Sindbad~EG File Manager

/* 6.17.13 problems read in from old .mhw files
   12.20.23 commented out one problem, search "deleted"
   12.25.23 author's comments have to be on one line only (fixed in problems39)
*/

/*  6.17.13,  problems read from grineq2.mhw */
char *problems21[] = {
"1. (x/a)^2 + (y/c)^2 < 1",
"2. (x/a)^2 + (y/c)^2 <= 1",
"3. (x-a)^2 + y^2 < r^2 | -5 < x < 5",
"4. x^2 + (y-c)^2 < r^2 | -5 < x < 5",
"5. (x-a)^2 + (y-c)^2 < r^2 | -5 < x < 5",
"6. x^2 + y^2 + 10y -9 < 0 | -20 < x < 20",
"7. x^2/4 + y^2 < 1 | -7 < x < 7",
"8. x^2/4 + y^2/9 < 1 | -5 < x < 5",
"9. (x/a)^2 + (y/c)^2 < 1 | -8 < x < 8",
"10. ((x-a)/4)^2 + (y-c)^2 < 1 | -8 < x < 8",
"11. y^2/9 -x^2/9 < 1 | -8 < x < 8",
"12. xy < 1 | -8 < x < 8, -8 < y < 8",
"13. 1 < ((x-a)/4)^2 - (y-c)^2 | -10 < x < 10",
"14. x^n y + y^n x < 1 | -8 < x < 8, -8 < y < 8",
"15. y^2 < x(x-1)(x-2) | -2 < x < 8, -10 < y < 10",
"16. x^(2/3) + y^(2/3) < a^(2/3) | -8 < x < 8       @astroid",
"17. x^4 < a^2(x^2-y^2)       @eight curve",
"18. x^4 + y^4 < 1",
"19. (x^2 + y^2)^2 < a^2(x^2-y^2)       @lemniscate of Bernoulli",
"2. abs(y) <= abs(sin x)",
"3. abs(x) < abs(cos y)",
""};

/*  6.17.13,  problems read from grcircle.mhw */
char *problems22[] = {
"1. x^2 + y^2 = r^2",
"2. (x-a)^2 + y^2 = 1",
"3. (x-a)^2 + y^2 = r^2",
"4. x^2 + (y-c)^2 = r^2",
"5. (x-a)^2 + (y-c)^2 = r^2",
"6. x^2 + y^2 = 4",
"7. x^2 + y^2 = 9",
"8. (x + 1)^2 + y^2 = 4",
"9. x^2 + (y-2)^2 = 4",
"10. (x - 2)^2 + (y + 3)^2 = 16",
"11. (x - 2)^2 + (y - 2)^2 = 25",
"12. (x - 3)^2 + y^2 = 9",
"13. x^2 + y^2 - 2x - 6y -6 = 0",
"14. x^2 + y^2 + 8x - 6y -15 = 0",
"15. x^2 + y^2 + 6x - 8y = 0",
"16. x^2 + y^2 + 10y - 9 = 0",
"17. 9x^2 + 9y^2 - 6x - 12y - 16 = 0",
"18. x^2 + y^2 + 7x -3y -10 = 0",
"19. 4x^2 + 4y^2 + 4x -32y + 33 = 0",
"20. ax^2 + cy^2 = 1",
"21. (x -3)^2 + (y - 2)^2 = 9",
"22. x^2 + y^2 - 4x + 3y - 2 = 0",
"23. x^2 + y^2 + 2x - 4y = 9",
"24. (x - a)^2 + (y + c)^2 = 36",
"25. 4x^2 + 4y^2 = 1",
"26. x^2 + y^2 = 3",
""};

/*  6.17.13,  problems read from grellips.mhw */
char *problems23[] = {
"1. (x/a)^2 + (y/c)^2 = 1",
"2. ((x-a)/4)^2 + (y/c)^2 = 1",
"3. ((x-a)/4)^2 + (y-c)^2 = 1",
"4. x^2 - 2x + 1 + (y/4)^2 = 1",
"5. x^2 - 2x + y^2/4 + y + 2 = 1",
"6. x^2/4 + y^2 = 1",
"7. x^2/4 + y^2/9 = 1 |  -3<x<3, -4<y<4",
"8. (x-2)^2/9 + y^2/25 = 1",
"9. x^2/36 + (y+3)^2/9 = 1",
"10. ((x-a)/4)^2 + (y/c)^2 = 1",
"11. ((x-a)/4)^2 + (y-c)^2 = 1",
"12. x^2 - 2x + 1 + (y/4)^2 = 1",
"13. x^2 - 2x + y^2/4 + y + 2 = 1",
"14. x^2/12 + y^2/4 = 1",
"15. 8x^2 + 3y^2 = 24",
"16. x^2 + y^2/36 = 1",
"17. x^2/4 + y^2/9 = 2 | -4 < x < 4, -6 < y < 6",
"18. 9x^2 + 4y^2 = 36",
"19. 8x^2 + 3y^2 = 24",
"20. 4x^2 = 9 - y^2",
"21. 2x^2 + 3y^2 = 6",
"22. 5x^2 + 7y^2 = 35",
""};

/*  6.17.13,  problems read from grparab.mhw */
char *problems24[] = {
"1. y = ax^2",
"2. y = (x-a)^2",
"3. y = x^2 + c",
"4. y = ax^2 + c",
"5. y = a(x-c)^2",
"6. y = a(x-c)^2 + b",
"7. y = x^2 + ax",
"9. x = y^2",
"10. y = sqrt x",
"11. x = ay^2",
"12. x = ay^2 + c",
"13. y = x^2 + 2",
"14. y = x^2 - 5",
"15. y = x^2 + 2x + 3",
"16. y = 3x^2",
"17. y = - 3x^2",
"18. y = -(1/2) x^2",
"19. y = -2x^2 - 4x + 1",
"20. y = -ax^2 + cx + d",
"21. y = (x + 1)^2",
"22. y = (x - 3)^2",
"23. y = a(x-c)^2 + d",
"24. y = 2x^2 + 2",
"25. y = 3x^2 + 3",
"26. y = -2x^2 - 2",
"27. y = (1/2) x - 2",
"28. y = (x - 1)^2 - 2",
"29. y = 3(x - 2)^2 - 4",
"30. y = -(1/2)(x + 1)^2 - 2",
"31. y = -3(x - 4)^2 -2",
"32. y = a(x-c)^2 - d",
"33. y = 3x^2 + 24x + 49",
"34. y = -2x^2 + x - 2",
"35. y = ax^2 + cx + d",
"36. x = y^2",
"37. x = - y^2",
"38. x = ay^2",
"39. x = y^2 - 1",
"40. x = -y^2 + 4",
"41. x = ay^2 + c",
"42. x = -2y^2",
"43. x = 4y^2",
"44. x = y^2 + 4y + 6",
"45. x = y^2 - 2y - 3",
"46. x = ay^2 + cy + d",
""};

/*  6.17.13,  problems read from grhyperb.mhw */
char *problems25[] = {
"1. (x/a)^2 - (y/c)^2 = 1",
"2. ((x-a)/4)^2 - (y/c)^2 = 1",
"3. ((x-a)/4)^2 - (y-c)^2 = 1",
"4. x^2 - 2x + 1 - (y/4)^2 = 1",
"5. x^2 - 2x - y^2/4 - y = 1",
"6. (y/a)^2 - (x/c)^2 = 1",
"7. xy = 1",
"8. y^2/9 - x^2/9 = 1 | -10 < x < 10, -8 < y < 8",
"9. y^2/16 - y^2/4 = 1",
"10. x^2/25 - y^2/16 = 1",
"11. x^2/16 - y^2/25 = 1",
"12. x^2 - y^2 = 4",
"13. 4y^2 - 9x^2 = 36",
"14. 25x^2 - 16y^2 = 36",
"15. xy = 6",
"16. xy = -2",
"17. xy = -9",
"18. xy = a",
"19. 9x^2 - 4y^2 - 36 = 0",
"20. x^2 - 2x + 1 - (y/4)^2 = 1",
"21. x^2 - 2x - y^2/4 - y = 1",
"22. (y/a)^2 - (x/c)^2 = 1",
"23. 4x^2 = 64 + y^2",
"24. y = 1/x",
"25. x = 1/y",
"26. x^2 = 16 + y^2",
"27. 16y^2 - 5x^2 = 80",
"28. ay^2 - cx^2 = 4",
"29. x -3/y = 0",
"30. x -a/y = 0",
"31. y - 4/x = 0",
"32. y - a/x = 0",
"33. x^2/4 - y^2/9 = 2 | -10 < x < 10, -10 < y < 10",
"34. xy = -8",
"35. x - 3/y = 1",
"36. x^2 = 16 + y^2",
"37. y^2/9 - x^2/9 = 1",
""};

/*  6.17.13,  problems read from graphrel.mhw */
char *problems26[] = {
"1. (x-a)^2 + (y-c)^2 = r^2 | -5 < x < 5       @Circle whose center is given by the parameters.",
"2. (x/a)^2 + (y/c)^2 = 1 | -8 < x < 8       @Ellipse whose major and minor axes are determined by the parameters.",
"3. ((x-a)/4)^2 + (y-c)^2 = 1 | -8 < x < 8       @An ellipse whose center is given by the parameters.",
"4. y^2/a^2 -x^2/c^2 = 1 | -8 < x < 8       @Hyperbola",
"5. xy = 1 | -8 < x < 8       @Hyperbola",
"6. x^n y + y^n x = 1 | -8 < x < 8",
"7. y^2 = x(x-1)(x-2)       @Elliptic curve, important in number theory.",
"8. y^2 = ax^3 + cx + 1       @Elliptic curve, important in number theory.",
"9. x^(2/3) + y^(2/3) = a^(2/3)       @astroid",
"10. x^4 = a^2(x^2-y^2)       @eight curve",
"11. x^n + y^n = 1          | -8 < x < 8       @Lamé curve, special case. Gabriel Lamé (1795-1870): French mathematician and engineer. ",
"12. (x/a)^n + (y/c)^n = 1  | -8 < x < 8       @Lamé curve, general case. Gabriel Lamé (1795-1870): French mathematician and engineer. ",
"13. (x^2+y^2)^2 = a^2(x^2-y^2)       @Lemniscate of Bernoulli",
"14. (x^2 + y^2)^2 = 4axy^2       @double folium",
"15. y^2(a^2-x^2) = (x^2+2ay-a)^2       @bicorn",
"16. (x^2+y^2-2ax)^2 = 4a^2(x^2+y^2) | -8 < x < 8       @cardiod",
"17. y^2 = x^3/(2a-x)       @cissoid of Diocles",
"18. (x^2 + xy + ax -b^2)^2 = (b^2-x^2)(x-y+a)^2       @shell curves",
"19. sin(x y) = cos(x+y)",
"20. sin x + cos y = 0",
""};

/*  problems for _polyroots */
char *problems27[] = {
    // Symmetrical roots
    "1. x^4 + a*x^2 + 1", // Roots depend on parameter 'a'. When a=0, roots lie symmetrically on the unit circle.

    // Interesting symmetry
    "2. x^4 + x^2 + b", // Parameter 'b' adjusts the magnitude of the roots.

    // Roots of unity with parameter
    "3. x^n - 1", // Roots of unity. Parameter 'n' controls the number of roots on the unit circle.

    // Complex conjugate roots
    "4. x^3 - x + a", // Parameter 'a' shifts the roots. Includes one real root and two complex conjugate roots.

    // Mixed real and complex roots
    "5. x^4 + a*x^2 + b", // Parameters 'a' and 'b' provide control over the real and complex roots.

    // Repeated complex roots
    "6. x^4 - 2x^2 +a^2", // Roots are repeated at ±sqrt(a) when a=1

    // Complex roots with symmetry
    "7. x^5 - a*x^3 + b", // Roots symmetrically distributed based on 'a' and 'b'.

    // Another form of roots of unity
    "8. x^6 + b", // When b=1, roots are on the unit circle. Parameter 'b' moves roots off the circle.

    // Challenging configuration
    "9. x^3 - a*x + b", // General cubic with parameterized roots.

    // Customized symmetry
    "10. x^4 + a*x^3 + b*x^2 + c*x + 1", // Parameterized quartic polynomial for experimentation.

    // Higher-order polynomial with roots of unity
    "11. x^7 - 1", // Roots of unity with n=7. All roots lie on the unit circle.

    // Polynomials with mixed roots
    "12. x^4 - 2*x^2 + b", // Real roots for b > 0, complex for b < 0.

    // Mixed real and complex roots with parameter
    "13. x^6 - a*x^3 + b", // Parameters 'a' and 'b' control root placement.

    // Unit circle with a parameter
    "14. x^8 + a*x^4 + b", // Roots form symmetrical patterns based on 'a' and 'b'.

    // Simple polynomial with a parameter
    "15. x^3 + a*x + b", // Includes complex conjugates and real root for some 'a', 'b'.

    // Parameterized higher-order polynomial
    "16. x^n - a", // Roots depend on 'n' and 'a'. Complex roots when 'a' < 0.

    // Roots with symmetry and parameter
    "17. x^4 - a*x^3 + b*x + c", // Parameters 'a', 'b', and 'c' provide a general quartic.

    // Challenging polynomial with parameters
    "18. x^6 + a*x^4 + b*x^2 + c", // Symmetrical root patterns with parameter control.

    // Purely complex roots
    "19. x^4 + 4*x^2 + b", // Includes complex conjugate roots, adjusted by 'b'.

    "" // Terminates the list
};


/*  6.17.13,  problems read from pargraph.mhw */
char *problems28[] = {
"1. sin nt, cos mt       @Lissajous patterns",
"2. b (theta -sin theta), b (1-cos theta)       @ Cycloid",
"3. b cos^3 theta, b sin^3 theta       @ Astroid, hypocycloid of four cusps",
"4. 3at/(1+t^3), 3at^2/(1+t^3)       @ Folium of Descartes",
"5. (a+b) cos theta - b cos((a+b)theta/b), (a+b)sin theta - b sin((a+b)theta/b)       @ Epicycloid--locus of a point on the circumference of a circle rolling around a smaller circle.",
"6. a(2 cos t + cos(2t)), a(2 sin t - sin 2t)       @Deltoid--locus of a point on the circumference of a circle"
  " rolling inside a circle three times as large.",
"7. a sin t, (a (cos^2 t)(2 + cos t))/(3 + sin^2 t)       @Bicorn (Sylvester, 1864)",
"8. a(1+sin t), (b cos t)(1 +sin t) | -pi/2 <= t <= 3pi/2       @Piriform (De Longchamps, 1866)",
"9. m cos t - b cos(m/b) t, m sin t - b sin (m/b) t | - pi <= t <= pi       @Epicycloid",
""};

/*  6.17.13,  problems read from polar.mhw */
char *problems29[] = {
"1. r = a sqrt(cos 2 theta)       @ lemniscate of Bernoulli",
"2. r = b csc theta + a       @ Conchoid of Nicomedes",
"3. r = a(1-cos theta)       @ Cardiod",
"4. r = a theta       @ Spiral of Archimedes",
"5. r = a cos(2 theta) sec theta       @ Strophoid",
"6. r = cos(n theta)       @ roses",
"7. r = sin(n theta)       @ roses",
"8. r = b - a cos theta       @ Limacon of Pascal",
"9. r = a ln theta       @ logarithmic spiral",
"10. r = a(1-b cos theta)       @ ellipse of eccentricity b",
"11. r = a/cos^3(theta/3)       @ Tschirnhausen's cubic, also known as the trisectrix of Catalan, or L'Hospital's cubic",
"12. r = a (sin theta) (tan theta)       @ cissoud of Diocles",
"13. r = a (sec theta- 2 cos theta)       @ right strophoid",
"14. r = a sec theta - 4 a cos theta       @Trisectrix of McLaurin",
"15. r = (3 a sin theta cos theta)/ (sin^3 theta + cos^3 theta)       @Folium of Descartes (1638)  ",
"16. r = (b^2 cot theta - a^2)/cos^2 theta       @Serpentine (Newton, 1701)",
"17. r = a sec^2 theta sqrt(cos(2 theta))       @Eight curve, also called the lemniscate of Gerono",
"18. r = sqrt(4 b (a - b sin^2 theta))       @Hippopede (Proclus, 75 BCE).  Also known as the \"horse fetter\".",
"19. r = (cos theta)(4 a sin^2 theta - b)       @Folia (Kepler, 1609)",
"20. r = root(4, b^4 - a^4 + 2a^2 r^2 cos(2 theta))       @Ovals of Cassini ",
""};

/*  6.17.13,  problems read from difgraf.mhw */
char *problems30[] = {
"1. x^2",
"2. x^3",
"3. x^4",
"4. sin x",
"5. cos x",
"6. sqrt x",
"7. 1/x",
"8. 1/x^2",
"9. tan x",
"10. x cos x",
"11. y = e^x",
"12. y = e^(-x)",
"13. y = e^(ax)",
"14. y = a^x",
"15. y = ln x",
"16. y = 1 - e^(-x)",
"17. y = x sin(1/x)",
"18. y = cosh x",
"19. y = sinh x",
"20. y = tanh x",
""};

/*  6.17.13,  problems read from difgraf.mhw */
char *problems31[] = {
"1. x^2",
"2. x^3",
"3. x^4",
"4. sin x",
"5. cos x",
"6. sqrt x",
"7. 1/x",
"8. 1/x^2",
"9. tan x",
"10. x cos x",
"11. y = e^x",
"12. y = e^(-x)",
"13. y = e^(ax)",
"14. y = a^x",
"15. y = ln x",
"16. y = 1 - e^(-x)",
"17. y = x sin(1/x)",
"18. y = cosh x",
"19. y = sinh x",
"20. y = tanh x",
""};

/*  6.17.13,  problems read from contour.mhw */
char *problems32[] = {
"1. xy",
"2. sin x sin y",
""};

/*  6.17.13,  problems read from contour2.mhw */
char *problems33[] = {
"1. re[sin z]",
"2. Re[e^z]",
"3. Re[J0(z)]",
"4. abs(z(z-1))",
"5. abs[sin z]",
"6. abs[J0(z)]",
""};

/*  problems for topic _solve_ode, many produced by ChatGPT 1.19.25 */
/*  The original ones are the first 24, dating from 1997 I guess, or earlier. */
char *problems34[] = {
    "1. y' = y",
    "2. y' = xy",
    "3. y' = y sin x",
    "4. y' = y cos x",
    "5. y' = x^2 y",
    "6. y' = sin y",
    "7. y' = cos y",
    "8. y' = y - ax",
    "9. x' = ax(1-x)",
    "10. x' = x-x^3",
    "11. x' = x(1-x)-b",
    "12. x' = x(x-a)",
    "13. x' = ax(1-x)-b(1+sin(2 pi t))",
    "14. x' = x^3-3x",
    "15. x' = x^4-x^2",
    "16. x' = sin^2 x",
    "17. x' = abs(1-x^2)",
    "18. x' = x^2-ax",
    "19. x' = x^3-xa",
    "20. x' = x^3 - x + a",
    "21. x' = x^4 - x^2 + a",
    "22. x' = ax + sin x",
    "23. x' = x^2 -1 - cos t",
    "24. y' = x sin y",
    "25. y' = x + y",
    "26. y' = x - y",
    "27. y' = x y",
    "28. y' = x^2 - y",
    "29. y' = x / y",
    "30. y' = y^2 - x",
    "31. y' = x^2 y - y",
    "32. y' = x sin(y)",
    "33. y' = y cos(x)",
    "34. y' = x + sin(y)",
    "35. y' = x^2 - y^2",
    "36. y' = e^(x - y)",
    "37. y' = ln(x + y)",
    "38. y' = y / (1 + x^2)",
    "39. y' = x tan(y)",
    "40. y' = sin(x + y)",
    "41. y' = abs(x - y)",
    "42. y' = x^2 / (1 + y^2)",
    "43. y' = x cos(x y)",
    "44. y' = sqrt(x^2 + y^2)",
    "45. y' = x y / (1 + y^2)",
    "46. y' = cosh(x) - sinh(y)",
    "47. y' = y^2 - x y",
    "48. y' = y sin(x y)",
    "49. y' = x^2 y - y^3",
    "50. x' = t + x",
    "51. x' = t - x",
    "52. x' = t x",
    "53. x' = t^2 - x",
    "54. x' = t / x",
    "55. x' = x^2 - t",
    "56. x' = t^2 x - x",
    "57. x' = t sin(x)",
    "58. x' = x cos(t)",
    "59. x' = t + sin(x)",
    "60. x' = t^2 - x^2",
    ""
};

/*  6.17.13,  problems for topic _solve_ode2 */
char *problems35[] = {
"1. x' = y, y' = -x       @ circle",
"2. x' = xy, y' = -sin x",
"3. x' = ay, y' = -x",
"4. x' = sin y, y' = -sin x",
"5. x' = y^2, y' = -x",
"6. x' = x + 2y, y' = 3y",
"7. x' = x+2y, y' = 3x+6y",
"8. x' = x + 2y, y' = x",
"9. x' = x + 2y, y' = 3x-3y",
"10. x' = x + 3y, y' = x-y",
"11. x' = 3x + 5y, y' = -2x-2y",
"12. x' = -3x-2y, y' = 5x-2y",
"13. x' = 3x-2y, y' = 5x-2y",
"14. x' = -3x + 5y, y' = -2x + 3y",
"15. x' = 3x + 5y, y' = -2x - 3y",
"16. x' = -3x + 5y, y' = -2x + 2y",
"17. x' = y sin x, y' = -x cos y",
"18. x' = y cos x, y' = -x sin y",
"19. x' = y sin x, y' = x cos y",
"20. x' = y cos x, y' = s sin y",
""};

/*  6.17.13,  problems for topic _high_order_ode */
char *problems36[] = {
"1. y'' = -y    @sines and cosines solve this equation",
"2. y'' =  xy + b",
"3. y'' = -y + bx",
"4. y'' = -(1+bx)y",
"5. y'' = -y + bx^2",
"6. y'' = sin y",
"7. y'' = x sin y",
"8. y'' = sqrt(1+y^2)",
"9. y'' = x^2 sin y",
"10. y'' = sin(x) sin y",
""};

/*  6.17.13,  problems for topic riemann_sums */
char *problems37[] = {
"1. x^2, 0, 1, 2^(n+1)",
"2. sin x, 0, pi, 2^(n+1)",
"3. 1/x, 1, 10, 9*2^(n+1)",
"4. cos x, -pi/2, pi/2, 2^(n+1)",
"5. x^3, 0,1,2^(n+1)",
"6. sqrt x, 0,1,2^(n+1)",
"7. sqrt x, 0,8,2^(n+1)",
"8. ln x , 1 , 100 ,2^(n+1)",
"9. x sin x , 0 , 2pi , 2^(n+1)",
""};

/*  6.17.13,  problems for topic _trapezoid_rule */
char *problems38[] = {
"1. x^2, 0, 1, 2^(n+1)",
"2. sin x, 0, pi, 2^(n+1)",
"3. 1/x, 1, 10, 9*2^(n+1)",
"4. cos x, -pi/2, pi/2, 2^(n+1)",
"5. x^3, 0,1,2^(n+1)",
"6. sqrt x, 0,1,2^(n+1)",
"7. sqrt x, 0,8,2^(n+1)",
"8. ln x , 1 , 100 ,2^(n+1)",
"9. x sin x , 0 , 2pi , 2^(n+1)",
""};

/*  6.17.13,  problems for topic simpsons_rule */
char *problems39[] = {
"1. x^2 , 0 , 1 , 2^(n+1)       @Of course, you get a perfect fit to a quadratic function.",
"2. sin x , 0, pi , 2^(n+1)       @Bet you didn't think it would be that close!",
"3. 1/x , 1, 10, 9*2^(n+1)",
"4. cos x, -pi/2, pi/2, 2^(n+1)",
"5. x^3, 0,1,2^(n+1)",
"6. sqrt(x), 0,1,2^(n+1)       @The approximation isn't so good because the derivative and the higher derivatives are large near the origin.",
"7. sqrt x, 0,8,2^(n+1)",
"8. ln x , 1 , 100 ,2^(n+1)",
"9. x sin x , 0 , 2pi , 2^(n+1)",
""};

/*  6.17.13,  problems read from spacecrv.mhw */
char *problems40[] = {
"1. x = r cos t, y = r sin t, z = t       @This is a \\it helix. \\rm",
"2. x = t r cos t, y = t r sin t, z = t",
""};