Rules for doing modulo 1 arithmetic

[svensl]

I was wondering whether there are any simplification/rules when doing modulo 1 arithmetic.

For example: <a+b>*<c+d> = ? or <a+b>^2=?
Here, <> is the fractional part, i.e <4.2> = 0.2

There is plenty I could find on mod N arithmetic with n>1 but nothing on mod 1.

thanks for any tips.

Svensl

 

[LouisSheffield]

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??