class CAS::Atan

Representation for the `arctan(x)` function. It is implemented as a `CAS::Op`. It is the inverse of the `tan(x)` function

Public Class Methods

init_simplify_dict() click to toggle source
# File lib/functions/fnc-trig.rb, line 485
def self.init_simplify_dict
  @simplify_dict = {
    CAS::Zero => CAS::Zero,
    CAS::One => (CAS::Pi/4),
    CAS::Infinity => (CAS::Pi/2)
  }
end

Public Instance Methods

call(f) click to toggle source

Call resolves the operation tree in a `Numeric` (if `Fixnum`) or `Float` (depends upon promotions). As input, it requires an hash with `CAS::Variable` or `CAS::Variable#name` as keys, and a `Numeric` as a value

* **argument**: `Hash` with feed dictionary
* **returns**: `Numeric`
# File lib/functions/fnc-trig.rb, line 462
def call(f)
  CAS::Help.assert(f, Hash)
  Math::atan(@x.call(f))
end
diff(v) click to toggle source

Return the derivative of the `arctan(x)` function using the chain rule. The input is a `CAS::Op` because it can handle derivatives with respect to functions.

* **argument**: `CAS::Op` object of the derivative
* **returns**: `CAS::Op` a derivated object, or `CAS::Zero` for constants
# File lib/functions/fnc-trig.rb, line 447
def diff(v)
  if @x.depend? v
    return (@x.diff(v) / (CAS.pow(@x, CAS::Two) + CAS::One))
  else
    return CAS::Zero
  end
end
simplify() click to toggle source

Simplification callback. It simplify the subgraph of each node until all possible simplification are performed (thus the execution time is not deterministic).

* **returns**: `CAS::Op` simplified version
Calls superclass method CAS::Op#simplify
# File lib/functions/fnc-trig.rb, line 479
def simplify
  super
  return @x.x if @x.is_a? CAS::Tan
  return self.simplify_dictionary
end
to_code() click to toggle source

Convert expression to code (internal, for `CAS::Op#to_proc` method)

* **returns**: `String` that represent Ruby code to be parsed in `CAS::Op#to_proc`
# File lib/functions/fnc-trig.rb, line 496
def to_code
  "Math::atan(#{@x.to_code})"
end
to_s() click to toggle source

Convert expression to string

* **returns**: `String` to print on screen
# File lib/functions/fnc-trig.rb, line 470
def to_s
  "atan(#{@x})"
end