Class: Integer
- Inherits:
-
Object
- Object
- Integer
- Defined in:
- lib/include/integer.rb
Class Method Summary collapse
- .*(other) ⇒ Object
- ./(other) ⇒ Object
- .coerce(other) ⇒ Object
- .one ⇒ Object
- .to_tex ⇒ Object
- .zero ⇒ Object
Instance Method Summary collapse
- #bit_size ⇒ Object
- #combination(r) ⇒ Object (also: #C)
-
#extended_pmod_factorial(prime) ⇒ Object
- Param
- prime Return
-
integer f > 0 and e >= 0 s.t.
-
#factorial ⇒ Object
- Param
- non-negative integer self Return
-
factorial self!.
-
#heptagonal? ⇒ Boolean
- Heptagonal numbers are generated by the formula, P7_n = n * (5 * n - 3) / 2 The first ten heptagonal numbers are: 1, 7, 18, 34, 55 Return
-
integer n s.t.
-
#hexagonal? ⇒ Boolean
Hexagonal numbers are generated by the formula, H_n = n * (2 * n - 1) The first ten hexagonal numbers are: 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, …
- #inverse ⇒ Object
-
#octagonal? ⇒ Boolean
Octagonal numbers are generated by the formula, P8_n = n * (3 * n - 2) The first ten octagonal numbers are: 1, 8, 21, 40, 65, …
-
#pentagonal? ⇒ Boolean
Pentagonal numbers are generated by the formula, P_n = n * (3 * n - 1) / 2.
- #pmod_combination(r, prime) ⇒ Object
-
#pmod_factorial(prime) ⇒ Object
- Param
- prime Return
-
self! mod prime.
-
#power_of?(m) ⇒ Boolean
Boolean whether self is power of m or not.
- #repeated_combination(r) ⇒ Object (also: #H)
-
#square? ⇒ Boolean
- Test whether self is a square number or not Param
- positive integer self Return
-
square root of self if self is square else false.
-
#squarefree? ⇒ Boolean
- Param
- positive integer self Return
-
true if self is squarefree, false otherwise.
-
#to_fs ⇒ Object
- Return
-
formatted string.
-
#triangle? ⇒ Boolean
Triangle numbers are generated by the formula, T_n = n * (n + 1) / 2.
Class Method Details
.*(other) ⇒ Object
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# File 'lib/include/integer.rb', line 11 def *(other) raise ArgumentError unless other.kind_of?(self) Abst::IntegerIdeal.new(other) end |
./(other) ⇒ Object
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# File 'lib/include/integer.rb', line 16 def /(other) if other.kind_of?(Integer) other = Integer * other else raise ArgumentError unless other.kind_of?(Abst::IntegerIdeal) end return residue_class(other) end |
.coerce(other) ⇒ Object
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# File 'lib/include/integer.rb', line 25 def coerce(other) return [self, other] end |
.one ⇒ Object
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# File 'lib/include/integer.rb', line 7 def one return 1 end |
.to_tex ⇒ Object
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# File 'lib/include/integer.rb', line 29 def to_tex return "\\mathbb{Z}" end |
.zero ⇒ Object
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# File 'lib/include/integer.rb', line 3 def zero return 0 end |
Instance Method Details
#bit_size ⇒ Object
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# File 'lib/include/integer.rb', line 34 def bit_size return Abst.ilog2(self) + 1 end |
#combination(r) ⇒ Object Also known as: C
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# File 'lib/include/integer.rb', line 81 def combination(r) r = self - r if self - r < r if r <= 0 return 1 if 0 == r return 0 end rslt = self 2.upto(r) do |i| rslt = rslt * (self - i + 1) / i end return rslt end |
#extended_pmod_factorial(prime) ⇒ Object
- Param
-
prime
- Return
-
integer f > 0 and e >= 0 s.t. prime ** e || self! and f == self! / (prime ** e) % prime
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# File 'lib/include/integer.rb', line 63 def extended_pmod_factorial(prime) q, r = self.divmod prime fac = q.even? ? 1 : prime - 1 fac = fac * r.pmod_factorial(prime) % prime a = nil e = q if prime <= q a, b = q.extended_pmod_factorial(prime) e += b else a = q.pmod_factorial(prime) end fac = fac * a % prime return fac, e end |
#factorial ⇒ Object
- Param
-
non-negative integer self
- Return
-
factorial self!
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# File 'lib/include/integer.rb', line 45 def factorial return 2.upto(self).inject(1, &:*) end |
#heptagonal? ⇒ Boolean
Heptagonal numbers are generated by the formula, P7_n = n * (5 * n - 3) / 2 The first ten heptagonal numbers are:
1, 7, 18, 34, 55
- Return
-
integer n s.t. self == P7_n if exist else false
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# File 'lib/include/integer.rb', line 231 def heptagonal? return false unless r = (self * 40 + 9).square? q, r = (3 + r).divmod(10) return false unless 0 == r return q end |
#hexagonal? ⇒ Boolean
Hexagonal numbers are generated by the formula, H_n = n * (2 * n - 1) The first ten hexagonal numbers are:
1, 6, 15, 28, 45, 66, 91, 120, 153, 190, ...
- Return
-
integer n s.t. self == H_n if exist else false
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# File 'lib/include/integer.rb', line 220 def hexagonal? return false unless r = ((self << 3) + 1).square? return false unless 0 == (1 + r) & 3 return (1 + r) >> 2 end |
#inverse ⇒ Object
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# File 'lib/include/integer.rb', line 49 def inverse return 1 / Rational(self) end |
#octagonal? ⇒ Boolean
Octagonal numbers are generated by the formula, P8_n = n * (3 * n - 2) The first ten octagonal numbers are:
1, 8, 21, 40, 65, ...
- Return
-
integer n s.t. self == P7_n if exist else false
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# File 'lib/include/integer.rb', line 244 def octagonal? return false unless r = (self * 3 + 1).square? q, r = (1 + r).divmod(3) return false unless 0 == r return q end |
#pentagonal? ⇒ Boolean
Pentagonal numbers are generated by the formula, P_n = n * (3 * n - 1) / 2. The first ten pentagonal numbers are:
1, 5, 12, 22, 35, 51, 70, 92, 117, 145, ...
- Return
-
integer n s.t. self == P_n if exist else false
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# File 'lib/include/integer.rb', line 207 def pentagonal? return false unless r = (24 * self + 1).square? q, r = (1 + r).divmod(6) return false unless 0 == r return q end |
#pmod_combination(r, prime) ⇒ Object
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# File 'lib/include/integer.rb', line 98 def pmod_combination(r, prime) f1, e1 = self.extended_pmod_factorial(prime) f2, e2 = r.extended_pmod_factorial(prime) f3, e3 = (self - r).extended_pmod_factorial(prime) return 0 if e2 + e3 < e1 return f1 * Abst.inverse(f2 * f3, prime) % prime end |
#pmod_factorial(prime) ⇒ Object
- Param
-
prime
- Return
-
self! mod prime
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# File 'lib/include/integer.rb', line 55 def pmod_factorial(prime) return 2.upto(self).inject(1) {|r, i| r * i % prime} end |
#power_of?(m) ⇒ Boolean
Returns boolean whether self is power of m or not.
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# File 'lib/include/integer.rb', line 114 def power_of?(m) n = self until 1 == n n, r = n.divmod(m) return false unless 0 == r end return true end |
#repeated_combination(r) ⇒ Object Also known as: H
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# File 'lib/include/integer.rb', line 107 def repeated_combination(r) return (self + r - 1).combination(r) end |
#square? ⇒ Boolean
Test whether self is a square number or not
- Param
-
positive integer self
- Return
-
square root of self if self is square else false
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# File 'lib/include/integer.rb', line 138 def square? check = { 11=>[true, true, false, true, true, true, false, false, false, true, false], 63=>[true, true, false, false, true, false, false, true, false, true, false, false, false, false, false, false, true, false, true, false, false, false, true, false, false, true, false, false, true, false, false, false, false, false, false, false, true, true, false, false, false, false, false, true, false, false, true, false, false, true, false, false, false, false, false, false, false, false, true,false, false, false, false], 64=>[true, true, false, false, true, false, false, false, false, true, false, false, false, false, false, false, true, true, false, false, false, false, false, false, false, true, false, false, false, false, false, false, false, true, false, false, true, false, false, false, false, true, false, false, false, false, false, false,false, true, false, false, false, false, false, false, false, true, false, false, false, false, false, false], 65=>[true, true, false, false, true, false, false, false, false, true, true, false, false, false, true, false, true, false, false, false, false, false, false, false, false, true, true, false, false, true, true, false, false, false, false, true, true, false, false, true, true, false, false, false, false, false, false, false, false, true, false, true, false, false, false, true, true, false, false, false, false, true, false, false, true] } # 64 t = self & 63 return false unless check[64][t] r = self % 45045 # == 63 * 65 * 11 [63, 65, 11].each do |c| return false unless check[c][r % c] end q = Abst.isqrt(self) return false unless q ** 2 == self return q end |
#squarefree? ⇒ Boolean
- Param
-
positive integer self
- Return
-
true if self is squarefree, false otherwise
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# File 'lib/include/integer.rb', line 164 def squarefree? n = self if n.even? return false if 0 == n[1] n >>= 1 end return true if self <= 3 return false if self.square? pl = Abst.primes_list # trial division limit = Abst.isqrt(n) 1.upto(pl.size - 1).each do |i| d = pl[i] return true if limit < d if n % d == 0 n /= d return false if n % d == 0 limit = Abst.isqrt(n) end end d = pl.last + 2 loop do return true if limit < d if n % d == 0 n /= d return false if n % d == 0 limit = Abst.isqrt(n) end d += 2 end end |
#to_fs ⇒ Object
- Return
-
formatted string
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# File 'lib/include/integer.rb', line 39 def to_fs return self.to_s.gsub(/(?<=\d)(?=(\d\d\d)+$)/, ' ') end |
#triangle? ⇒ Boolean
Triangle numbers are generated by the formula, T_n = n * (n + 1) / 2. The first ten triangle numbers are:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
- Return
-
integer n s.t. self == T_n if exist else false
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# File 'lib/include/integer.rb', line 128 def triangle? return false unless r = ((self << 3) + 1).square? return false unless (r - 1).even? return (r - 1) >> 1 end |