public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
using (Context ctx = new Context(cfg))
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
RatNum zero = ctx.MkReal(0);
RatNum two = ctx.MkReal(2);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGe(ctx.MkSub(ctx.MkPower(x, two), ctx.MkPower(y, two)), zero));
Probe p = ctx.MkProbe("num-consts");
Probe p2 = ctx.Gt(p, ctx.Const(2));
Tactic t = ctx.Cond(p2, ctx.MkTactic("simplify"), ctx.MkTactic("factor"));
Console.WriteLine(t[g]);
g = ctx.MkGoal();
g.Assert(ctx.MkGe(ctx.MkAdd(x, x, y, z), zero));
g.Assert(ctx.MkGe(ctx.MkSub(ctx.MkPower(x, two), ctx.MkPower(y, two)), zero));
Console.WriteLine(t[g]);
}
}
public static decimal AsDecimal([NotNull] this RatNum number)
{
var numerator = (decimal)number.BigIntNumerator;
var denominator = (decimal)number.BigIntDenominator;
return(numerator / denominator);
}
public void testTwoArgCtor()
{
RatNum one_I_two = new RatNum(1, 2);
eq(one_I_two, "1/2");
RatNum two_I_one = new RatNum(2, 1);
eq(two_I_one, "2");
RatNum three_I_two = new RatNum(3, 2);
eq(three_I_two, "3/2");
RatNum negOne_I_thirteen = new RatNum(-1, 13);
eq(negOne_I_thirteen, "-1/13");
RatNum fiftyThree_I_seven = new RatNum(53, 7);
eq(fiftyThree_I_seven, "53/7");
RatNum zero_I_one = new RatNum(0, 1);
eq(zero_I_one, "0");
}
public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
using (Context ctx = new Context(cfg))
{
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RatNum zero = ctx.MkReal(0);
RatNum two = ctx.MkReal(2);
Goal g = ctx.MkGoal();
g.Assert(ctx.MkGt(x, zero));
g.Assert(ctx.MkGt(y, zero));
g.Assert(ctx.MkEq(x, ctx.MkAdd(y, two)));
Console.WriteLine(g);
Tactic t1 = ctx.MkTactic("simplify");
Tactic t2 = ctx.MkTactic("solve-eqs");
Tactic t = ctx.AndThen(t1, t2);
Console.WriteLine(t[g]);
}
}
public static double GetRealValue(ArithExpr expr, Context localContext)
{
RatNum xRatNum = expr.Simplify() as RatNum;
IntNum d = xRatNum.Denominator;
IntNum n = xRatNum.Numerator;
BigRational bigRational = new BigRational(n.BigInteger, d.BigInteger);
return((double)bigRational);
}
/** @requires: arg != null
* @return a new RatNum equal to (this / arg).
* If arg is zero, or if either argument is NaN, then returns NaN.
*/
public RatNum div(RatNum arg)
{
// (a/b) / (x/y) = ay/bx
if (arg.isNaN())
{
return(arg);
}
else
{
return(new RatNum(this.numer * arg.denom,
this.denom * arg.numer));
}
}
public static void Main(string[] args)
{
RationalNumber RatNum1 = new RationalNumber();
RationalNumber RatNum2 = new RationalNumber(Convert.ToInt32(Console.ReadLine()), Convert.ToInt32(Console.ReadLine()));
RationalNumber RatNum;
RatNum = RatNum1 + RatNum2;
Console.WriteLine(RatNum.GetNumerator());
Console.WriteLine(RatNum.GetDenominator());
Console.WriteLine(RatNum1 > RatNum2);
Console.WriteLine(RatNum1 != RatNum2);
}
public void testApprox()
{
approxEq(zero.approx(), 0.0);
approxEq(one.approx(), 1.0);
approxEq(negOne.approx(), -1.0);
approxEq(two.approx(), 2.0);
approxEq(one_I_two.approx(), 0.5);
approxEq(two_I_three.approx(), 2.0 / 3.0);
approxEq(three_I_four.approx(), 0.75);
// cannot test that one_I_zero.approx() approxEq double.NaN,
// because it WON'T!!! Instead, construct corresponding
// instance of double and use .Equals(..) method
/*
* assertTrue( (new System.Double(double.NaN)).
* Equals
* (new double(one_I_zero.approx())) );
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(negOne_I_zero.approx())) );
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(two_I_zero.approx())) );
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(negTwo_I_zero.approx())) );
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(hundred_I_zero.approx())) );
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(negOne_I_zero.approx())) );
*
* assertTrue( (new double(double.NaN)).
* Equals
* (new double(nine_I_zero.approx())) );
*/
// use left-shift operator "<<" to create integer for 2^30
RatNum one_I_twoToThirty = new RatNum(1, (1 << 30));
double quiteSmall = 1.0 / System.Math.Pow(2, 30);
approxEq(one_I_twoToThirty.approx(), quiteSmall);
}
/** @requires: rn != null
* @return a negative number if this < rn,
* 0 if this = rn,
* a positive number if this > rn.
*/
public int CompareTo(RatNum rn)
{
if (this.isNaN() && rn.isNaN())
{
return(0);
}
else if (this.isNaN())
{
return(1);
}
else if (rn.isNaN())
{
return(-1);
}
else
{
RatNum diff = this.sub(rn);
return(diff.numer);
}
}
public void testOneArgCtor()
{
eq(zero, "0");
eq(one, "1");
RatNum four = new RatNum(4);
eq(four, "4");
eq(negOne, "-1");
RatNum negFive = new RatNum(-5);
eq(negFive, "-5");
RatNum negZero = new RatNum(-0);
eq(negZero, "0");
}
public void Run()
{
Dictionary <string, string> cfg = new Dictionary <string, string>()
{
{ "AUTO_CONFIG", "true" }
};
Context ctx = new Context(cfg);
RealExpr x = ctx.MkRealConst("x");
RealExpr y = ctx.MkRealConst("y");
RealExpr z = ctx.MkRealConst("z");
RatNum two = ctx.MkReal(2);
Console.WriteLine(ctx.MkAdd(ctx.MkSub(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkSub(ctx.MkAdd(ctx.MkMul(x, y), ctx.MkPower(y, two)), ctx.MkPower(z, two)));
Console.WriteLine(ctx.MkMul(ctx.MkAdd(x, y), z));
}
/** Standard equality operation.
* @return true if and only if 'obj' is an instance of a RatNum
* and 'this' = 'obj'. Note that NaN = NaN for RatNums.
*/
public override bool Equals(object obj)
{
if (obj is RatNum)
{
RatNum rn = (RatNum)obj;
// special case: check if both are NaN
if (this.isNaN() && rn.isNaN())
{
return(true);
}
else
{
return(this.numer == rn.numer && this.denom == rn.denom);
}
}
else
{
return(false);
}
}
public void testTwoArgCtorOnNaN()
{
RatNum one_I_zero = new RatNum(1, 0);
eq(one_I_zero, "NaN");
RatNum two_I_zero = new RatNum(2, 0);
eq(two_I_zero, "NaN");
RatNum negOne_I_zero = new RatNum(-1, 0);
eq(negOne_I_zero, "NaN");
RatNum zero_I_zero = new RatNum(0, 0);
eq(zero_I_zero, "NaN");
RatNum negHundred_I_zero = new RatNum(-100, 0);
eq(negHundred_I_zero, "NaN");
}
public void testReduction()
{
RatNum negOne_I_negTwo = new RatNum(-1, -2);
eq(negOne_I_negTwo, "1/2");
RatNum two_I_four = new RatNum(2, 4);
eq(two_I_four, "1/2");
RatNum six_I_four = new RatNum(6, 4);
eq(six_I_four, "3/2");
RatNum twentySeven_I_thirteen = new RatNum(27, 13);
eq(twentySeven_I_thirteen, "27/13");
RatNum negHundred_I_negHundred = new RatNum(-100, -100);
eq(negHundred_I_negHundred, "1");
}
/** @requires: c != null
* @effects:
* constructs a new RatTerm, t, with t.coeff = c and t.expt = e.
*/
public RatTerm(RatNum c, int e)
{
coeff = c;
expt = e;
}
// helper function, "decode-and-check"
private void decChk(string s, RatNum expected)
{
eq(RatNum.parse(s), expected.unparse());
}
private void assertGreater(RatNum larger, RatNum smaller)
{
assertTrue(larger.CompareTo(smaller) > 0);
assertTrue(smaller.CompareTo(larger) < 0);
}
/** @requires: arg != null
* @return a new RatNum equal to (this - arg).
* If either argument is NaN, then returns NaN.
*/
public RatNum sub(RatNum arg)
{
// a/b - x/y = a/b + -x/y
return(this.add(arg.negate()));
}
/** @requires: arg != null
* @return a new RatNum equal to (this * arg).
* If either argument is NaN, then returns NaN.
*/
public RatNum mul(RatNum arg)
{
// (a/b) * (x/y) = ax/by
return(new RatNum(this.numer * arg.numer,
this.denom * arg.denom));
}
/** @requires: arg != null
* @return a new RatNum equal to (this + arg).
* If either argument is NaN, then returns NaN.
*/
public RatNum add(RatNum arg)
{
// a/b + x/y = ay/by + bx/by = (ay + bx)/by
return(new RatNum(this.numer * arg.denom + arg.numer * this.denom,
this.denom * arg.denom));
}
public static Rational ToRational(RatNum r)
{
return(ToRational(r.BigIntNumerator) / ToRational(r.BigIntDenominator));
}
private void assertNeg(RatNum n)
{
assertTrue(n.isNegative());
assertTrue(!n.isPositive());
}
public static Decimal CreateDecimal(RatNum val)
{
return(new Decimal(new BigDecimal(val.longValue())));
}
// self-explanatory helper function
private void eq(RatNum ratNum, string rep)
{
assertEquals(rep, ratNum.unparse());
}
