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Workaround? "Simplify" complicates this expression

Anonymous User
Posted 4 months ago
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This gives the simplest answer (True):

Refine[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

This does not:

Simplify[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

My understanding of Refine vs. Simplify comes from this tutorial, which only indicates that Simplify should yield something simpler than Refine:

http://reference.wolfram.com/language/tutorial/UsingAssumptions.html

POSTED BY: Anonymous User
Answer
3 Replies
In[14]:= Simplify[a^b (c^d)^b - a^b c^(d b), b \[Element] Integers && d \[Element] Integers]
Out[14]= 0

In[15]:= $Version
Out[15]= "10.4.1 for Microsoft Windows (64-bit) (April 11, 2016)"
Anonymous User
Anonymous User
Posted 4 months ago

Thanks. That does get me around the problem.

More generally, I am curious why the algorithm used by Simplify prefers anything besides True, if anyone knows. Is there some reason for Simplify not to conform with its description in the tutorial?

POSTED BY: Anonymous User
Answer
Posted 4 months ago
FullSimplify[a^b (c^d)^b == a^b c^(d b), 
 b \[Element] Integers && d \[Element] Integers]

Gives True as well (all I did was replace Simplify with FullSimplify). Generally I just use FullSimplify. It can take a little longer, but many times gets a better result.

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