class Object

Constants

A
AEF
AFF
B
C
CRT
D
F
F5
Foo
Fx
Fxy

Polynimial is a commutative multi-variable ring

Fy
G

include Algebra

H

> y^7 + (7x + 7)y^6 + 8xy^5 + 4y^4 + (4x + 4)y^3 + 5xy^2 + 7y + x + 1

K

A = Polynomial.create(Rational, “x”) x = A.var B = Polynomial.create(A, “y”) y = B.var C = Polynomial.create(B, “z”) z = C.var D = Polynomial.create(C, “w”) w = D.var p( (x+y+z+w)**4 )

M

M = SquareMatrix(Rational, 8)

M3
M33

include Algebra

M34
M43

m = m0 * m2

M44
MP

Algebra::MPolynomial.instance_eval do

p AUTO_LOAD

end P.instance_eval do

p ['try convert_to', self, AUTO_LOAD]

end

P

P = Polynomial(Z7, “x”, “y”)

P0
PF
PQ

PQ = Polynomial(Rational, “x”)

PS
PZ
Px
Pxy
Py
Pyx
Q
QRx
QRxy
QSx
QZ13x
R

R = MPolynomial(Integer)

Rx
S
S3
Z13
Z13x
Z7

P = MPolynomial(Rational)

Zp

Public Instance Methods

auto_req(*a, &b) click to toggle source
# File lib/algebra/auto-require.rb, line 71
def auto_req(*a, &b)
  Object.auto_req(*a, &b)
end
auto_req_init() click to toggle source
# File lib/algebra/auto-require.rb, line 67
def auto_req_init
  Object.auto_req_init
end
gb(f, sw = false) click to toggle source

include Algebra

# File lib/algebra/groebner-basis.rb, line 162
def gb(f, sw = false)
  f0 = f.first
  print "Basis of: "
  sw ? puts('', *f) : puts(f.join(", "))
  gbase = Algebra::Groebner.reduced_basis(f)
  print "Is: "
  sw ? puts('', *gbase) : puts(gbase.join(", "))
  puts
end
gbc(f) click to toggle source

include Algebra

# File lib/algebra/groebner-basis-coeff.rb, line 182
def gbc(f)
  f0 = f.first
  print 'Basis of: '
  puts(f.join(', '))
  c, g = Algebra::Groebner.basis_coeff(f)
  print 'is: '
  puts(g.join(', '))
  puts 'Coeefitients are: '
  c.each do |x|
    puts x.join(', ')
  end
  p 3333
  p g
  p c.collect { |x| f.inner_product x }

  if g == c.collect { |x| f.inner_product x }
    puts 'Success!'
  else
    puts 'Fail.'
  end
  puts
end
p!(x) click to toggle source
# File lib/algebra/sets-system.rb, line 41
def p!(x); puts x.inspect!; end
test(f) click to toggle source
# File lib/algebra/m-polynomial-factor-int.rb, line 152
def test(f)
  print "#{f}\n  => \n"
  a = f.factorize_int
  sw = (f == a.pi)
  puts "#{a.inspect}, #{sw}"
  raise unless sw
end