SymEngine::Interval Class Reference

Inheritance diagram for SymEngine::Interval:

Collaboration diagram for SymEngine::Interval:

Public Member Functions
void	accept (Visitor &v) const override
void	accept (EvalRealDoubleVisitorFinal &v) const override
hash_t	__hash__ () const override
bool	__eq__ (const Basic &o) const override
	Test equality.
int	compare (const Basic &o) const override
	Interval (const RCP< const Number > &start, const RCP< const Number > &end, const bool left_open=false, const bool right_open=false)
RCP< const Set >	open () const
RCP< const Set >	close () const
RCP< const Set >	Lopen () const
RCP< const Set >	Ropen () const
RCP< const Set >	set_union (const RCP< const Set > &o) const override
RCP< const Set >	set_intersection (const RCP< const Set > &o) const override
RCP< const Set >	set_complement (const RCP< const Set > &o) const override
RCP< const Boolean >	contains (const RCP< const Basic > &a) const override
vec_basic	get_args () const override
	Returns the list of arguments.
const RCP< const Number > &	get_start () const
const RCP< const Number > &	get_end () const
const bool &	get_left_open () const
const bool &	get_right_open () const
Public Member Functions inherited from SymEngine::Set
vec_basic	get_args () const override=0
	Returns the list of arguments.
virtual RCP< const Set >	set_intersection (const RCP< const Set > &o) const =0
virtual RCP< const Set >	set_union (const RCP< const Set > &o) const =0
virtual RCP< const Set >	set_complement (const RCP< const Set > &o) const =0
virtual RCP< const Boolean >	contains (const RCP< const Basic > &a) const =0
bool	is_subset (const RCP< const Set > &o) const
bool	is_proper_subset (const RCP< const Set > &o) const
bool	is_superset (const RCP< const Set > &o) const
bool	is_proper_superset (const RCP< const Set > &o) const
Public Member Functions inherited from SymEngine::Basic
TypeID	get_type_code () const
	Basic ()
	Constructor.
	Basic (const Basic &)=delete
	Delete the copy constructor and assignment.
Basic &	operator= (const Basic &)=delete
	Assignment operator in continuation with above.
	Basic (Basic &&)=delete
	Delete the move constructor and assignment.
Basic &	operator= (Basic &&)=delete
	Assignment operator in continuation with above.
virtual hash_t	__hash__ () const =0
hash_t	hash () const
virtual bool	__eq__ (const Basic &o) const =0
	Test equality.
bool	__neq__ (const Basic &o) const
	true if this is not equal to o.
int	__cmp__ (const Basic &o) const
	Comparison operator.
virtual int	compare (const Basic &o) const =0
std::string	__str__ () const
std::string	dumps () const
	Returns a string of the instance serialized.
RCP< const Basic >	subs (const map_basic_basic &subs_dict) const
	Substitutes 'subs_dict' into 'self'.
RCP< const Basic >	xreplace (const map_basic_basic &subs_dict) const
virtual RCP< const Basic >	expand_as_exp () const
	expands the special function in terms of exp function
virtual vec_basic	get_args () const =0
	Returns the list of arguments.
virtual void	accept (Visitor &v) const =0
virtual void	accept (EvalRealDoubleVisitorFinal &v) const =0
RCP< const Basic >	diff (const RCP< const Symbol > &x, bool cache=true) const
Public Member Functions inherited from SymEngine::EnableRCPFromThis< Basic >
RCP< Basic >	rcp_from_this ()
	Get RCP<T> pointer to self (it will cast the pointer to T)
RCP< const Basic >	rcp_from_this () const
	Get RCP<const T> pointer to self (it will cast the pointer to const T)
RCP< const T2 >	rcp_from_this_cast () const
	Get RCP<T2> pointer to self (it will cast the pointer to T2)
unsigned int	use_count () const

Static Public Member Functions
static bool	is_canonical (const RCP< const Number > &start, const RCP< const Number > &end, bool left_open, bool right_open)
Static Public Member Functions inherited from SymEngine::Basic
static RCP< const Basic >	loads (const std::string &)
	Creates an instance of a serialized string.

Static Public Attributes
static const TypeID	type_code_id = SYMENGINE_INTERVAL

Private Attributes
RCP< const Number >	start_
RCP< const Number >	end_
bool	left_open_
bool	right_open_

Additional Inherited Members
Data Fields inherited from SymEngine::Basic
TypeID	type_code_

Detailed Description

Definition at line 145 of file sets.h.

Constructor & Destructor Documentation

Interval()

SymEngine::Interval::Interval	(	const RCP< const Number > &	start,
		const RCP< const Number > &	end,
		const bool	left_open = false,
		const bool	right_open = false
	)

Definition at line 10 of file sets.cpp.

    : start_(start), end_(end), left_open_(left_open), right_open_(right_open)
{
    SYMENGINE_ASSIGN_TYPEID()
    SYMENGINE_ASSERT(
        Interval::is_canonical(start_, end_, left_open_, right_open_));
}

Member Function Documentation

__eq__()

bool SymEngine::Interval::__eq__ ( const Basic &  o ) const

overridevirtual

Test equality.

A virtual function for testing the equality of two Basic objects

Deprecated:

Use eq(const Basic &a, const Basic &b) non-member method

Parameters

o	a constant reference to object to test against

Returns

True if this is equal to o

Implements SymEngine::Basic.

Definition at line 43 of file sets.cpp.

{
    if (is_a<Interval>(o)) {
        const Interval &s = down_cast<const Interval &>(o);
        return ((this->left_open_ == s.left_open_)
                and (this->right_open_ == s.right_open_)
                and eq(*this->start_, *s.start_) and eq(*this->end_, *s.end_));
    }
    return false;
}

__hash__()

hash_t SymEngine::Interval::__hash__ ( ) const

overridevirtual

Calculates the hash of the given SymEngine class. Use Basic.hash() which gives a cached version of the hash.

Returns

64-bit integer value for the hash

Implements SymEngine::Basic.

Definition at line 33 of file sets.cpp.

{
    hash_t seed = SYMENGINE_INTERVAL;
    hash_combine<Basic>(seed, *start_);
    hash_combine<Basic>(seed, *end_);
    hash_combine<bool>(seed, left_open_);
    hash_combine<bool>(seed, right_open_);
    return seed;
}

accept() [1/2]

void SymEngine::Interval::accept ( EvalRealDoubleVisitorFinal &  v ) const

overridevirtual

Implements SymEngine::Basic.

accept() [2/2]

void SymEngine::Interval::accept ( Visitor &  v ) const

overridevirtual

Implements SymEngine::Basic.

close()

RCP< const Set > SymEngine::Interval::close

(

)

const

Definition at line 92 of file sets.cpp.

{
    return interval(start_, end_, false, false);
}

compare()

int SymEngine::Interval::compare ( const Basic &  o ) const

overridevirtual

Returns -1, 0, 1 for this < o, this == o, this > o. This method is used when you want to sort things like x+y+z into canonical order. This function assumes that o is the same type as this. Use __cmp__ if you want general comparison.

Implements SymEngine::Basic.

Definition at line 54 of file sets.cpp.

{
    // compares two interval based on their length
    SYMENGINE_ASSERT(is_a<Interval>(s))
    const Interval &o = down_cast<const Interval &>(s);
    if (left_open_ and not o.left_open_) {
        return -1;
    } else if (not left_open_ and o.left_open_) {
        return 1;
    } else if (right_open_ and not o.right_open_) {
        return 1;
    } else if (not right_open_ and o.right_open_) {
        return -1;
    } else {
        auto temp = start_->__cmp__(*(o.start_));
        if (temp != 0) {
            return temp;
        } else {
            return end_->__cmp__(*(o.end_));
        }
    }
}

contains()

RCP< const Boolean > SymEngine::Interval::contains ( const RCP< const Basic > &  a ) const

overridevirtual

Implements SymEngine::Set.

Definition at line 97 of file sets.cpp.

{
    if (not is_a_Number(*a)) {
        if (is_a_Set(*a)) {
            return boolean(false);
        } else {
            return make_rcp<Contains>(a, rcp_from_this_cast<const Set>());
        }
    }
    if (eq(*start_, *a))
        return boolean(not left_open_);
    if (eq(*end_, *a))
        return boolean(not right_open_);
    if (eq(*min({end_, a}), *end_) or eq(*max({start_, a}), *start_))
        return boolean(false);
    return boolean(true);
}

get_args()

vec_basic SymEngine::Interval::get_args ( ) const

overridevirtual

Returns the list of arguments.

Implements SymEngine::Set.

Definition at line 275 of file sets.cpp.

{
    return {start_, end_, boolean(left_open_), boolean(right_open_)};
}

get_end()

const RCP< const Number > & SymEngine::Interval::get_end ( ) const

inline

Definition at line 180 of file sets.h.

    {
        return end_;
    }

get_left_open()

const bool & SymEngine::Interval::get_left_open ( ) const

inline

Definition at line 184 of file sets.h.

    {
        return this->left_open_;
    }

get_right_open()

const bool & SymEngine::Interval::get_right_open ( ) const

inline

Definition at line 188 of file sets.h.

    {
        return this->right_open_;
    }

get_start()

const RCP< const Number > & SymEngine::Interval::get_start ( ) const

inline

Definition at line 176 of file sets.h.

    {
        return start_;
    }

is_canonical()

bool SymEngine::Interval::is_canonical ( const RCP< const Number > &  start, const RCP< const Number > &  end, bool  left_open, bool  right_open  )

static

Definition at line 19 of file sets.cpp.

{
    if (is_a<Complex>(*s) or is_a<Complex>(*e))
        throw NotImplementedError("Complex set not implemented");
    if (eq(*e, *s)) {
        return false;
    } else if (eq(*min({s, e}), *e)) {
        return false;
    }
    return true;
}

Lopen()

RCP< const Set > SymEngine::Interval::Lopen

(

)

const

Definition at line 82 of file sets.cpp.

{
    return interval(start_, end_, true, false);
}

open()

RCP< const Set > SymEngine::Interval::open

(

)

const

Definition at line 77 of file sets.cpp.

{
    return interval(start_, end_, true, true);
}

Ropen()

RCP< const Set > SymEngine::Interval::Ropen

(

)

const

Definition at line 87 of file sets.cpp.

{
    return interval(start_, end_, false, true);
}

set_complement()

RCP< const Set > SymEngine::Interval::set_complement ( const RCP< const Set > &  o ) const

overridevirtual

Implements SymEngine::Set.

Definition at line 257 of file sets.cpp.

{
    if (is_a<Interval>(*o)) {
        set_set cont;
        const Interval &other = down_cast<const Interval &>(*o);
        if (eq(*max({start_, other.start_}), *start_)) {
            cont.insert(interval(other.get_start(), start_,
                                 other.get_left_open(), not left_open_));
        }
        if (eq(*min({end_, other.end_}), *end_)) {
            cont.insert(interval(end_, other.get_end(), not right_open_,
                                 other.get_right_open()));
        }
        return SymEngine::set_union(cont);
    }
    return SymEngine::set_complement_helper(rcp_from_this_cast<const Set>(), o);
}

set_intersection()

RCP< const Set > SymEngine::Interval::set_intersection ( const RCP< const Set > &  o ) const

overridevirtual

Implements SymEngine::Set.

Definition at line 131 of file sets.cpp.

{
    if (is_a<Interval>(*o)) {
        const Interval &other = down_cast<const Interval &>(*o);
        RCP<const Number> start, end;
        bool left_open, right_open;
        RCP<const Basic> start_end, end_start;
        start_end = min({this->start_, other.end_});
        end_start = min({this->end_, other.start_});
 
        if (eq(*this->start_, *start_end) and eq(*other.start_, *end_start)) {
            RCP<const Basic> start_start, end_end;
            start_start = min({this->start_, other.start_});
            end_end = min({this->end_, other.end_});
            if (neq(*this->start_, *other.start_)) {
                if (eq(*this->start_, *start_start)) {
                    start = other.start_;
                    left_open = other.left_open_;
                } else {
                    start = this->start_;
                    left_open = this->left_open_;
                }
            } else {
                start = this->start_;
                left_open = this->left_open_ or other.left_open_;
            }
 
            if (neq(*this->end_, *other.end_)) {
                if (eq(*this->end_, *end_end)) {
                    end = this->end_;
                    right_open = this->right_open_;
                } else {
                    end = other.end_;
                    right_open = other.right_open_;
                }
            } else {
                end = this->end_;
                right_open = this->right_open_ or other.right_open_;
            }
            return interval(start, end, left_open, right_open);
        } else {
            return emptyset();
        }
    }
    if (is_a<Integers>(*o) or is_a<Naturals>(*o) or is_a<Naturals0>(*o)) {
        if (is_a_Number(*start_) and is_a_Number(*end_)) {
            auto first = SymEngine::ceiling(start_);
            auto last = SymEngine::floor(end_);
            if (is_a<Naturals>(*o)
                and not down_cast<const Integer &>(*first).is_positive()) {
                first = integer(1);
            } else if (is_a<Naturals0>(*o)
                       and down_cast<const Integer &>(*first).is_negative()) {
                first = integer(0);
            }
            if (eq(*first, *start_) and left_open_) {
                first = add(first, integer(1));
            }
            if (eq(*last, *end_) and right_open_) {
                last = add(last, integer(-1));
            }
            if (eq(*Lt(last, first), *boolTrue)) {
                return emptyset();
            }
            set_basic container;
            while (eq(*Ge(last, first), *boolTrue)) {
                container.insert(first);
                first = add(first, integer(1));
            }
            return finiteset(container);
        } else {
            return SymEngine::set_intersection(
                {rcp_from_this_cast<const Set>(), o});
        }
    }
    if (is_a<UniversalSet>(*o) or is_a<EmptySet>(*o) or is_a<FiniteSet>(*o)
        or is_a<Union>(*o) or is_a<Rationals>(*o) or is_a<Reals>(*o)
        or is_a<Complexes>(*o)) {
        return (*o).set_intersection(rcp_from_this_cast<const Set>());
    }
    return make_set_intersection({rcp_from_this_cast<const Set>(), o});
}

set_union()

RCP< const Set > SymEngine::Interval::set_union ( const RCP< const Set > &  o ) const

overridevirtual

Implements SymEngine::Set.

Definition at line 214 of file sets.cpp.

{
    if (is_a<Interval>(*o)) {
        const Interval &other = down_cast<const Interval &>(*o);
        RCP<const Basic> start_start, end_end, m;
        RCP<const Number> start, end;
        bool left_open, right_open;
        start_start = max({this->start_, other.start_});
        end_end = min({this->end_, other.end_});
        m = min({start_start, end_end});
        if ((eq(*end_end, *start_start) and eq(*end_end, *m)
             and ((eq(*end_end, *this->end_) and this->right_open_)
                  or (eq(*end_end, *other.end_) and other.right_open_)))
            or (eq(*end_end, *m) and not eq(*end_end, *start_start))) {
            return SymEngine::make_set_union(
                {rcp_from_this_cast<const Set>(), o});
        } else {
            if (eq(*min({this->start_, other.start_}), *this->start_)) {
                start = this->start_;
            } else {
                start = other.start_;
            }
            if (eq(*max({this->end_, other.end_}), *this->end_)) {
                end = this->end_;
            } else {
                end = other.end_;
            }
            left_open = ((neq(*this->start_, *start) or this->left_open_)
                         and (neq(*other.start_, *start) or other.left_open_));
            right_open = ((neq(*this->end_, *end) or this->right_open_)
                          and (neq(*other.end_, *end) or other.right_open_));
            return interval(start, end, left_open, right_open);
        }
    }
    if (is_a<UniversalSet>(*o) or is_a<EmptySet>(*o) or is_a<FiniteSet>(*o)
        or is_a<Union>(*o) or is_a<Complexes>(*o) or is_a<Reals>(*o)
        or is_a<Rationals>(*o) or is_a<Integers>(*o) or is_a<Naturals>(*o)
        or is_a<Naturals0>(*o)) {
        return (*o).set_union(rcp_from_this_cast<const Set>());
    }
    return SymEngine::make_set_union({rcp_from_this_cast<const Set>(), o});
}

Field Documentation

end_

RCP<const Number> SymEngine::Interval::end_

private

Definition at line 149 of file sets.h.

left_open_

bool SymEngine::Interval::left_open_

private

Definition at line 150 of file sets.h.

right_open_

bool SymEngine::Interval::right_open_

private

Definition at line 150 of file sets.h.

start_

RCP<const Number> SymEngine::Interval::start_

private

Definition at line 148 of file sets.h.

type_code_id

const TypeID SymEngine::Interval::type_code_id = SYMENGINE_INTERVAL

static

Type_code_id shared by all instances

Definition at line 153 of file sets.h.

---

The documentation for this class was generated from the following files:

• /home/runner/work/symengine/symengine/symengine/sets.h
• /home/runner/work/symengine/symengine/symengine/sets.cpp