Module: SyMath::Operation::DistributiveLaw

Included in:
Value
Defined in:
lib/symath/operation/distributivelaw.rb

Instance Method Summary collapse

Instance Method Details

#combfrac_add_term(sum, t) ⇒ Object 



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# File 'lib/symath/operation/distributivelaw.rb', line 272

def combfrac_add_term(sum, t)
  c = 1
  dc = 1
  fact = 1.to_m
  divf = 1.to_m

  t.factors.each do |f|
    if f.is_number?
      c *= f.value
      next
    end

    if f == -1
      fact *= -1
      next
    end

    if f.is_divisor_factor?
      if f.base.is_number?
        dc *= (f.base.value**f.exponent.argument.value)
      else
        divf *= f.base
      end
      next
    end

    fact *= f
  end

  if !sum.key?(divf)
    sum[divf] = {}
    sum[divf][:fact] = fact
    sum[divf][:c] = c
    sum[divf][:dc] = dc
    return
  end

  s = sum[divf]
  lcm = dc.lcm(s[:dc])

  if lcm > dc
    c *= lcm/dc
    dc = lcm
  end

  if lcm > s[:dc]
    s[:c] *= lcm/s[:dc]
    s[:dc] = lcm
  end

  if fact.nil?
    fact = c.to_m
  elsif c > 1
    fact = fact.mul(c.to_m)
  end

  if s[:fact].nil?
    fact = fact.add(s[:c].to_m) if s[:c] > 1
  else
    fact = fact.add(s[:c] > 1 ? s[:c].to_m*s[:fact] : s[:fact])
  end
  
  s[:fact] = fact
  s[:c] = 1
end

#combfrac_sum ⇒ Object 



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# File 'lib/symath/operation/distributivelaw.rb', line 338

def combfrac_sum
  sum = {}

  terms.each do |t|
    combfrac_add_term(sum, t)
  end

  ret = 0.to_m

  sum.keys.each do |divf|
    s = sum[divf]
    if s[:c] > 1
      r = s[:c].to_m.mul(s[:fact])
    else
      r = s[:fact]
    end

    if divf.nil?
      r = r.div(s[:dc]) if s[:dc] > 1
    elsif s[:dc] > 1
      r = r.div(s[:dc].to_m*divf)
    else
      r = r.div(divf)
    end

    ret += r
    return ret
  end
end

#combine_fractions ⇒ Object

The combine_fractions() method combines fractions by first determining their least common denominator, then applying the distributive law. Examples:

a/c + b/c   -> (a + b)/c
2/3 + 3/4   -> 17/12
a/2 + 2*a/3 -> 7*a/6
2*a/b + 2*c/(3*b) -> (6*a + 2*c)/(3*b)



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# File 'lib/symath/operation/distributivelaw.rb', line 264

def combine_fractions()
  if is_sum_exp?
    return combfrac_sum
  end

  return recurse('combine_fractions', nil)
end

#expand ⇒ Object

The expand() method expands a product using the distributive law over products of sums:

a*(b + c) -> a*b + a*c
a*(b - c) -> a*b - a*c

The transformation iterates until no changes occur. Thus, the expression

(a + b)*(c + d) transforms to a*c + a*d + b*c + b*d



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# File 'lib/symath/operation/distributivelaw.rb', line 11

def expand()
  return iterate('expand_single_pass')
end

#expand_product(exp1, exp2) ⇒ Object 



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# File 'lib/symath/operation/distributivelaw.rb', line 51

def expand_product(exp1, exp2)
  sign = 1.to_m

  if exp1.is_a?(SyMath::Minus)
    exp1 = exp1.argument
    sign = -sign
  end

  if exp2.is_a?(SyMath::Minus)
    exp2 = exp2.argument
    sign = -sign
  end

  ret = 0.to_m
    
  exp1.terms.each do |t1|
    exp2.terms.each do |t2|
      ret += sign*t1*t2
    end
  end

  return ret
end

#expand_single_pass ⇒ Object 



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# File 'lib/symath/operation/distributivelaw.rb', line 15

def expand_single_pass
  if is_a?(SyMath::Minus)
    return -argument.expand_single_pass
  end

  if is_a?(SyMath::Power) or is_a?(SyMath::Product)
    ret = 1.to_m

    factors.each do |f|
      if f.is_a?(SyMath::Power)
        if f.exponent.is_number?
          f.exponent.value.times { ret = expand_product(ret, f.base) }
        else
          ret = expand_product(ret, f)
        end
      else
        ret = expand_product(ret, f)
      end
    end

    return ret
  end

  if is_sum_exp?
    ret = 0.to_m
    
    terms.each do |t|
      ret += t.expand_single_pass
    end

    return ret
  end
  
  return self
end

#factorize ⇒ Object

The factorize() method factorizes a univariate polynomial expression with integer coefficients.



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# File 'lib/symath/operation/distributivelaw.rb', line 226

def factorize()
  if (has_fractional_terms?)
    e = combine_fractions
    if e.is_a?(SyMath::Fraction)
      return e.dividend.factorize_integer_poly.div(e.divisor)
    end
  else
    return factorize_integer_poly
  end
end

#factorize_integer_poly ⇒ Object 



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# File 'lib/symath/operation/distributivelaw.rb', line 237

def factorize_integer_poly()
  dup = SyMath::Poly::DUP.new(self)
  factors = dup.factor
    
  ret = factors[1].map do |f|
    if f[1] != 1
      f[0].to_m.power(f[1])
    else
      f[0].to_m
    end
  end

  if factors[0] != 1
    ret.unshift(factors[0].to_m)
  end

  return ret.inject(:mul)
end

#factorize_simple ⇒ Object

Collect factors which occur in each term.



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# File 'lib/symath/operation/distributivelaw.rb', line 88

def factorize_simple()
  return self if !self.is_sum_exp?

  sfactors = {}
  vfactors = {}
  coeffs = []
  dcoeffs = []
  vectors = []
  
  terms.each_with_index do |t, i|
    c = 1
    dc = 1
    vf = 1.to_m
    
    t.factors.each do |f|
      # Sign
      if f == -1
        c *= -1
        next
      end

      # Constant
      if f.is_number?
        c *= f.value
        next
      end

      if f.is_divisor_factor?
        # Divisor constant
        if f.base.is_number?
          dc *= f.base.value**f.exponent.argument.value
          next
        end

        # Divisor factor
        ex = f.base

        if !sfactors.key?(ex)
          sfactors[ex] = []
        end

        if sfactors[ex][i].nil?
          sfactors[ex][i] = - f.exponent.argument.value
        else
          sfactors[ex][i] -= f.exponent.argument.value
        end
        next
      end

      # Vector factor
      if f.type.is_subtype?(:tensor)
        vf *= f
        next
      end

      # Scalar factor
      if f.exponent.is_number?
        ex = f.base
        n = f.exponent.value
      else
        ex = f
        n = 1
      end
    
      if !sfactors.key?(ex)
        sfactors[ex] = []
      end
    
      sfactors[ex][i] = n.value        
    end
    
    coeffs.push(c)
    dcoeffs.push(dc)
    vectors.push(vf)
  end

  # If there is only one term, there is nothing to factorize
  if coeffs.length == 1
    return self
  end

  # Try to factorize the scalar part
  spart = 1.to_m
  dpart = 1.to_m
  sfactors.each do |ex, pow|
    # Replace nil with 0 and extend array to full length
    pow.map! { |i| i || 0 }
    (coeffs.length - pow.length).times { pow << 0 }

    if pow.max > 0 and pow.min > 0
      f = pow.min
      pow.map! { |i| i - f }
      spart = spart*ex**f
    end
    
    if pow.max < 0 and pow.min < 0
      f = pow.max
      pow.map! { |i| i - f }
      dpart = dpart*ex**(-f)
    end
  end
  
  # Return self if there were no common factors.
  if spart == 1 and dpart == 1
    return self
  end

  # Extract gcd from coeffs and dcoeffs
  gcd_coeffs = coeffs.inject(:gcd)
  gcd_dcoeffs = dcoeffs.inject(:gcd)
  coeffs.map! { |i| i/gcd_coeffs }
  dcoeffs.map! { |i| i/gcd_dcoeffs }
  
  newsum = 0.to_m

  (0..coeffs.length-1).each do |i|
    t = coeffs[i].to_m
    
    sfactors.each do |ex, pow|
      next if pow[i].nil?
      if pow[i] > 0
        t *= ex**pow[i]
      elsif pow[i] < 0
        t /= ex**(-pow[i])
      end
    end

    t /= dcoeffs[i]
    t *= vectors[i]

    newsum += t
  end

  return gcd_coeffs*spart*newsum/(gcd_dcoeffs*dpart)
end

#has_fractional_terms? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/operation/distributivelaw.rb', line 75

def has_fractional_terms?()
  terms.each do |t|
    t.factors.each do |f|
      if f.is_divisor_factor?
        return true
      end
    end
  end

  return false
end