets the C++ Swappable requirements.

Parameters

lhs	the intersection form whose contents should be swapped with rhs.
rhs	the intersection form whose contents should be swapped with lhs.

swap() [7/7]

void regina::swap ( MarkedAbelianGroup &  lhs, MarkedAbelianGroup &  rhs  )

inlinenoexcept

Swaps the contents of the two given abelian groups.

This global routine simply calls MarkedAbelianGroup::swap(); it is provided so that MarkedAbelianGroup meets the C++ Swappable requirements.

Parameters

lhs	the group whose contents should be swapped with rhs.
rhs	the group whose contents should be swapped with lhs.