Class: SyMath::Definition::Sqrt

Inherits:
Function show all
Defined in:
lib/symath/definition/sqrt.rb

Instance Attribute Summary

Attributes inherited from Operator

#args, #exp

Attributes inherited from SyMath::Definition

#name

Instance Method Summary collapse

Methods inherited from Function

#check_pi_fraction, functions, init_builtin, #is_function?, #latex_format

Methods inherited from Operator

#<=>, #==, #arity, #call, #compose_with_simplify, #dump, #evaluate_call, init_builtin, #is_operator?, #latex_format, operators, #replace, #to_s, #validate_args

Methods inherited from SyMath::Definition

#<=>, #==, #arity, define, defined?, definitions, get, #hash, init_builtin, #inspect, #is_constant?, #is_function?, #is_operator?, #replace, #to_s, undefine, #variables

Methods inherited from Value

#*, #**, #+, #-, #-@, #/, #<, #<=, #<=>, #>, #>=, #^, #add, #base, compose_with_simplify, create, #deep_clone, #div, #dump, #evaluate, #exponent, #factors, #inspect, #inv, #is_divisor_factor?, #is_finite?, #is_nan?, #is_negative?, #is_negative_number?, #is_number?, #is_positive?, #is_prod_exp?, #is_sum_exp?, #is_unit_quaternion?, #is_zero?, #mul, #neg, #power, #reduce, #reduce_modulo_sign, #sign, #sub, #terms, #to_m, #type, #wedge

Methods included from Operation::Exterior

#flat, #hodge, #sharp

Methods included from Operation::Integration

#anti_derivative, #get_linear_constants, initialize, #int_constant, #int_failure, #int_function, #int_inv, #int_pattern, #int_power, #int_product, #int_sum, #integral_bounds

Methods included from Operation::Differential

#_d_wedge, #d, #d_failure, #d_fraction, #d_function, #d_function_def, #d_power, #d_product, initialize

Methods included from Operation

#iterate, #recurse

Methods included from Operation::DistributiveLaw

#combfrac_add_term, #combfrac_sum, #combine_fractions, #expand, #expand_product, #expand_single_pass, #factorize, #factorize_integer_poly, #factorize_simple, #has_fractional_terms?

Methods included from Operation::Normalization

#combine_factors, #compare_factors_and_swap, #normalize, #normalize_matrix, #normalize_power, #normalize_product, #normalize_single_pass, #normalize_sum, #order_product, #product_on_fraction_form, #reduce_constant_factors, #replace_combined_factors, #swap_factors

Methods included from Operation::Match

#build_assoc_op, #match, #match_assoc, #match_replace

Constructor Details

#initialize ⇒ Sqrt

Returns a new instance of Sqrt.



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# File 'lib/symath/definition/sqrt.rb', line 5

def initialize()
  super(:sqrt)
end

Instance Method Details

#description ⇒ Object 



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# File 'lib/symath/definition/sqrt.rb', line 9

def description()
  return 'sqrt(x) - square root'
end

#reduce_call(call) ⇒ Object 



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# File 'lib/symath/definition/sqrt.rb', line 13

def reduce_call(call)
  arg = call.args[0]
  i = 1.to_m

  # Real: sqrt(-n) = NaN
  # Complex: sqrt(-n) = i*sqrt(n)
  if arg.is_a?(SyMath::Minus)
    if SyMath.setting(:complex_arithmetic)
      i = :i.to_m
      arg = -arg
    else
      return :nan.to_m
    end
  end

  if arg.is_number?
    # sqrt(n*n) = n
    # sqrt(-n*n) = i*n
    if (Math.sqrt(arg.value) % 1).zero?
      return i*Math.sqrt(arg.value).to_i
    end
  elsif arg.is_a?(SyMath::Power)
    # sqrt(n**(2*a)) = n^a
    # sqrt(-n**(2*a)) = i*n**a

    # Find coefficient of exponent
    c = 1
    arg.exponent.factors.each do |ef|
      if ef.is_number?
        c *= ef.value
      end
    end
    
    if c.even?
      return i*arg.base**(arg.exponent/2)
    end
  end

  if i != 1
    return i*fn(:sqrt, arg)
  else
    return call
  end
end

#to_latex(args = nil) ⇒ Object 



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# File 'lib/symath/definition/sqrt.rb', line 58

def to_latex(args = nil)
  return '\sqrt{'.to_s + args[0].to_latex + '}'.to_s
end