It is not so hard to expand bitwise operators to reals, we just need to start the sum from -infinity:
.
But for instance, it is harder to do it with complexes.
Here is a graph of y = x xor pi*x
https://www.dropbox.com/s/51zz9lnzce53vi...).bmp?dl=0
We can iterate them, for exapmple: x iand y = x and x and ... and x, y times.
Here is my pari/gp code:
r kneser.gp
tenyez=2^200;
xor(x,y)={return(bitxor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
or(x,y)={return(bitor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
and(x,y)={return(bitand(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
nand(x,y)={return(bitnegimply(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
not(x)={return(bitneg(round(x*tenyez))/tenyez);}
ixor(x,y)={return(if(y>2,ixor(x,y-1),xor(x,x)))}
ior(x,y)={return(if(y>1,ixor(x,y-1),or(x,x)))}
iand(x,y)={return(if(y>1,ixor(x,y-1),and(x,x)))}
inand(x,y)={return(if(y>1,ixor(x,y-1),nand(x)))}
My question is that: What is the uniterated op of these ones? So I have been looking for operators whose iterated ops are the and, or, nand, xor ... etc.
Any idea?
But for instance, it is harder to do it with complexes.
Here is a graph of y = x xor pi*x
https://www.dropbox.com/s/51zz9lnzce53vi...).bmp?dl=0
We can iterate them, for exapmple: x iand y = x and x and ... and x, y times.
Here is my pari/gp code:
r kneser.gp
tenyez=2^200;
xor(x,y)={return(bitxor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
or(x,y)={return(bitor(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
and(x,y)={return(bitand(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
nand(x,y)={return(bitnegimply(round(x*tenyez),round(y*tenyez))/tenyez*1.0);}
not(x)={return(bitneg(round(x*tenyez))/tenyez);}
ixor(x,y)={return(if(y>2,ixor(x,y-1),xor(x,x)))}
ior(x,y)={return(if(y>1,ixor(x,y-1),or(x,x)))}
iand(x,y)={return(if(y>1,ixor(x,y-1),and(x,x)))}
inand(x,y)={return(if(y>1,ixor(x,y-1),nand(x)))}
My question is that: What is the uniterated op of these ones? So I have been looking for operators whose iterated ops are the and, or, nand, xor ... etc.
Any idea?
Xorter Unizo