Class: SyMath::Definition::Trig

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

Direct Known Subclasses

Cos, Cot, Csc, Sec, Sin, Tan

Constant Summary collapse

@@trig_reductions = 
{}

Instance Attribute Summary

Attributes inherited from Operator

#args, #exp

Attributes inherited from SyMath::Definition

#description, #name

Class Method Summary collapse

Instance Method Summary collapse

Methods inherited from Function

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

Methods inherited from Operator

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

Methods inherited from SyMath::Definition

#<=>, #==, #arity, define, defined?, definitions, get, #hash, init_builtin, #initialize, #inspect, #is_constant?, #is_function?, #is_operator?, #reduce_call, #replace, #to_latex, #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, #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

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

This class inherits a constructor from SyMath::Definition::Operator

Class Method Details

.initialize ⇒ Object 



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# File 'lib/symath/definition/trig.rb', line 7

def self.initialize()
  sqrt3 = fn(:sqrt, 3)
  sqrt2 = fn(:sqrt, 2)

  @@trig_reductions = {
    :sin_div6 => [ 0.to_m,   1.to_m/2,     sqrt3/2,
                   1.to_m,   sqrt3/2,      1.to_m/2,
                   0.to_m,  -(1.to_m/2),  -(sqrt3/2),
                   -1.to_m,  -(sqrt3/2),   -(1.to_m/2)],
  
    :sin_div4 => [ 0.to_m,   sqrt2/2,
                   1.to_m,   sqrt2/2,
                   0.to_m,  -(sqrt2/2),
                   -1.to_m,  -(sqrt2/2)],
  
    :sec_div6 => [ 1.to_m,    2.to_m*sqrt3/3,     2.to_m,
                   nil,      -2.to_m,            -(2.to_m*sqrt3/2),
                   -1.to_m,   -(2.to_m*sqrt3/3),  -2.to_m,
                   nil,       2.to_m,             2.to_m*sqrt3/3],
  
    :sec_div4 => [ 1.to_m,   sqrt2/2,
                   nil,     -(sqrt2/2),
                   -1.to_m,  -(sqrt2/2),
                   nil,      sqrt2/2],
    
    :tan_div6 => [0.to_m,   sqrt3/3,   sqrt3,
                  nil,     -sqrt3,    -(sqrt3/3)],
  
    :tan_div4 => [0.to_m,   1.to_m,
                  nil,     -1.to_m],
  }
end

Instance Method Details

#reduce_sec_and_csc(f, off) ⇒ Object 



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# File 'lib/symath/definition/trig.rb', line 76

def reduce_sec_and_csc(f, off)
  c, dc = check_pi_fraction(f.args[0], false)
  return f if c.nil?

  # Divisor is divisible by 6
  if 6 % dc == 0
    ret = @@trig_reductions[:sec_div6][(off*3 + c*6/dc) % 12]
    return ret.nil? ? f : ret
  end

  # Divisor is divisible by 4
  if 4 % dc == 0
    ret = @@trig_reductions[:sec_div4][(off*2 + c*4/dc) % 8]
    return ret.nil? ? f : ret
  end

  return f
end

#reduce_sin_and_cos(f, off) ⇒ Object 



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# File 'lib/symath/definition/trig.rb', line 40

def reduce_sin_and_cos(f, off)
  c, dc = check_pi_fraction(f.args[0], false)
  return f if c.nil?

  # Divisor is divisible by 6
  if 6 % dc == 0
    return @@trig_reductions[:sin_div6][(off*3 + c*6/dc) % 12]
  end

  # Divisor is divisible by 4
  if 4 % dc == 0
    return @@trig_reductions[:sin_div4][(off*2 + c*4/dc) % 8]
  end

  return f
end

#reduce_tan_and_cot(f, off, sign) ⇒ Object 



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# File 'lib/symath/definition/trig.rb', line 57

def reduce_tan_and_cot(f, off, sign)
  c, dc = check_pi_fraction(f.args[0], false)
  return f if c.nil?

  # Divisor is divisible by 6
  if 6 % dc == 0
    ret = @@trig_reductions[:tan_div6][(off*3 + sign*c*6/dc) % 6]
    return ret.nil? ? f : ret
  end

  # Divisor is divisible by 4
  if 4 % dc == 0
    ret = @@trig_reductions[:tan_div4][(off*2 + sign*c*4/dc) % 4]
    return ret.nil? ? f : ret
  end

  return f
end