yu2 shu4 han2 shu4 (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)

zhong3 lei4

ke3 ji4 cheng2 guan1 xi4

er4 yuan2 han2 shu4
is instance of

zhong3 lei4

ke3 ji4 cheng2 guan1 xi4

yu3 liang4 guan1 xi4
is instance of

yu2 shu4 han2 shu4

Coordinate term(s)

jia1 fa3 han2 shu4 ri4 han2 shu4 mi4 du4 han2 shu4 chu2 fa3 han2 shu4 wen2 ben3 ban3 ben3 han2 shu4 zhi3 shu4 han2 shu4 tu2 lu4 jing4 han2 shu4 xiao3 shi2 han2 shu4 jiao1 ji2 han2 shu4 jian1 ge2 han2 shu4 zhong3 lei4 miao2 shu4 han2 shu4 lie4 jie2 han2 shu4 lie4 xu4 han2 shu4 dui4 shu4 han2 shu4 zui4 da4 zhi2 han2 shu4 zui4 da4 liang4 lu4 jing4 han2 shu4 ce4 liang4 han2 shu4 bu4 fen5 zheng3 ti1 cha4 yi4 han2 shu4 bu4 fen5 zheng3 ti1 jiao1 ji2 han2 shu4 bu4 fen5 zheng3 ti1 jia1 zong1 han2 shu4 zui4 xiao3 zhi2 han2 shu4 zui4 xiao3 liang4 lu4 jing4 han2 shu4 fen1 zhong1 han2 shu4 yue4 fen4 han2 shu4 cheng2 fa3 han2 shu4 qi1 kan1 yi1 qi1 han2 shu4 dao3 shu4 han2 shu4 zhou1 qi1 xing4 shi2 ju4 han2 shu4 guan1 xi4 hu4 bu3 han2 shu4 xiang4 dui4 shi2 jian1 han2 shu4 zheng3 shu4 han2 shu4 miao3 zhong1 han2 shu4 xi4 lie4 yi1 juan4 han2 shu4 su4 du4 han2 shu4 jian3 fa3 han2 shu4 shi2 jian1 dan1 wei4 han2 shu4 shi2 jian1 li4 cheng2 han2 shu4 lian2 ji2 han2 shu4 wei4 zhi4 han2 shu4 xiang1 deng3 da4 yu1 da4 yu1 huo4 deng3 yu1 xiao3 yu1 xiao3 yu1 huo4 deng3 yu1

Type restrictions

shu4 liang4 RemainderFn(shu4 liang4, shu4 liang4)

Axioms (10)

if " de5 zui4 da4 gong1 yue1 shu4" deng3 yu1 number,
then for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "element qu3 yu2 shu4 number" deng3 yu1

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

if " de5 zui4 da4 gong1 yue1 shu4" deng3 yu1 number,
then there doesn't exist greater so_that_not greater (bu2) da4 yu1 number and for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "element qu3 yu2 shu4 greater" deng3 yu1

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

if " de5 zui4 xiao3 gong1 bei4 shu4" deng3 yu1 number,
then for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "number qu3 yu2 shu4 element" deng3 yu1

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

if " de5 zui4 xiao3 gong1 bei4 shu4" deng3 yu1 number,
then there doesn't exist less so_that_not less xiao3 yu1 number and for all element holds: if element shi4 "()" de5 yi1 cheng2 yuan2, then "less qu3 yu2 shu4 element" deng3 yu1

(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?LESS)
                  (and
                        (lessThan ?LESS ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?LESS ?ELEMENT)
                                          0)))))))

"number1 qu3 yu2 shu4 number2" deng3 yu1 number if and only if "(""zui4 da4 zheng3 shu4 xiao3 yu1 huo4 deng3 yu1 "number1/number2""*number2"+number)" deng3 yu1 number1.

(<=>
      (equal
            (RemainderFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (equal
            (AdditionFn
                  (MultiplicationFn
                        (FloorFn
                              (DivisionFn ?NUMBER1 ?NUMBER2))
                        ?NUMBER2)
                  ?NUMBER)
            ?NUMBER1))

If "number1 qu3 yu2 shu4 number2" deng3 yu1 number, then "number2 de5 zheng4 fu4 hao4" deng3 yu1 "number de5 zheng4 fu4 hao4".

(=>
      (equal
            (RemainderFn ?NUMBER1 ?NUMBER2)
            ?NUMBER)
      (equal
            (SignumFn ?NUMBER2)
            (SignumFn ?NUMBER)))

If number shi4 ou3 zheng3 shu4 de5 shi2 li4, then "number qu3 yu2 shu4 " deng3 yu1 .

(=>
      (instance ?NUMBER EvenInteger)
      (equal
            (RemainderFn ?NUMBER 2)
            0))

If number shi4 qi2 zheng3 shu4 de5 shi2 li4, then "number qu3 yu2 shu4 " deng3 yu1 .

(=>
      (instance ?NUMBER OddInteger)
      (equal
            (RemainderFn ?NUMBER 2)
            1))

if prime shi4 zhi4 shu4 de5 shi2 li4,
then for all number holds: if "prime qu3 yu2 shu4 number" deng3 yu1 , then number deng3 yu1 or number deng3 yu1 prime

(=>
      (instance ?PRIME PrimeNumber)
      (forall
            (?NUMBER)
            (=>
                  (equal
                        (RemainderFn ?PRIME ?NUMBER)
                        0)
                  (or
                        (equal ?NUMBER 1)
                        (equal ?NUMBER ?PRIME)))))

If leap shi4 run4 nian2 de5 shi2 li4 and leap deng3 yu1 "number nian2(s)", then

"number qu3 yu2 shu4 " deng3 yu1 and "number qu3 yu2 shu4 " deng3 yu1
"number qu3 yu2 shu4 " deng3 yu1

(=>
      (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)))