簡単化                                                            条件                        
                                                                       
                      ln(a^b) ==> b*ln(a)                     signum(a) = 1 かつ b が real      
                      ln(a^b) ==> b*ln(-a)                    signum(a) = - 1 かつ b が even  
                      ln(a^b) ==> b*ln(a)                     signum(a) = - 1 かつ b が odd     
                      ln(a^b) ==> b/2*ln(a^2)                 a が real かつ b が even          
                      ln(a^b) ==> b*ln(a)                     a が real かつ b が odd           
                                                                       
                      ln(x*y) ==> ln(x) + ln(y)               x>0 かつ signum(y) が 未知       
                      ln(x*y) ==> ln(-x) + ln(-y)             signum(x) = -1                   
                      ln(x*y) ==> ln(-x) + ln(y) + I*Pi       signum(x) = -1 かつ signum(y) = 1
                                                                       
                      ln(exp(x)) ==> x                        x が real                        
                      ln(LambertW(x)) ==> ln(x)+LambertW(x)   x が real                             
                                                                        

n, x, y に、なにも情報が与えられていないため、これらの式に simplify/ln を行っても、簡単化は行われません。簡単化を行うには、上の条件が必要です。

変数に適切な仮定を行い、十分な情報を与えると、正しく簡単化が行われます。

整数因数を含む数式を簡単化する例です。

simplify, combine, assume