Examples of jmathexpr.relation.Equality

jmathexpr.relation.Equality
The binary relation equality (=). @author Elemér Furka

        }


        @Override
        public List<Equation> convertedEquations() {
            List<Equation> equations = new ArrayList();
            Equality eq = (Equality) target;
            
            equations.add(new LinearEquation(eq, x));
            
            return equations;
        }

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        }


        @Override
        public List<Equation> convertedEquations() {
            List<Equation> equations = new ArrayList();
            Equality eq = (Equality) target;
            
            equations.add(new QuadraticEquation(eq, x));
            
            return equations;
        }

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            if (a instanceof ANumber && ((ANumber) a).isNegative()) {
                reduced = reduced.negate();
            }


            return new Equality(reduced, Naturals.zero());
        }

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            return new Sqrt(arg).matches(a);
        }


        @Override
        public Expression apply() {
            return new Equality(new Multiplication(p, new Sqrt(arg.hit())), Naturals.zero());
        }

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            if (c instanceof ANumber) {
                if (((ANumber) c).isZero()) {
                    Expression x1 = Naturals.zero();
                    
                    ExpressionContext.getInstance().addExpression(new Equality(x, x1));
                    
                    return new FiniteSet(x1);
                } else if (!((ANumber) c).isNegative()) {
                    return new EmptySet();
                }
            }
            
            Expression x1 = new Sqrt(new Division(new Negation(c), a));
            Expression x2 = new Negation(x1);
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 1), x1));
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 2), x2));
            
            x1 = x1.evaluate();
            x2 = x2.evaluate();
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 1), x1));
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 2), x2));
            
            return new FiniteSet(x1, x2);
        }

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        @Override
        public Expression apply() {
            OrderedPair factor = p.euclideanDivision(Polynomial.create(x, x));
            
            return new Equality(new Multiplication(factor.a(), x), Naturals.zero());
        }

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        private final TerminationPattern a = new AnyPattern();
        private final TerminationPattern b = new AnyPattern();


        @Override
        public boolean matches(Expression expr) {
            return new Equality(new Multiplication(a, b), Naturals.zero()).matches(expr);
        }

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        @Override
        public Expression apply() {
            Expression dd = p.discriminant();
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.constant("D"), dd));
            
            dd = dd.evaluate();
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.constant("D"), dd));
            
            Expression a = p.getCoefficient(2);
            Expression b = p.getCoefficient(1);
            Expression c = p.getCoefficient(0);
            NaturalNumber two = Naturals.getInstance().create(2);
            
            if (dd instanceof ANumber) {
                ANumber d = (ANumber) dd;
                
                if (d.isNegative()) {
                    return new EmptySet();
                } else if (d.isZero()) {
                    return new FiniteSet(new Division(new Negation(b),
                            new Multiplication(two, a)).evaluate());
                }
            }
            
            Expression sd = new Sqrt(dd);
            Expression x1 = new Division(
                    new Addition(new Negation(b), sd),
                    new Multiplication(two, a));
            Expression x2 = new Division(
                    new Subtraction(new Negation(b), sd),
                    new Multiplication(two, a));
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 1), x1));
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 2), x2));
            
            x1 = x1.evaluate();
            x2 = x2.evaluate();
            
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 1), x1));
            ExpressionContext.getInstance().addExpression(new Equality(Numbers.variable("x", 2), x2));
            
            return new FiniteSet(x1, x2);
        }

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            @Override
            public boolean matches(Expression expr) {
                ExpressionPattern sum = new Sum(s, a);
                
                return new Equality(sum, b).matches(expr);
            }

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                return new Equality(sum, b).matches(expr);
            }


            @Override
            public Expression apply() {
                Equality eq = (Equality) target;
                Expression lhs = Sum.subtract(eq.lhs(), a.hit());
                Expression rhs = Sum.subtract(eq.rhs(), a.hit());


                return new Equality(lhs, rhs);
            }

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