Mathematics

Implements a rudimentary symbolic mathematical model. The entities of the model are termed operations. A system of operations is termed a program.

In namespace mathematics:

Operations

#include<hysj/mathematics/operations.hpp>

Datum

enum class datum

enumerator zero

enumerator one

enumerator minus_one

enumerator two

enumerator infinity

enumerator pi

enumerator e

Enum for representing symbolic constants.

Operation

The operation is the building blocks of our mathematical model.

enum class operation_tag

enumerator constant

enumerator negation

enumerator sign

enumerator addition

enumerator subtraction

enumerator multiplication

enumerator division

enumerator power

enumerator logarithm

enumerator differentiation

enumerator symbol

enumerator sine

enumerator equality

enumerator inequality

enumerator strict_inequality

enumerator boolean

enumerator assertion

enumerator complement

enumerator conjunction

enumerator disjunction

Names the different types of operations.

template<operation_tag t>
struct operation_id

static constexpr operation_tag tag = t

natural number

Each operation has a unique id consiting of a tag which denotes the type of operation, and an number which is unique to all operation ids of that type.

Shorthands

using constant_id = operation_id<operation_tag::constant>

using negation_id = operation_id<operation_tag::negation>

using sign_id = operation_id<operation_tag::sign>

using addition_id = operation_id<operation_tag::addition>

using subtraction_id = operation_id<operation_tag::subtraction>

using multiplication_id = operation_id<operation_tag::multiplication>

using division_id = operation_id<operation_tag::division>

using power_id = operation_id<operation_tag::power>

using logarithm_id = operation_id<operation_tag::logarithm>

using differentiation_id = operation_id<operation_tag::differentiation>

using symbol_id = operation_id<operation_tag::symbol>

using sine_id = operation_id<operation_tag::sine>

using equality_id = operation_id<operation_tag::equality>

using inequality_id = operation_id<operation_tag::inequality>

using strict_inequality_id = operation_id<operation_tag::strict_inequality>

using boolean_id = operation_id<operation_tag::boolean>

using assertion_id = operation_id<operation_tag::assertion>

using complement_id = operation_id<operation_tag::complement>

using conjunction_id = operation_id<operation_tag::conjunction>

using disjunction_id = operation_id<operation_tag::disjunction>

template<operation_tag i>
using operation_ids = std::vector<operation_id<i>>

Alias template for list of operation ids.

Shorthands

using constant_ids = operation_ids<operation_tag::constant>

using negation_ids = operation_ids<operation_tag::negation>

using sign_ids = operation_ids<operation_tag::sign>

using addition_ids = operation_ids<operation_tag::addition>

using subtraction_ids = operation_ids<operation_tag::subtraction>

using multiplication_ids = operation_ids<operation_tag::multiplication>

using division_ids = operation_ids<operation_tag::division>

using power_ids = operation_ids<operation_tag::power>

using logarithm_ids = operation_ids<operation_tag::logarithm>

using differentiation_ids = operation_ids<operation_tag::differentiation>

using symbol_ids = operation_ids<operation_tag::symbol>

using sine_ids = operation_ids<operation_tag::sine>

using equality_ids = operation_ids<operation_tag::equality>

using inequality_ids = operation_ids<operation_tag::inequality>

using strict_inequality_ids = operation_ids<operation_tag::strict_inequality>

using boolean_ids = operation_ids<operation_tag::boolean>

using assertion_ids = operation_ids<operation_tag::assertion>

using complement_ids = operation_ids<operation_tag::complement>

using conjunction_ids = operation_ids<operation_tag::conjunction>

using disjunction_ids = operation_ids<operation_tag::disjunction>

Groups

enum class operation_group_tag

enumerator expression

enumerator equation

enumerator logical_expression

Names the different types of operation-groups.

template<operation_group_tag G>
unspecified operation_group_members

An operation group is defined in terms of a tuple of operation_tag-constants, with:

expression \(\rightarrow\) constant, sign, negation, addition, subtraction, multiplication, division, power, logarithm, differentiation, sine, symbol

equation \(\rightarrow\) equality, inequality, strict_inequality

logical_expression \(\rightarrow\) boolean, symbol, assertion, complement, conjunction, disjunction

template<operation_group_tag>
struct operation_group_id

unspecified operation

A group-id holds a variant over the operation-ids of its member-operations.

Shorthands

using expression_id = operation_group_id<operation_group_tag::expression>

using equation_id = operation_group_id<operation_group_tag::equation>

using logical_expression_id = operation_group_id<operation_group_tag::logical_expression>

template<operation_group_tag g>
using operation_group_ids = std::vector<operation_group_id<g>>

List of operation group ids.

Shorthands

using expression_ids = operation_group_ids<operation_group_tag::expression>

using equation_ids = operation_group_ids<operation_group_tag::equation>

using logical_expression_ids = operation_group_ids<operation_group_tag::logical_expression>

Operands

template<operation_tag>
struct operation_operands

Models the operands of an operation. The primary template is an empty struct, and signifies a nullary operator. Its members are operation-ids, operation-group-ids or list of these.

Specializations

template<>
struct operation_operands<operation_tag::constant>

template<>
struct operation_operands<operation_tag::negation>

unspecified expression

template<>
struct operation_operands<operation_tag::sign>

unspecified expression

template<>
struct operation_operands<operation_tag::addition>

unspecified terms

template<>
struct operation_operands<operation_tag::subtraction>

unspecified terms

template<>
struct operation_operands<operation_tag::multiplication>

unspecified factors

template<>
struct operation_operands<operation_tag::division>

unspecified dividend

unspecified divisor

template<>
struct operation_operands<operation_tag::power>

unspecified base

unspecified exponent

template<>
struct operation_operands<operation_tag::logarithm>

unspecified base

unspecified exponent

template<>
struct operation_operands<operation_tag::differentiation>

unspecified expression

unspecified variables

template<>
struct operation_operands<operation_tag::symbol>

template<>
struct operation_operands<operation_tag::sine>

unspecified angle

template<>
struct operation_operands<operation_tag::equality>

unspecified lhs

unspecified rhs

template<>
struct operation_operands<operation_tag::inequality>

unspecified lhs

unspecified rhs

template<>
struct operation_operands<operation_tag::strict_inequality>

unspecified lhs

unspecified rhs

template<>
struct operation_operands<operation_tag::boolean>

template<>
struct operation_operands<operation_tag::assertion>

unspecified equation

template<>
struct operation_operands<operation_tag::complement>

unspecified expression

template<>
struct operation_operands<operation_tag::conjunction>

unspecified expressions

template<>
struct operation_operands<operation_tag::disjunction>

unspecified expressions

Infos

Some operations have semantics beyond operand-relations. This information is taken care of by a operation-type specific operation info-type.

unspecified operation_info_type

Function mapping from operation-tag to the operation-info-type.

The only operations with a non nothing info-type are:

Constants \(\rightarrow\) std::variant<datum, integer, real>

Booleans \(\rightarrow\) bool

Symbols \(\rightarrow\) natural

Programs

#include<hysj/mathematics/programs.hpp>

struct program

A program represents a system of operations. This system consists of a set of operations for each type, the operation infos and operands.

unspecified counts

Maintains the arity of the operation-sets.

unspecified graph

Models operand-relations between operations.

unspecified vertex_map

Mapping between operation_id and graph vertex.

unspecified infos

Mapping between operation_id and operation_info vertex.