combine integer powers in a product
The combine(e,'icombine') function tries to combine products of powers of integers in such a way that the bases of the powers in the resulting product have no common factors. It does not, however, necessarily rewrite a product of integer powers as a product of prime powers.
More generally, powers of rational numbers are rewritten in such a way that if abe and cdf are two distinct rational powers in the resulting product, with a,b,c,d∈ℤ and gcd⁡a,b=1=gcd⁡c,d, then gcd⁡a⁢b,c⁢d=1.
In addition, the following simplifications are performed:
Nested powers abc are combined as ab⁢c if a∈ℚ and one of the following conditions is satisfied:
b∈ℚ and a<0or−1<b<1
Powers whose exponents are rational multiples of each other are combined into a single power, whose base may be a rational number greater than 1.
Every rational base b>1 is made power-free, i.e., if there is a rational number a>1 and a positive integer n satisfying an=b, then n=1 and a=b.
Unless there is only a single power of a rational number and that base is negative, powers of −1 are pulled out of all rational powers.
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