zuletzt SPOILER WARNING On 2017-09-05 15:08, Pacher Christoph wrote:
Re[(1-I)I^k] (12chars)
Originalnachricht Von: Bill Gosper Gesendet: Dienstag, 5. September 2017 19:40 An: math-fun@mailman.xmission.com Antwort an: math-fun Betreff: [math-fun] ++--++--...
For alternating sign, multiply by (-1)^k. In[524]:= "(-1)^k" //StringLength Out[524]= 6
Mathematica won't go 5: Syntax::sntxb: Expression cannot begin with "(-)^k".
What's your favorite recipe for ++--++--...?
In[515]:= "(-1)^Floor[k/2]" // StringLength Out[515]= 15
is a little clumsy. But Mathematica accepts Floor brackets:
In[525]:= "(-1)^⎣k/2⎦" // StringLength Out[525]= 10
and then underunderstands Floor: In[518]:= Assuming[k∈Integers, FullSimplify[DiscreteRatio[(-1)^Floor[k/2], k]]]
Out[518]= (-1)^(Floor[k/2] + Floor[(1 + k)/2])
I have ten characters where
In[529]:= FullSimplify[DiscreteRatio[**********, k], k∈Integers] Out[529]= (-1)^k
How about you? --rwg
In[529]:= FullSimplify[DiscreteRatio[I^(k (k - 1)), k], k∈Integers] Out[529]= (-1)^k In[541]:= Table[I^(k (k - 1)), {k, 0, 9}] Out[541]= {1, 1, -1, -1, 1, 1, -1, -1, 1, 1} --rwg