File: issues.mpt

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NextTest("Problems reported as Issues");

//Issue02
Verify(Rationalize( 1.5 / 0.5 ),3);             // OK

//Issue03
Verify(N(Sqrt(17.032 * 3.22), 5), 7.4056);      // OK
Verify(N(Sqrt(17.032 * 3.22), 4), 7.406);       // OK
Verify(N(Sqrt(17.032 * 3.22), 3), 7.41);        // OK

//Issue04
Verify(Factor( Sqrt(61/10-Sqrt(36/5)) ), Sqrt(61/10-Sqrt(36/5)));       // OK

//Issue05
Verify(Factor( a^2 + 2*a*b + b^2 ), (a+b)^2);   // OK

//Issue06
//Verify(Simplify( Sqrt(6.1 - Sqrt(7.2)) ), Sqrt(610-120*Sqrt(5))/10);    // NOT OK

//Issue08
Verify(Factor(x^2 + x^3), x^2*(x+1) );          // OK

//Issue09
Verify(Solve(x^2==21,x), {x==Sqrt(21),x==-Sqrt(21)} );      // OK

//Issue10
Verify(Solve({x + y == 2, y == x}, {x, y}), {x==1,y==1} );          //  OK

//Issue11
Verify(Solve(x^3==x,x), {x==0,x==1,x==(-1)});
Verify(Solve(x^3==x^2,x), {x==0,x==1} );
Verify(Solve(x^4==x^2,x), {x==0,x==1,x==(-1)});        // OK 

//Issue12
Verify(Factor( t^2-9 ), (t-3)*(t+3));       // OK




//Issue 23
TestMathPiper(Factor(x^8+2*x^6+3*x^4+2*x^2+1),(x^2+x+1)*(x^2+x+1)*(x^2-x+1)*(x^2-x+1));

//Issue 24
TestMathPiper(Factor(x^5+4*x^4-22*x^2+59*x-30),x^5+4*x^4-22*x^2+59*x-30);

//Issue 25
Verify(Limit(x,Infinity)((1)/(x)) * (Sin(x)), 0);

//Issue 28
Verify(Limit(x,Infinity)(Sin(x))/(x), 0);

// Issue 30
KnownFailure(Limit(x,-Infinity)(Sin(1/x)*x^2-x*Cos(1/x))/x^2 = 0);
Verify(Limit(x,Infinity)(Sqrt((4 * (x)^(2)) - (2 * x))) - (2 * x), 0);

//Issue 37
Verify(Solve((x) * (Ln(x)) == 0, x), {x==1});

// Issue 39
Verify(AntiDeriv(x,(x + 4)/(x + 3)^2), Ln(x+3)-(x+3)^(-1));

//Issue 40
Verify(Factor(x^2-2),x^2-2);

//Issue 41
Verify(FactorCancel((1-x)/(x-1)),-1);

//Issue 43
Verify(FactorCancel((x^2)/(x)), x);
Verify(FactorCancel((x^2+1)/(x+1)),(x^2+1)/(x+1));
Verify(FactorCancel((x+3)/(x^2+2)),(x+3)/(x^2+2));

//Issue 44
//Verify(Solve(pmt == loan * (rate * (1+rate)^n) / ((1+rate)^n -1), rate), );
Verify(Solve(E == R * r * (r^n - 1)/(r - 1), n), {n==Ln(((E-(-R*r)/(r-1))*(r-1))/(R*r))/Ln(r)});

//Issue 50
TestEquivalent(Factor(5*a*x+5*b*x-2*b*y-2*a*y),(5*x-2*y)*(a+b));

//Issue 54
Verify(ExpandBrackets((x-y)*(a+b)),x*a+x*b-y*a-y*b);

//Issue 55
TestEquivalent(Factor(s^2 - r^2),(s-r)*(r+s));

//Issue 56
TestEquivalent(Factor(5 * a - 10 * b^2),5*(a-2*b^2));

//Issue 57a
Verify(Solve(3*(3*x-4)+2*(3*x-7)==3*(5*x-6)-8, x),{x==x});

//Issue 57b
Verify(Solve((2*x - 1)*(4*x + 3) == (8*x - 3)*(x + 4) - 3*(9*x + 1), x),{});

//Issue 58
Verify(Simplify(Ln(3)),Ln(3));

//Issue 59
Verify(Solve((x - 1)*(x - 2)*(x - 3)==0, x),{x==3,x==2,x==1});

//Issue 60
Verify(Solve(-3*x^3+10*x^2-11*x+4==0, x),{x==1,x==4/3});

//Issue 61
Verify(TrigSimpCombine(ExpandBrackets((2*x^2-x+3)-(2*x^2-x+3))),0);

//Issue 65
Verify(Limit(x, Infinity) ((x)^(2) * ((3) + (x)))^(1/3)/x, 1);
Verify(Limit(x, Infinity) (((x)^(2)) + (1))/(Sqrt(3) * x)/x, Sqrt(1/3));
Verify(Limit(x, Infinity) ((Sqrt(2) * (x)^(2)) + (1))/(3 * x)/x, Sqrt(2/9));

//Issue 67(a)
Verify(Factor(Rationalize(x^2+0.5*x+0.5)), Hold(1/2*(2*x^2+x+1)));

//Issue 67(b)
Verify(Factor(Rationalize(x^2+0.5*x-0.5)), Hold(1/2*(x+1)*(2*x-1)));

//Issue 67(c)
Verify(Factor(Rationalize(x^2-0.5*x-0.5)), Hold(1/2*(x-1)*(2*x+1)));

//Issue 67(d)
Verify(Factor(Rationalize(x^2-0.5*x+0.5), Hold(1/2*(2*x^2-x+1))));

//Issue 68
Verify(Factor(Rationalize(x^2-0.7*x-2.6)), Hold(1/10*(x-2)*(10*x+13)));

//Issue 80
Verify(Solve((-((10 * c) + (3)))/(2 * ((4 * (c)^(2)) - (9))) == (-1)/(2 * ((2 * c) - (3))), c), {c==0});

//Issue 82
Verify(Solve((x^3-6*x^2+32)/8==x^2-4, x),{x==(-2),x==8+2^(5/2),x==8-2^(5/2)});

// Issue 83
Verify(Solve({a*x + b*y == c, d*x + e*y == f}, {x, y}),{x==f/d-((c-(a*f)/d)*e)/(d*(b-(a*e)/d)),y==(c-(a*f)/d)/(b-(a*e)/d)});

//Issue 84
TestEquivalent(Factor((9 * (a)^(2)) - (3 * a * b)),3*a*(3*a-b));

//Issue 90
Verify(Sum(i, 0, n-1, r^i), (1-r^(n-1+1))/(1-r));

// Issue 93
Verify(Solve({x + y == 2, 2*y+2*x==4}, {x, y}), {x==2-y,y==y});

// Issue 98
Verify(Simplify(3.15 * 3), 9.45);

// Issue 99
Verify(0*Infinity, Undefined);
Verify(0*(-Infinity), Undefined);
Verify(Infinity*0, Undefined);
Verify((-Infinity)*0, Undefined);

// Issue 106
Verify(ExpandBrackets(-(2*x+2*y)), Hold(-2*x-2*y));

// Issue 107
Verify(ExpandBrackets(1/4 * (x+1)), Hold(x/4+1/4));

// Issue 108
Verify(CForm(2.), "2.");

// Issue 109
Verify(Rationalize({2.25,-33.333,8}),{9/4,(-33333)/1000,8});
Verify(Rationalize(Sqrt(6.1 - Sqrt(7.2))),Sqrt(61/10-Sqrt(36/5)));

// Issue 113
Verify(Simplify(TrigSimpCombine(FactorCancel((x) + (0.2 * x)))), (6*x)/5);

// Issue 115
Verify(Solve(a * b^x == c, x), {x==Ln(c/a)/Ln(b)});

// Issue 116
Verify(a/3+2*a/3,a);
Verify(a/3+(2*a)/3,a);
Verify(a/2+3*a/2,2*a);
Verify(a/2+(3*a)/2,2*a);
Verify(1/(2*a)+3/(2*a),2/a);
Verify(a/(2*b)+3*a/(2*b),(2*a)/b);

// Issue 117
Verify(Differentiate(x, 1) ArcSin(Sin(x)), Cos(x)/Sqrt(1-Sin(x)^2));

// Issue 118
Verify(Factor(a^2 - a*f + f^2), a^2-a*f+f^2);

// Issue 119
Verify(Integrate(x) 1/(4 * x^2 + 1), ArcTan(2*x)/2);

// Issue 120
Verify(Simplify(x^2*(1/x)^2+1), 2);

// Issue 121
Verify(Limit(x, Infinity) ((x)^(2)) + (Sin(x)), Infinity);

// Issue 122
Verify(PAdicExpand(x^3, x-1), 3*(x-1)+3*(x-1)^2+(x-1)^3+1);

// Issue 123
Verify(Apart((x+4)/(x+3)^2), 1/(x+3)+1/(x+3)^2);

// Issue 124
Verify(N(Zeta(-11.5)), 0.02039697872);

// Issue 125
[
    Local(x,y);

    x := -0.15;
    y := x;

    Verify(N(y,1), -0.2);
    Verify(x,-0.15);
    Verify(y,-0.15);
];