public static IDictionary <TVar, Sequence <TInterval> > GreaterEqualThanZero <TEnv, TVar, TExpr, TInterval>
(TExpr expr, IExpressionDecoder <TVar, TExpr> decoder, TEnv env)
where TEnv : IIntervalEnvironment <TVar, TExpr, TInterval, Rational>
where TVar : IEquatable <TVar>
where TInterval : IntervalBase <TInterval, Rational>
{
var result = new Dictionary <TVar, Sequence <TInterval> > ();
var variable = decoder.UnderlyingVariable(expr);
AddToResult(result, variable, env.Eval(expr).Meet(env.Context.Positive));
if (!decoder.IsVariable(expr))
{
Polynomial <TVar, TExpr> zeroPoly; // poly(0)
if (!Polynomial <TVar, TExpr> .TryToPolynomial(new[] { Monomial <TVar> .From(Rational.Zero) }, out zeroPoly))
{
throw new AbstractInterpretationException(
"It can never be the case that the conversion of a list of monomials into a polynomial fails.");
}
Polynomial <TVar, TExpr> exprPoly; // poly(expr)
Polynomial <TVar, TExpr> fullPoly; // '0 <= poly(expr)' polynome
if (Polynomial <TVar, TExpr> .TryBuildFrom(expr, decoder, out exprPoly) &&
Polynomial <TVar, TExpr> .TryToPolynomial(ExpressionOperator.LessEqualThan, zeroPoly, exprPoly, out fullPoly) &&
fullPoly.IsIntervalForm)
{
var k = fullPoly.Left[0].Coeff; // k != 0
TVar x;
fullPoly.Left[0].IsSingleVariable(out x);
Rational constraint;
if (Rational.TryDivide(fullPoly.Right[0].Coeff, k, out constraint))
{
TInterval interval;
if (k > 0L) // +x <= constraint
{
interval = env.Eval(x).Meet(env.Context.For(Rational.MinusInfinity, constraint));
}
else // -x <= -constraint ==> x >= constraint
{
interval = env.Eval(x).Meet(env.Context.For(constraint, Rational.PlusInfinity));
}
AddToResult(result, x, interval);
}
}
}
return(result);
}
/// <summary>
/// Get constraints for variables from polynome in form 'a*x <= k'
/// </summary>
/// <param name="poly">Polynome in canonical form. Two monomes involved. </param>
static IDictionary <TVar, Sequence <TInterval> > TestTrueLessEqualThan_AxLtK <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>
{
isBottom = false;
var ax = poly.Left[0];
var k = poly.Right[1];
if (ax.IsConstant)
{
if (ax.Coeff >= k.Coeff)
{
isBottom = true;
return(result);
}
}
else
{
TVar x;
ax.IsSingleVariable(out x);
Rational div;
if (Rational.TryDivide(k.Coeff, ax.Coeff, out div))
{
var intv = env.Eval(x);
var boundByDivPlus = !div.IsInteger
? env.Context.For(div.NextInt32, Rational.PlusInfinity)
: env.Context.For(div + 1L, Rational.PlusInfinity);
var boundByDivMinus = !div.IsInteger
? env.Context.For(Rational.MinusInfinity, div.NextInt32 - 1L)
: env.Context.For(Rational.MinusInfinity, div - 1L);
var refined = intv.Meet(ax.Coeff.Sign < 1 ? boundByDivPlus : boundByDivMinus);
if (refined.IsBottom)
{
isBottom = true;
return(result);
}
AddToResult(result, x, refined);
}
}
return(result);
}