We did "not" assume this; the only assumption we made was that the distributions factorize, and the form of the distributions followed naturally.
The special number field sieve can factorize numbers with more than one large factor.
The difficulty with the standard representation is revealed by this formula, which does not factorize into the product of the marginal one-dimensional distributions.
Say we want to factorize an integer "n".
This property seems to be neither fully physical nor fully mental, but nor does it seem to ' factorize ' into more primitive properties which are fully physical or fully mental.
Here, the idea is to use a flat, highly factorized variant of first-order logic with generalized quantifiers as a means for representing analyses from both shallow and deep processing.
However, that is not enough to show that there are no ' mixed ' properties which do not ' factorize ' into more primitive properties which are fully physical or fully mental.
When the dressing is neglected, the u-dependence factorizes out as follows: 1 d s 62!
