I.4.4.1 “deriveScalToScal” method

“deriveScalToScal” method builds a new Result object by performing an operation on all the values of the Result object to which it is applied. Both Result objects correspond to scalar values. The Possible values of the “Method” argument are:

• “sin”: returns $\sin <!--FUNCTION\; APPLICATION-->\left(\text{arg}\right)$ (angle in radians).
• “cos”: returns $\cos <!--FUNCTION\; APPLICATION-->\left(\text{arg}\right)$ (angle in radians).
• “tan”: returns $\tan <!--FUNCTION\; APPLICATION-->\left(\text{arg}\right)$ (angle in radians).
• “asin”: returns ${\sin <!--FUNCTION\; APPLICATION-->}^{-1}\left(\text{arg}\right)$ (angle in radians).
• “acos”: returns ${\cos <!--FUNCTION\; APPLICATION-->}^{-1}\left(\text{arg}\right)$ (angle in radians).
• “atan”: returns ${\tan <!--FUNCTION\; APPLICATION-->}^{-1}\left(\text{arg}\right)$ (angle in radians).
• “exp”: returns $e^{\text{arg}}$.
• “log”: returns ${\text{log}}_e\left(\text{arg}\right)$.
• “exp10”: return $10^{\text{arg}}$.
• “log10”: returns ${\text{log}}_{10}\left(\text{arg}\right)$.
• “abs”: returns $\left|\text{arg}\right|$.
• “inv”: returns $1∕\text{arg}$.
• “sinh”: returns $\text{sinh}\left(\text{arg}\right)$.
• “cosh”: returns $\text{cosh}\left(\text{arg}\right)$.
• “tanh”: returns $\text{tanh}\left(\text{arg}\right)$.
• “sq”: returns ${\text{arg}}^2$.
• “sqrt”: $\sqrt{\text{arg}}$.
• “sgn”: +1, 0 or -1 depending on the value of argument (arg>0, arg==0 or arg<0 respectively).

The method works for Real Results as well as Complex Results. However, some of the methods are not available for Complex Results: “asin”, “acos”, “atan” and “sgn” can be used with Real Results only. Note that when used with a Complex Result object, the method returns a Complex Result object. There is however one exception to this rule: the “abs” derivation method returns a Real Result.