Rational Number Arithmetic

Source: R/rational-add.R, R/rational-multiply.R, R/rational-divide.R, and 5 more

Rational Number Arithmetic

# S4 method for rationalS4,rationalS4
+(e1, e2)

# S4 method for integer,rationalS4
+(e1, e2)

# S4 method for rationalS4,integer
+(e1, e2)

# S4 method for numeric,rationalS4
+(e1, e2)

# S4 method for rationalS4,numeric
+(e1, e2)

# S3 method for rationalS3
+(e1, e2)

# S3 method for rationalR6
+(e1, e2)

# S4 method for rationalS4,rationalS4
*(e1, e2)

# S4 method for integer,rationalS4
*(e1, e2)

# S4 method for rationalS4,integer
*(e1, e2)

# S4 method for numeric,rationalS4
*(e1, e2)

# S4 method for rationalS4,numeric
*(e1, e2)

# S3 method for rationalS3
*(e1, e2)

# S3 method for rationalR6
*(e1, e2)

# S4 method for rationalS4,rationalS4
/(e1, e2)

# S4 method for integer,rationalS4
/(e1, e2)

# S4 method for rationalS4,integer
/(e1, e2)

# S4 method for numeric,rationalS4
/(e1, e2)

# S4 method for rationalS4,numeric
/(e1, e2)

# S3 method for rationalS3
/(e1, e2)

# S3 method for rationalR6
/(e1, e2)

# S4 method for rationalS4,rationalS4
^(e1, e2)

# S4 method for rationalS4,integer
^(e1, e2)

# S4 method for integer,rationalS4
^(e1, e2)

# S4 method for rationalS4,numeric
^(e1, e2)

# S4 method for numeric,rationalS4
^(e1, e2)

# S3 method for rationalS3
^(e1, e2)

# S3 method for rationalR6
^(e1, e2)

# S4 method for rationalS4,rationalS4
%/%(e1, e2)

# S4 method for integer,rationalS4
%/%(e1, e2)

# S4 method for rationalS4,integer
%/%(e1, e2)

# S4 method for numeric,rationalS4
%/%(e1, e2)

# S4 method for rationalS4,numeric
%/%(e1, e2)

# S3 method for rationalS3
%/%(e1, e2)

# S3 method for rationalR6
%/%(e1, e2)

# S4 method for rationalS4,rationalS4
%%(e1, e2)

# S4 method for integer,rationalS4
%%(e1, e2)

# S4 method for rationalS4,integer
%%(e1, e2)

# S4 method for numeric,rationalS4
%%(e1, e2)

# S4 method for rationalS4,numeric
%%(e1, e2)

# S3 method for rationalS3
%%(e1, e2)

# S3 method for rationalR6
%%(e1, e2)

# S4 method for rationalS4,rationalS4
-(e1, e2)

# S4 method for integer,rationalS4
-(e1, e2)

# S4 method for rationalS4,integer
-(e1, e2)

# S4 method for numeric,rationalS4
-(e1, e2)

# S4 method for rationalS4,numeric
-(e1, e2)

# S3 method for rationalS3
-(e1, e2)

# S3 method for rationalR6
-(e1, e2)

Arguments

e1

rational numbers, integers, or numerics
e2

rational numbers, integers, or numerics

Fields

add

for R6 classes, using the $add(e1) to do addition is the fastest method

Examples

  a <- rational(1L,2L,"S4")
  b <- rational(3L,5L,"S4")
  d <- a + b
  stopifnot(d@n == 11)
  stopifnot(d@d == 10)
  a <- 7L
  b <- rational(3L,5L,"S4")
  d <- a + b
  stopifnot(d@n == 38)
  stopifnot(d@d == 5)
  a <- rational(1L,2L,"S4")
  b <- 7L
  d <- a + b
  stopifnot(d@n == 15)
  stopifnot(d@d == 2)
  a <- 7
  b <- rational(3L,5L,"S4")
  d <- a + b
  stopifnot(abs(d - 7.6) < 1E-12)
  a <- rational(1L,2L,"S4")
  b <- 7
  d <- a + b
  stopifnot(abs(d - 7.5) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- a + b
  stopifnot(d$n == 11)
  stopifnot(d$d == 10)
  a <- 7L
  b <- rational(3L,5L,"S3")
  d <- a + b
  stopifnot(d$n == 38)
  stopifnot(d$d == 5)
  a <- rational(1L,2L,"S3")
  b <- 7L
  d <- a + b
  stopifnot(d$n == 15)
  stopifnot(d$d == 2)
  a <- 7
  b <- rational(3L,5L,"S3")
  d <- a + b
  stopifnot(abs(d - 7.6) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- 7
  d <- a + b
  stopifnot(abs(d - 7.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- a + b
  stopifnot(d$getNumerator() == 11)
  stopifnot(d$getDenominator() == 10)
  a <- 7L
  b <- rational(3L,5L,"R6")
  d <- a + b
  stopifnot(d$getNumerator() == 38)
  stopifnot(d$getDenominator() == 5)
  a <- rational(1L,2L,"R6")
  b <- 7L
  d <- a + b
  stopifnot(d$getNumerator() == 15)
  stopifnot(d$getDenominator() == 2)
  a <- 7
  b <- rational(3L,5L,"R6")
  d <- a + b
  stopifnot(abs(d - 7.6) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- 7
  d <- a + b
  stopifnot(abs(d - 7.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  a$add(b)
#> [1] "(11 / 10) = 1.1"
  stopifnot(a$getNumerator() == 11)
  stopifnot(a$getDenominator() == 10)
  a <- rational(1L,2L,"R6")
  b <- 7L
  a$add(b)
#> [1] "(15 / 2) = 7.5"
  stopifnot(a$getNumerator() == 15)
  stopifnot(a$getDenominator() == 2)
  a <- rational(1L,2L,"S4")
  b <- rational(3L,5L,"S4")
  d <- a * b
  stopifnot(d@n == 3)
  stopifnot(d@d == 10)
  a <- 7L
  b <- rational(3L,5L,"S4")
  d <- a * b
  stopifnot(d@n == 21)
  stopifnot(d@d == 5)
  a <- rational(1L,2L,"S4")
  b <- 7L
  d <- a * b
  stopifnot(d@n == 7)
  stopifnot(d@d == 2)
  a <- 7
  b <- rational(3L,5L,"S4")
  d <- a * b
  stopifnot(abs(d - 4.2) < 1E-12)
  a <- rational(1L,2L,"S4")
  b <- 7
  d <- a * b
  stopifnot(abs(d - 3.5) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- a * b
  stopifnot(d$n == 3)
  stopifnot(d$d == 10)
  a <- 7L
  b <- rational(3L,5L,"S3")
  d <- a * b
  stopifnot(d$n == 21)
  stopifnot(d$d == 5)
  a <- rational(1L,2L,"S3")
  b <- 7L
  d <- a * b
  stopifnot(d$n == 7)
  stopifnot(d$d == 2)
  a <- 7
  b <- rational(3L,5L,"S3")
  d <- a * b
  stopifnot(abs(d - 4.2) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- 7
  d <- a * b
  stopifnot(abs(d - 3.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- a * b
  stopifnot(d$getNumerator() == 3)
  stopifnot(d$getDenominator() == 10)
  a <- 7L
  b <- rational(3L,5L,"R6")
  d <- a * b
  stopifnot(d$getNumerator() == 21)
  stopifnot(d$getDenominator() == 5)
  a <- rational(1L,2L,"R6")
  b <- 7L
  d <- a * b
  stopifnot(d$getNumerator() == 7)
  stopifnot(d$getDenominator() == 2)
  a <- 7
  b <- rational(3L,5L,"R6")
  d <- a * b
  stopifnot(abs(d - 4.2) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- 7
  d <- a * b
  stopifnot(abs(d - 3.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  a$multiply(b)
#> [1] "(3 / 10) = 0.3"
  stopifnot(a$getNumerator() == 3)
  stopifnot(a$getDenominator() == 10)
  a <- rational(1L,2L,"R6")
  b <- 7L
  a$multiply(b)
#> [1] "(7 / 2) = 3.5"
  stopifnot(a$getNumerator() == 7)
  stopifnot(a$getDenominator() == 2)
  a <- rational(1L,2L,"S4")
  b <- rational(3L,5L,"S4")
  d <- a / b
  stopifnot(d@n == 5)
  stopifnot(d@d == 6)
  a <- 7L
  b <- rational(3L,5L,"S4")
  d <- a / b
  stopifnot(d@n == 35)
  stopifnot(d@d == 3)
  a <- rational(1L,2L,"S4")
  b <- 7L
  d <- a / b
  stopifnot(d@n == 1)
  stopifnot(d@d == 14)
  a <- 7
  b <- rational(3L,5L,"S4")
  d <- a / b
  stopifnot(abs(d - 7*5/3) < 1E-12)
  a <- rational(1L,2L,"S4")
  b <- 7
  d <- a / b
  stopifnot(abs(d - 1/14) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- a / b
  stopifnot(d$n == 5)
  stopifnot(d$d == 6)
  a <- 7L
  b <- rational(3L,5L,"S3")
  d <- a / b
  stopifnot(d$n == 35)
  stopifnot(d$d == 3)
  a <- rational(1L,2L,"S3")
  b <- 7L
  d <- a / b
  stopifnot(d$n == 1)
  stopifnot(d$d == 14)
  a <- 7
  b <- rational(3L,5L,"S3")
  d <- a / b
  stopifnot(abs(d - 7*5/3) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- 7
  d <- a / b
  stopifnot(abs(d - 1/14) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- a / b
  stopifnot(d$getNumerator() == 5)
  stopifnot(d$getDenominator() == 6)
  a <- 7L
  b <- rational(3L,5L,"R6")
  d <- a / b
  stopifnot(d$getNumerator() == 35)
  stopifnot(d$getDenominator() == 3)
  a <- rational(1L,2L,"R6")
  b <- 7L
  d <- a / b
  stopifnot(d$getNumerator() == 1)
  stopifnot(d$getDenominator() == 14)
  a <- 7
  b <- rational(3L,5L,"R6")
  d <- a / b
  stopifnot(abs(d - 7*5/3) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- 7
  d <- a / b
  stopifnot(abs(d - 1/14) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  a$divide(b)
#> [1] "(5 / 6) = 0.833333333333333"
  stopifnot(a$getNumerator() == 5)
  stopifnot(a$getDenominator() == 6)
  a <- rational(1L,2L,"R6")
  b <- 7L
  a$divide(b)
#> [1] "(1 / 14) = 0.0714285714285714"
  stopifnot(a$getNumerator() == 1)
  stopifnot(a$getDenominator() == 14)
  a <- rational(1L,2L,"S4")
  b <- rational(3L,5L,"S4")
  a ^ b
#> [1] 0.659754
  a <- rational(1L,2L,"S4")
  b <- 3L
  a ^ b
#> (1 / 8) = 0.125
  a <- 2L
  b <- rational(3L,5L,"S4")
  a ^ b
#> [1] 1.515717
  a <- rational(1L,2L,"S4")
  b <- 1.5
  a ^ b
#> [1] 0.3535534
  a <- 3.1
  b <- rational(3L,5L,"S4")
  a ^ b
#> [1] 1.971592
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- 3L
  e <- 1.5
  a ^ b
#> [1] 0.659754
  d ^ b
#> [1] 1.933182
  a ^ d
#> [1] "(1 / 8) = 0.125"
  e ^ b
#> [1] 1.275425
  d ^ e
#> [1] 5.196152
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- 3L
  e <- 1.5
  a ^ b
#> [1] 0.659754
  d ^ b
#> [1] 1.933182
  a ^ d
#> [1] "(1 / 8) = 0.125"
  e ^ b
#> [1] 1.275425
  d ^ e
#> [1] 5.196152
  a <- rational(3L,1L,"S4")
  b <- rational(2L,1L,"S4")
  a %/% b
#> [1] 1
  a <- 3L
  b <- rational(2L,1L,"S4")
  a %/% b
#> [1] 1
  a <- rational(3L,1L,"S4")
  b <- 2L
  a %/% b
#> [1] 1
  a <- 3.5
  b <- rational(2L,1L,"S4")
  a %/% b
#> [1] 1
  a <- rational(3L,1L,"S4")
  b <- 2.1
  a %/% b
#> [1] 1
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- 3L
  e <- 1.5
  a %/% b
#> [1] 0
  d %/% b
#> [1] 5
  a %/% d
#> [1] 0
  e %/% b
#> [1] 2
  d %/% e
#> [1] 2
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- 3L
  e <- 1.5
  a %/% b
#> [1] 0
  d %/% b
#> [1] 5
  a %/% d
#> [1] 0
  e %/% b
#> [1] 2
  d %/% e
#> [1] 2
a <- rational(5L, 1L, "S4")
b <- rational(2L, 1L, "S4")
d <- rational(3L, 2L, "S4")
e <- rational(1L, 2L, "S4")
stopifnot(rational(1L, 1L, "S4") == a %% b)
stopifnot(rational(0L, 1L, "S4") == d %% e)
stopifnot(rational(1L, 1L, "S4") == 5L %% b)
stopifnot(rational(1L, 1L, "S4") == a %% 2L)
stopifnot(rational(0L, 1L, "S4") == 2L %% e)
stopifnot(1 == 5 %% b)
stopifnot(1 == a %% 2)
a <- rational(5L, 1L, "S3")
b <- rational(2L, 1L, "S3")
d <- rational(3L, 2L, "S3")
e <- rational(1L, 2L, "S3")
stopifnot(rational(1L, 1L, "S3") == a %% b)
stopifnot(rational(0L, 1L, "S3") == d %% e)
stopifnot(rational(1L, 1L, "S3") == 5L %% b)
stopifnot(rational(1L, 1L, "S3") == a %% 2L)
stopifnot(rational(0L, 1L, "S3") == 2L %% e)
stopifnot(1 == 5 %% b)
stopifnot(1 == a %% 2)
a <- rational(5L, 1L, "R6")
b <- rational(2L, 1L, "R6")
d <- rational(3L, 2L, "R6")
e <- rational(1L, 2L, "R6")
stopifnot(rational(1L, 1L, "R6") == a %% b)
stopifnot(rational(0L, 1L, "R6") == d %% e)
stopifnot(rational(1L, 1L, "R6") == 5L %% b)
stopifnot(rational(1L, 1L, "R6") == a %% 2L)
stopifnot(rational(0L, 1L, "R6") == 2L %% e)
stopifnot(1 == 5 %% b)
stopifnot(1 == a %% 2)
  a <- rational(1L,2L,"S4")
  b <- rational(3L,5L,"S4")
  d <- a - b
  stopifnot(d@n == -1)
  stopifnot(d@d == 10)
  a <- 7L
  b <- rational(3L,5L,"S4")
  d <- a - b
  stopifnot(d@n == 32)
  stopifnot(d@d == 5)
  a <- rational(1L,2L,"S4")
  b <- 7L
  d <- a - b
  stopifnot(d@n == -13)
  stopifnot(d@d == 2)
  a <- 7
  b <- rational(3L,5L,"S4")
  d <- a - b
  stopifnot(abs(d - 6.4) < 1E-12)
  a <- rational(1L,2L,"S4")
  b <- 7
  d <- a - b
  stopifnot(abs(d - -6.5) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- rational(3L,5L,"S3")
  d <- a - b
  stopifnot(d$n == -1)
  stopifnot(d$d == 10)
  a <- 7L
  b <- rational(3L,5L,"S3")
  d <- a - b
  stopifnot(d$n == 32)
  stopifnot(d$d == 5)
  a <- rational(1L,2L,"S3")
  b <- 7L
  d <- a - b
  stopifnot(d$n == -13)
  stopifnot(d$d == 2)
  a <- 7
  b <- rational(3L,5L,"S3")
  d <- a - b
  stopifnot(abs(d - 6.4) < 1E-12)
  a <- rational(1L,2L,"S3")
  b <- 7
  d <- a - b
  stopifnot(abs(d - -6.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  d <- a - b
  stopifnot(d$getNumerator() == -1)
  stopifnot(d$getDenominator() == 10)
  a <- 7L
  b <- rational(3L,5L,"R6")
  d <- a - b
  stopifnot(d$getNumerator() == 32)
  stopifnot(d$getDenominator() == 5)
  a <- rational(1L,2L,"R6")
  b <- 7L
  d <- a - b
  stopifnot(d$getNumerator() == -13)
  stopifnot(d$getDenominator() == 2)
  a <- 7
  b <- rational(3L,5L,"R6")
  d <- a - b
  stopifnot(abs(d - 6.4) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- 7
  d <- a - b
  stopifnot(abs(d - -6.5) < 1E-12)
  a <- rational(1L,2L,"R6")
  b <- rational(3L,5L,"R6")
  a$subtract(b)
#> [1] "(-1 / 10) = -0.1"
  stopifnot(a$getNumerator() == -1)
  stopifnot(a$getDenominator() == 10)
  a <- rational(1L,2L,"R6")
  b <- 7L
  a$subtract(b)
#> [1] "(-13 / 2) = -6.5"
  stopifnot(a$getNumerator() == -13)
  stopifnot(a$getDenominator() == 2)