#
# 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;


# 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;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
gist is given known;

codegen is;

# 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;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
gist is given known;

codegen is;

is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+256*alpha && j = i+8*beta)  };
is;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+256*alpha) };
gist is given known;

codegen is;

# 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;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+4*alpha) };
gist is given known;
codegen is;

is := { [i,j] : 1 <= i <= n && i <= j <= n && exists (alpha, beta: i= 1+6*alpha && j = i+4*beta)  };
is;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+6*alpha) };
gist is given known;
codegen is;

# 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;
known := { [i,j] : 1 <= i <= n && exists (alpha: i = 1+12*alpha) };
gist is given known;
codegen is;