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QQ
QQ  the class of all rational numbers
Description
i1 : 1/2 + 3/5 11 o1 =  10 o1 : QQ
Functions and methods returning a rational number :
"QQ * QQ"
 see
*
 a binary operator, usually used for multiplication
"QQ * ZZ"
 see
*
 a binary operator, usually used for multiplication
"ZZ * QQ"
 see
*
 a binary operator, usually used for multiplication
"+ QQ"
 see
+
 a unary or binary operator, usually used for addition
"QQ + QQ"
 see
+
 a unary or binary operator, usually used for addition
"QQ + ZZ"
 see
+
 a unary or binary operator, usually used for addition
"ZZ + QQ"
 see
+
 a unary or binary operator, usually used for addition
" QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ  QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ  ZZ"
 see

 a unary or binary operator, usually used for negation or subtraction
"ZZ  QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ / QQ"
 see
/
 a binary operator, usually used for division
"QQ / ZZ"
 see
/
 a binary operator, usually used for division
"ZZ / QQ"
 see
/
 a binary operator, usually used for division
"gcd(QQ,QQ)"
 see
gcd
 greatest common divisor
"gcd(QQ,ZZ)"
 see
gcd
 greatest common divisor
"gcd(ZZ,QQ)"
 see
gcd
 greatest common divisor
Methods that use a rational number :
"QQ !"
 see
!
 factorial
"CC % QQ"
 see
%
 a binary operator, usually used for remainder and reduction
"QQ % QQ"
 see
%
 a binary operator, usually used for remainder and reduction
"QQ % ZZ"
 see
%
 a binary operator, usually used for remainder and reduction
"RR % QQ"
 see
%
 a binary operator, usually used for remainder and reduction
"CC * QQ"
 see
*
 a binary operator, usually used for multiplication
"QQ * CC"
 see
*
 a binary operator, usually used for multiplication
"QQ * RR"
 see
*
 a binary operator, usually used for multiplication
"QQ * RRi"
 see
*
 a binary operator, usually used for multiplication
"RR * QQ"
 see
*
 a binary operator, usually used for multiplication
"RRi * QQ"
 see
*
 a binary operator, usually used for multiplication
"CC + QQ"
 see
+
 a unary or binary operator, usually used for addition
"QQ + CC"
 see
+
 a unary or binary operator, usually used for addition
"QQ + RR"
 see
+
 a unary or binary operator, usually used for addition
"QQ + RRi"
 see
+
 a unary or binary operator, usually used for addition
"RR + QQ"
 see
+
 a unary or binary operator, usually used for addition
"RRi + QQ"
 see
+
 a unary or binary operator, usually used for addition
"CC  QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ  CC"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ  RR"
 see

 a unary or binary operator, usually used for negation or subtraction
"QQ  RRi"
 see

 a unary or binary operator, usually used for negation or subtraction
"RR  QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"RRi  QQ"
 see

 a unary or binary operator, usually used for negation or subtraction
"CC / QQ"
 see
/
 a binary operator, usually used for division
"QQ / CC"
 see
/
 a binary operator, usually used for division
"QQ / RR"
 see
/
 a binary operator, usually used for division
"QQ / RRi"
 see
/
 a binary operator, usually used for division
"RR / QQ"
 see
/
 a binary operator, usually used for division
"RRi / QQ"
 see
/
 a binary operator, usually used for division
"CC // QQ"
 see
//
 a binary operator, usually used for quotient
"InfiniteNumber // QQ"
 see
//
 a binary operator, usually used for quotient
"QQ // QQ"
 see
//
 a binary operator, usually used for quotient
"QQ // ZZ"
 see
//
 a binary operator, usually used for quotient
"RR // QQ"
 see
//
 a binary operator, usually used for quotient
"CC == QQ"
 see
==
 equality
"QQ == CC"
 see
==
 equality
"QQ == QQ"
 see
==
 equality
"QQ == RR"
 see
==
 equality
"QQ == RRi"
 see
==
 equality
"QQ == ZZ"
 see
==
 equality
"RR == QQ"
 see
==
 equality
"RRi == QQ"
 see
==
 equality
"ZZ == QQ"
 see
==
 equality
"abs(QQ)"
 see
abs
 absolute value function
"QQ * BettiTally"
 see
BettiTally
 the class of all Betti tallies
"factor(QQ)"
 see
factor(RingElement)
 factor a ring element
"interval(QQ)"
 see
interval
 construct an interval
"interval(QQ,QQ)"
 see
interval
 construct an interval
"interval(QQ,RR)"
 see
interval
 construct an interval
"interval(QQ,ZZ)"
 see
interval
 construct an interval
"interval(RR,QQ)"
 see
interval
 construct an interval
"interval(ZZ,QQ)"
 see
interval
 construct an interval
isMember(QQ,RRi)
 membership test in an interval
"isReal(QQ)"
 see
isReal
 whether a number is real
"lcm(QQ,QQ)"
 see
lcm
 least common multiple
"lcm(QQ,ZZ)"
 see
lcm
 least common multiple
"lcm(ZZ,QQ)"
 see
lcm
 least common multiple
"lift(CC,type of QQ)"
 see
lift
 lift to another ring
"lift(Ideal,type of QQ)"
 see
lift
 lift to another ring
"lift(Matrix,type of CC_*,type of QQ)"
 see
lift
 lift to another ring
"lift(Matrix,type of QQ,type of QQ)"
 see
lift
 lift to another ring
"lift(Matrix,type of QQ,type of ZZ)"
 see
lift
 lift to another ring
"lift(Matrix,type of RR_*,type of QQ)"
 see
lift
 lift to another ring
"lift(Matrix,type of RRi_*,type of QQ)"
 see
lift
 lift to another ring
"lift(QQ,type of QQ)"
 see
lift
 lift to another ring
"lift(QQ,type of ZZ)"
 see
lift
 lift to another ring
"lift(RR,type of QQ)"
 see
lift
 lift to another ring
"lift(RRi,type of QQ)"
 see
lift
 lift to another ring
"lngamma(QQ)"
 see
lngamma
 logarithm of the Gamma function
"promote(RR,type of QQ)"
 see
promote
 promote to another ring
"round(QQ)"
 see
round
 round a number
"toCC(QQ)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,QQ)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,QQ,QQ)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,QQ,RR)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,QQ,ZZ)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,RR,QQ)"
 see
toCC
 convert to highprecision complex number
"toCC(ZZ,ZZ,QQ)"
 see
toCC
 convert to highprecision complex number
For the programmer
The object
QQ
is
a
ring
, with ancestor classes
Number
<
Thing
.