class CAS::Pow
Power function.
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 118 def call(f) CAS::Help.assert(f, Hash) @x.call(f).overloaded_pow(@y.call(f)) end
diff(v)
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Performs the power between two `CAS::Op`
“`
d
—- (f(x)^a) = f(x)^(a - 1) * a * f'(x)
dx d
—- (a^f(x)) = a^f(x) * f'(x) * ln a
dx d
—- (f(x)^g(x)) = (f(x)^g(x)) * (g'(x) * ln f(x) + g(x) * f'(x) / f(x))
dx
“`
* **argument**: `CAS::Op` argument of derivative * **returns**: `CAS::Op` derivative
Calls superclass method
CAS::BinaryOp#diff
# File lib/functions/fnc-base.rb, line 99 def diff(v) diff_x, diff_y = super v if diff_y == CAS::Zero return ((@x ** (@y - 1.0)) * @y * diff_x) elsif diff_x == CAS::Zero return (@x ** @y) * diff_y * CAS.ln(@x) else return (@x ** @y) * ((diff_y * CAS.ln(@x)) + (@y * diff_x / @x)) end end
simplify()
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Same as `CAS::Op`
Simplifcation engine supports:
* 0 ^ y = 0 * x ^ 0 = 1 * a ^ b = c (constants reduction) * x ^ 1 = x * 1 ^ y = 1 * **returns**: `CAS::Op` simplified version
Calls superclass method
CAS::BinaryOp#simplify
# File lib/functions/fnc-base.rb, line 141 def simplify super return self if (@x == CAS::Zero and @y == CAS::Zero) return self if (@x == CAS::Infinity and @y == CAS::Infinity) return self if (@x == CAS::Infinity and @y == CAS::Zero) return self if (@x == CAS::Zero and @y == CAS::Infinity) return CAS::Zero if @x == CAS::Zero return CAS::One if @x == CAS::One return @x if @y == CAS::One return CAS::One if @y == CAS::Zero 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 159 def to_code "(#{@x.to_code} ** #{@y.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 126 def to_s "(#{@x})^(#{@y})" end