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Macaulay2 web site
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
RR * 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
RR + 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
RR - 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
RR / QQ, see
/
-- a binary operator, usually used for division
CC // 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 == ZZ, see
==
-- equality
RR == QQ, see
==
-- equality
ZZ == QQ, see
==
-- equality
abs(QQ), see
abs
-- absolute value function
acos(QQ), see
acos
-- arccosine
agm(CC,QQ), see
agm
-- arithmetic-geometric mean
agm(QQ,CC), see
agm
-- arithmetic-geometric mean
agm(QQ,QQ), see
agm
-- arithmetic-geometric mean
agm(QQ,RR), see
agm
-- arithmetic-geometric mean
agm(QQ,ZZ), see
agm
-- arithmetic-geometric mean
agm(RR,QQ), see
agm
-- arithmetic-geometric mean
agm(ZZ,QQ), see
agm
-- arithmetic-geometric mean
asin(QQ), see
asin
-- arcsine
atan(QQ), see
atan(RR)
-- compute the arctangent of a number
atan2(QQ,QQ), see
atan2(RR,RR)
-- compute an angle of a certain triangle
atan2(QQ,RR), see
atan2(RR,RR)
-- compute an angle of a certain triangle
atan2(QQ,ZZ), see
atan2(RR,RR)
-- compute an angle of a certain triangle
atan2(RR,QQ), see
atan2(RR,RR)
-- compute an angle of a certain triangle
atan2(ZZ,QQ), see
atan2(RR,RR)
-- compute an angle of a certain triangle
BesselJ(ZZ,QQ), see
BesselJ
-- Bessel function of the first kind
BesselY(ZZ,QQ), see
BesselY
-- Bessel function of the second kind
QQ * BettiTally, see
BettiTally
-- the class of all Betti tallies
cos(QQ), see
cos
-- compute the cosine
cosh(QQ), see
cosh
-- compute the hyperbolic cosine
cot(QQ), see
cot
-- cotangent
coth(QQ), see
coth
-- hyperbolic cotangent
csc(QQ), see
csc
-- cosecant
csch(QQ), see
csch
-- hyperbolic cosecant
eint(QQ), see
eint
-- exponential integral
erf(QQ), see
erf
-- error function
erfc(QQ), see
erfc
-- complementary error function
exp(QQ), see
exp
-- exponential function
expm1(QQ), see
expm1
-- exponential minus 1
factor(QQ), see
factor(RingElement)
-- factor a ring element
floor(QQ), see
floor
-- floor function
Gamma(QQ), see
Gamma
-- Gamma function
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 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(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
lngamma(QQ), see
lngamma
-- logarithm of the Gamma function
log(QQ), see
log
-- logarithm function
log(QQ,CC), see
log
-- logarithm function
log(QQ,QQ), see
log
-- logarithm function
log(QQ,RR), see
log
-- logarithm function
log(QQ,ZZ), see
log
-- logarithm function
log(RR,QQ), see
log
-- logarithm function
log(ZZ,QQ), see
log
-- logarithm function
log1p(QQ), see
log1p
-- logarithm of 1+x
promote(RR,type of QQ), see
promote
-- promote to another ring
round(QQ), see
round
-- round a number
sec(QQ), see
sec
-- secant
sech(QQ), see
sech
-- hyperbolic secant
sin(QQ), see
sin
-- compute the sine
sinh(QQ), see
sinh
-- compute the hyperbolic sine
sqrt(QQ), see
sqrt
-- square root function
tan(QQ), see
tan
-- compute the tangent
tanh(QQ), see
tanh
-- compute the hyperbolic tangent
toCC(QQ), see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ), see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,QQ), see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,RR), see
toCC
-- convert to high-precision complex number
toCC(ZZ,QQ,ZZ), see
toCC
-- convert to high-precision complex number
toCC(ZZ,RR,QQ), see
toCC
-- convert to high-precision complex number
toCC(ZZ,ZZ,QQ), see
toCC
-- convert to high-precision complex number
zeta(QQ), see
zeta
-- Riemann zeta function
For the programmer
The object
QQ
is
a
ring
, with ancestor classes
Number
<
Thing
.