Re: modulo 1 arithmetic
Think of each value being a sum of an integer and a fractional portion:
i.e. a = aI+aF, etc
Clearly, <a+b> = <(aI+aF)+(bI+bF)> = <(aI+bI)+(aF+bF)> = <aF+bF>
In the case of multiplication, <(cI+cF)*(dI+dF)> = <(cI*dI)+(cI*dF)+(dI*cF)+(cF*dF)> = <(cI*dF)+(dI*cF)+(cF*dF)>
These simplifications aren't much - only one term goes away - but unless you know something extra about c or d, etc., I don't think much more can be done validly. Fascinating question - any other thoughts??