greatest common divisor fn (GreatestCommonDivisorFn)

(GreatestCommonDivisorFn number1 number2 ... number) returns the greatest common divisor of number1 through number.

Ontology

SUMO / NUMERIC-FUNCTIONS

Class(es)

varga

inheritable relation

prakaarya

parivartaniiya sanbandha
is instance of

greatest common divisor fn

Coordinate term(s)

assignment fn least common multiple fn list fn contrary attribute disjoint decomposition disjoint relation exhaustive attribute exhaustive decomposition holds partition

Axioms (2)

agar "the greatest common divisor of " is equal to number,
to sab-kuch element ke lie hai, ki: agar element is a member of "()", to "element mod number" is equal to

(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (forall
            (?ELEMENT)
            (=>
                  (inList
                        ?ELEMENT
                        (ListFn @ROW))
                  (equal
                        (RemainderFn ?ELEMENT ?NUMBER)
                        0))))

agar "the greatest common divisor of " is equal to number,
to yah kuch greater nahin, ki greater is greater than number aur sab-kuch element ke lie hai, ki: agar element is a member of "()", to "element mod greater" is equal to

(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?GREATER)
                  (and
                        (greaterThan ?GREATER ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?ELEMENT ?GREATER)
                                          0)))))))