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)
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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 297 def call(f) CAS::Help.assert(f, Hash) Math::sqrt @x.call(f) end
diff(v)
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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 281 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()
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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 320 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()
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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 332 def to_code "Math::sqrt(#{@x.to_code})" end
to_s()
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Convert expression to string
* **returns**: `String` to print on screen
# File lib/functions/fnc-base.rb, line 306 def to_s "√(#{@x})" end