static bool BoundVariable <TVar, TInterval>
(IntervalContextBase <TInterval, Rational> ctx, Rational a, TInterval xIntervalOld, TInterval boundingInterval, TVar x,
IDictionary <TVar, Sequence <TInterval> > result, out bool isBottom,
Func <Rational, TInterval> upperBounded, Func <Rational, TInterval> lowerBounded)
where TVar : IEquatable <TVar>
where TInterval : IntervalBase <TInterval, Rational>
{
isBottom = false;
if (a.IsZero)
{
TInterval boundingForVariable;
if (a.Sign > 0L)
{
boundingForVariable = upperBounded(boundingInterval.UpperBound);
}
else
{
boundingForVariable = lowerBounded(boundingInterval.LowerBound);
}
var refined = xIntervalOld.Meet(boundingForVariable);
if (refined.IsBottom)
{
isBottom = true;
return(true);
}
AddToResult(result, x, refined);
}
return(false);
}
static IDictionary <TVar, Sequence <TInterval> > TestTrueLessEqualThan_AxByLtK <TEnv, TVar, TExpr, TInterval>
(Polynomial <TVar, TExpr> poly, TEnv env, IDictionary <TVar, Sequence <TInterval> > result, out bool isBottom)
where TEnv : IIntervalEnvironment <TVar, TExpr, TInterval, Rational>
where TVar : IEquatable <TVar>
where TInterval : IntervalBase <TInterval, Rational>
{
// ax + by <= k
var ax = poly.Left[0];
var by = poly.Left[1];
TVar x, y;
ax.IsSingleVariable(out x);
by.IsSingleVariable(out y);
var k = poly.Right[0].Coeff;
var a = ax.Coeff;
var b = by.Coeff;
var aInterval = env.Context.For(a);
var bInterval = env.Context.For(b);
var kInterval = env.Context.For(k);
var xInterval = env.Eval(x);
var yInterval = env.Eval(y);
IntervalContextBase <TInterval, Rational> ctx = env.Context;
Func <Rational, TInterval> upperBounded =
(i) => ctx.For(Rational.MinusInfinity, !i.IsInteger ? i.PreviousInt32 : i - 1L);
Func <Rational, TInterval> lowerBounded =
(i) => ctx.For(!i.IsInteger ? i.NextInt32 : i + 1L, Rational.PlusInfinity);
// x <= (k - (b * y)) / a;
var boundingInterval = ctx.Div(ctx.Sub(kInterval, ctx.Mul(bInterval, yInterval)), aInterval);
if (BoundVariable(ctx, a, xInterval, boundingInterval, x, result, out isBottom, upperBounded, lowerBounded))
{
return(result);
}
// y <= (k - (a * x)) / b;
boundingInterval = ctx.Div(ctx.Sub(kInterval, ctx.Mul(aInterval, xInterval)), bInterval);
if (BoundVariable(ctx, b, yInterval, boundingInterval, y, result, out isBottom, upperBounded, lowerBounded))
{
return(result);
}
return(result);
}
