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緇计ㄧ计 (RemainderFn)

(RemainderFn number divisor) is the remainder of the number number divided by the number divisor. The result has the same sign as divisor.

Ontology

SUMO / NUMERIC-FUNCTIONS

Class(es)

贺摸
is instance of
  膥┯闽玒  
is instance of
  じㄧ计  
is instance of
贺摸
is instance of
  膥┯闽玒  
is instance of
  籔秖闽玒  
is instance of
is instance of
  緇计ㄧ计  

Coordinate term(s)

猭ㄧ计  らㄧ计  盞ㄧ计  埃猭ㄧ计  ゅセセㄧ计  计ㄧ计  瓜隔畖ㄧ计  ㄧ计  ユ栋ㄧ计  丁筳ㄧ计  贺摸磞瓃ㄧ计  挡ㄧ计  ㄧ计  癸计ㄧ计  程ㄧ计  程秖隔畖ㄧ计  代秖ㄧ计  场だ俱砰畉钵ㄧ计  场だ俱砰ユ栋ㄧ计  场だ俱砰羆ㄧ计  程ㄧ计  程秖隔畖ㄧ计  だ牧ㄧ计  るㄧ计  猭ㄧ计  戳戳ㄧ计  计ㄧ计  秅戳┦禯ㄧ计  闽玒が干ㄧ计  癸丁ㄧ计  俱计ㄧ计  牧ㄧ计  ╰ㄧ计  硉ㄧ计  搭猭ㄧ计  丁虫ㄧ计  丁菌祘ㄧ计  羛栋ㄧ计  竚ㄧ计  单    ┪单    ┪单 

Type restrictions

计秖 RemainderFn(计秖, 计秖)

Axioms (10)

(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (forall
            (?ELEMENT)
            (=>
                  (inList
                        ?ELEMENT
                        (ListFn @ROW))
                  (equal
                        (RemainderFn ?ELEMENT ?NUMBER)
                        0))))
(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?GREATER)
                  (and
                        (greaterThan ?GREATER ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?ELEMENT ?GREATER)
                                          0)))))))
(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (forall
            (?ELEMENT)
            (=>
                  (inList
                        ?ELEMENT
                        (ListFn @ROW))
                  (equal
                        (RemainderFn ?NUMBER ?ELEMENT)
                        0))))
(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?LESS)
                  (and
                        (lessThan ?LESS ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?LESS ?ELEMENT)
                                          0)))))))
"number1 緇计 number2" 单 number if and only if "(""程 俱计  ┪ 单 "number1/number2""*number2"+number)" 单 number1. 
(<=>
      (equal
            (RemainderFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (equal
            (AdditionFn
                  (MultiplicationFn
                        (FloorFn
                              (DivisionFn ?NUMBER1 ?NUMBER2))
                        ?NUMBER2)
                  ?NUMBER)
            ?NUMBER1))
If "number1 緇计 number2" 单 number, then "number2タ璽腹" 单 "numberタ璽腹". 
(=>
      (equal
            (RemainderFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (equal
            (SignumFn ?NUMBER2)
            (SignumFn ?NUMBER)))
If number 琌 案俱计龟ㄒ, then "number 緇计 " 单 . 
(=>
      (instance ?NUMBER EvenInteger)
      (equal
            (RemainderFn ?NUMBER 2)
            0))
If number 琌 俱计龟ㄒ, then "number 緇计 " 单 . 
(=>
      (instance ?NUMBER OddInteger)
      (equal
            (RemainderFn ?NUMBER 2)
            1))
(=>
      (instance ?PRIME PrimeNumber)
      (forall
            (?NUMBER)
            (=>
                  (equal
                        (RemainderFn ?PRIME ?NUMBER)
                        0)
                  (or
                        (equal ?NUMBER 1)
                        (equal ?NUMBER ?PRIME)))))
If leap 琌 秥龟ㄒ and leap 单 "number (s)", then 
(=>
      (and
            (instance ?LEAP LeapYear)
            (equal
                  ?LEAP
                  (MeasureFn ?NUMBER Year)))
      (or
            (and
                  (equal
                        (RemainderFn ?NUMBER 4)
                        0)
                  (not
                        (equal
                              (RemainderFn ?NUMBER 100)
                              0)))
            (equal
                  (RemainderFn ?NUMBER 400)
                  0)))