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|
>>> #
>>> # Test gist function and code generation for modular equations
>>> #
>>>
>>> symbolic n;
>>>
>>> # basic gist function
>>> #
>>> R:={[t1,t2]: exists (aa : 2aa = t1 && 2 <= t1 && t1 <= 8)};
>>> known := {[t1,t2]: 1 <= t1 <= 9};
>>> gist R given known;
{[t1,t2]: exists ( alpha : 2alpha = t1)}
>>>
>>>
>>> # test modulo equations by coprime numbers
>>> #
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+4*alpha && j = i+3*beta) };
>>> is;
{[i,j]: exists ( alpha : 3+i = 4j+12alpha && 1 <= i <= j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : j = i+3alpha && i <= j <= n)}
>>>
>>> codegen is;
for(t1 = 1; t1 <= n; t1 += 4) {
for(t2 = t1; t2 <= n; t2 += 3) {
s0(t1,t2);
}
}
>>>
>>> # test modulo equations by numbers in multiple
>>> #
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+4*alpha && j = i+8*beta) };
>>> is;
{[i,j]: exists ( alpha,beta : j = i+8alpha && i = 1+4beta && 1 <= i <= j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : j = i+8alpha && i <= j <= n)}
>>>
>>> codegen is;
for(t1 = 1; t1 <= n; t1 += 4) {
for(t2 = t1; t2 <= n; t2 += 8) {
s0(t1,t2);
}
}
>>>
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+256*alpha && j = i+8*beta) };
>>> is;
{[i,j]: exists ( alpha,beta : j = 1+8alpha && i = 1+256beta && 1 <= i <= j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+256*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : j = 1+8alpha && i <= j <= n)}
>>>
>>> codegen is;
for(t1 = 1; t1 <= n; t1 += 256) {
for(t2 = t1; t2 <= n; t2 += 8) {
s0(t1,t2);
}
}
>>>
>>> # test modulo equations by gcd != 1
>>> #
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+4*alpha && j = i+1+6*beta) };
>>> is;
{[i,j]: exists ( alpha,beta : i+2j = 5+12alpha && i = 1+4beta && 1 <= i < j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : i+2j = 5+12alpha && i < j <= n)}
>>> codegen is;
for(t1 = 1; t1 <= n-1; t1 += 4) {
for(t2 = t1+1; t2 <= n; t2 += 6) {
s0(t1,t2);
}
}
>>>
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+6*alpha && j = i+4*beta) };
>>> is;
{[i,j]: exists ( alpha,beta : 3j = 2+i+12alpha && i = 1+6beta && 1 <= i <= j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+6*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : i+j = 2+4alpha && i <= j <= n)}
>>> codegen is;
for(t1 = 1; t1 <= n; t1 += 6) {
for(t2 = t1; t2 <= n; t2 += 4) {
s0(t1,t2);
}
}
>>>
>>> # gist won't simpilfy to the result we want, but the code generation
>>> # takes care of it
>>> #
>>> is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+12*alpha && j = i+8*beta) };
>>> is;
{[i,j]: exists ( alpha,beta : 3j = 2+i+24alpha && i = 1+12beta && 1 <= i <= j <= n)}
>>> known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+12*alpha) };
>>> gist is given known;
{[i,j]: exists ( alpha : 2+i = 3j+8alpha && i <= j <= n)}
>>> codegen is;
for(t1 = 1; t1 <= n; t1 += 12) {
for(t2 = t1; t2 <= n; t2 += 8) {
s0(t1,t2);
}
}
>>>
|
