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>>> #
>>> # Some examples from the documentation for the Omega Calculator
>>> # This is the input for figures 2 and 3.
>>> #
>>>
>>> R := { [i] -> [i'] : 1 <= i,i' <= 10 && i' = i+1 };
>>> R;
{[i] -> [i+1] : 1 <= i <= 9}
>>> inverse R;
{[i] -> [i-1] : 2 <= i <= 10}
>>> domain R;
{[i]: 1 <= i <= 9}
>>> range R;
{[i]: 2 <= i <= 10}
>>> R compose R;
{[i] -> [i+2] : 1 <= i <= 8}
>>> R+;
{[i] -> [i'] : 1 <= i < i' <= 10}
>>> # closure of R = R union (R compose R) union (R compose R ...
>>> complement R;
{[i] -> [i'] : i <= 0} union
{[i] -> [i'] : 10 <= i} union
{[i] -> [i'] : 1, i' <= i <= 9} union
{[i] -> [i'] : 1 <= i <= 9, i'-2}
>>> S := {[i] : 5 <= i <= 25};
>>> S;
{[i]: 5 <= i <= 25}
>>> R(S);
{[i]: 6 <= i <= 10}
>>> # apply R to S
>>> R \ S;
{[i] -> [i+1] : 5 <= i <= 9}
>>> # restrict domain of R to S
>>> R / S;
{[i] -> [i+1] : 4 <= i <= 9}
>>> # restrict range of R to S
>>> (R\S) union (R/S);
{[i] -> [i+1] : 4 <= i <= 9}
>>> (R\S) intersection (R/S);
{[i] -> [i+1] : 5 <= i <= 9}
>>> (R/S) - (R\S);
{[4] -> [5] }
>>> S*S;
{[i] -> [i'] : 5 <= i <= 25 && 5 <= i' <= 25}
>>> # cross product
>>> D := S - {[9:16:2]} - {[17:19]};
>>> D;
{[i]: 5 <= i <= 8} union
{[i]: exists ( alpha : 2alpha = i && 10 <= i <= 16)} union
{[i]: 20 <= i <= 25}
>>> T := { [i] : 1 <= i <= 11 & exists (a : i = 2a) };
>>> T;
{[i]: exists ( alpha : 2alpha = i && 2 <= i <= 10)}
>>> Hull T;
{[i]: exists ( alpha : 2alpha = i && 2 <= i <= 10)}
>>> Hull D;
{[i]: 5 <= i <= 25}
>>> codegen D;
for(t1 = 5; t1 <= 8; t1++) {
s0(t1);
}
for(t1 = 10; t1 <= 16; t1 += 2) {
s0(t1);
}
for(t1 = 20; t1 <= 25; t1++) {
s0(t1);
}
>>> codegen {[i,j] : 1 <= i+j,j <= 10};
for(t1 = -9; t1 <= 9; t1++) {
for(t2 = max(1,-t1+1); t2 <= min(-t1+10,10); t2++) {
s0(t1,t2);
}
}
>>>
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