Set Assertions KC

6.4.1 Set Assertions $KC$

bool disjoint(const kc_interval<T>& a, const kc_interval<T>& b); 
bool proper_subset(const kc_interval<T>& a, const kc_interval<T>& b); 
bool subset(const kc_interval<T>& a, const kc_interval<T>& b); 
bool proper_superset(const kc_interval<T>& a, const kc_interval<T>& b); 
bool superset(const kc_interval<T>& a, const kc_interval<T>& b); 
bool overlap(const kc_interval<T>& a, const kc_interval<T>& b); 
 
bool inside(const kc_interval<T>& a, const std::complex<T>& v);

These functions assert set properties between two given circular intervals $A,B ∈KC$ .

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

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