class CAS::Sqrt

Square Root of a function. Even if it can be implemented as a power function, it is a separated class.

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. In this case it will call the `Fixnum#overloaded_plus`, that is the old plus function.

* **argument**: `Hash` with feed dictionary
* **returns**: `Numeric`
# File lib/functions/fnc-base.rb, line 320
def call(f)
  CAS::Help.assert(f, Hash)

  Math::sqrt @x.call(f)
end
diff(v) click to toggle source

Performs the square root between two `CAS::Op`

“`

d

—- √f(x) = 1/2 * f'(x) * √f(x)

dx

“`

* **argument**: `CAS::Op` argument of derivative
* **returns**: `CAS::Op` derivative
# File lib/functions/fnc-base.rb, line 304
def diff(v)
  if @x.depend? v
    return (@x.diff(v) / (CAS.const(2.0) * CAS.sqrt(@x)))
  else
    return CAS::Zero
  end
end
simplify() click to toggle source

Same as `CAS::Op`

Simplifcation engine supports:

* √(x^z) = x^(z - 1/2)
* √x = 0
* √x = 1
* √a = b (constants reduction)

* **returns**: `CAS::Op` simplified version
Calls superclass method CAS::Op#simplify
# File lib/functions/fnc-base.rb, line 343
def simplify
  super
  return (CAS.pow(@x.x, @x.y - 0.5)).simplify if @x.is_a? CAS::Pow
  return CAS::Zero if @x == CAS::Zero
  return CAS::One if @x == CAS::One
  return CAS.const(self.call({})) if (@x.is_a? CAS::Constant and @y.is_a? CAS::Constant)
  return self
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-base.rb, line 355
def to_code
  "Math::sqrt(#{@x.to_code})"
end
to_s() click to toggle source

Convert expression to string

* **returns**: `String` to print on screen
# File lib/functions/fnc-base.rb, line 329
def to_s
  "√(#{@x})"
end