Set Assertions RC

Stable Numerics Subroutine Library
Programming Reference Manual
Version 1.0 DD-00006-010

6.4.2 Set Assertions $RC$

bool disjoint(const rc_interval<T>& a, const rc_interval<T>& b);
bool proper_subset(const rc_interval<T>& a, const rc_interval<T>& b);
bool subset(const rc_interval<T>& a, const rc_interval<T>& b);
bool proper_superset(const rc_interval<T>& a, const rc_interval<T>& b);
bool superset(const rc_interval<T>& a, const rc_interval<T>& b);
bool overlap(const rc_interval<T>& a, const rc_interval<T>& b);

bool inside(const rc_interval<T>& a, const std::complex<T>& v);

These functions assert set properties between two given rectangular intervals $A,B ∈RC$ .

disjoint(const rc_interval<T>& a, const rc_interval<T>& b): Whether the two intervals are disjoint to each other.
proper_subset(const rc_interval<T>& a, const rc_interval<T>& b);: Determines whether $A$ is a proper subset of $B$ , that is $A ⊂ B$ .
subset(const rc_interval<T>& a, const rc_interval<T>& b);: Determines whether $A$ is a subset of $B$ , that is $A ⊆ B$ .
proper_superset(const rc_interval<T>& a, const rc_interval<T>& b);: Determines whether $A$ is a proper superset of $B$ , that is $A ⊃B$ .
superset(const rc_interval<T>& a, const rc_interval<T>& b);: Determines whether $A$ is a superset of $B$ , that is $A ⊇ B$ .
overlap(const rc_interval<T>& a, const rc_interval<T>& b);: Determines whether $A$ intersects or overlaps with $B$ .
inside(const rc_interval<T>& a, const std::complex<T>& v);: Whether the complex number $v∈ C$ is within the span of the given rectangular complex interval $A$ .

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