DERIVE for Windows version 5.06 DfW file saved on 05 Apr 2006 +ARROW_2(s, b, c):=IF(s1 = s2, s, [s1, s2 + c(s1 - s2), s2 + (c + b)(s1 - s2) + b[(s1 - s2)2, (s2 - s1)1]/3, s2 + c(s1 - s2), s2 + c(s1 - s2), s2 + (c + b)(s1 - s2) - b[(s1 - s2)2, (s2 - s1)1]/3, s2 + c(s1 - s2), s2]) ARROW_3(s, b, c):=IF(s1 = s2, s, IF(s12 = s22 s13 = s23, [s1, s2 + c(s1 - s2), s2 + (b + c)(s1 - s2) + [0, 0, b(ABS(s2 - s1))1/3], s2 + c(s1 - s2), s2 + c(s1 - s2), s2 + (b + c)(s1 - s2) - [0, 0, b(ABS(s2 - s1))1/3], s2 + c(s1 - s2), s2], [s1, s2 + c(s1 - s2), s2 + (b + c)(s1 - s2) + b[0, (s1 - s2)3, (s2 - s1)2]/3, s2 + c(s1 - s2), s2 + c(s1 - s2), s2 + (b + c)(s1 - s2) - b[0, (s1 - s2)3, (s2 - s1)2]/3, s2 + c(s1 - s2), s2])) EQU_VECT_FIELD_2D(v, c, x, y, x0, y0, x1, y1, contour := 1, m := 100, n := 10, h, i, f, points, x_, y_, y_1, f_, f_1, arrow_pts, size):=PROG(points := [], f := ABS(v)^2 - c^2, h := (x1 - x0)/m, i := (y1 - y0)/n, x_ := x0, LOOP(IF(x_ > x1, exit), y_ := y0, LOOP(y_1 := y_ + i, IF(y_1 > y1, exit), f_ := SUBST(f, [x, y], [x_, y_]), f_1 := SUBST(f, [x, y], [x_, y_1]), IF(f_ = 0, points := APPEND([[x_, y_]], points), IF(f_1 = 0, points := APPEND([[x_, y_1]], points), IF(SIGN(f_) SIGN(f_1), points := APPEND([[x_, (NSOLUTIONS(SUBST(f, x, x_), y, y_, y_1))1]], points)))), y_ := y_1), x_ :+ h), size := DIM(points), arrow_pts := VECTOR([pointsr, pointsr + SUBST(v, [x, y], pointsr)], r, 1, size), arrows := VECTOR(ARROW_2(arrow_ptsr, 1/20, 0), r, 1, size), IF(contour = 1, RETURN [f = 0, arrows]), IF(contour = 0, RETURN arrows), arrows) EQU_VECT_FIELD_3D(v, c, x, y, z, x0, y0, z0, x1, y1, z1, m := 10, n := 10, l := 10, h, i, j, f, points, x_, y_, z_, z_1, f_, f_1, arrow_pts, size):=PROG(points := [], f := ABS(v)^2 - c^2, h := (x1 - x0)/m, i := (y1 - y0)/n, j := (z1 - z0)/l, x_ := x0, LOOP(IF(x_ > x1, exit), y_ := y0, LOOP(IF(y_ > y1, exit), z_ := z0, LOOP(z_1 := z_ + j, IF(z_1 > z1, exit), f_ := SUBST(f, [x, y, z], [x_, y_, z_]), f_1 := SUBST(f, [x, y, z], [x_, y_, z_1]), IF(f_ = 0, points := APPEND([[x_, y_, z_]], points), IF(f_1 = 0, points := APPEND([[x_, y_, z_1]], points), IF(SIGN(f_) SIGN(f_1), points := APPEND([[x_, y_, (NSOLUTIONS(SUBST(f, [x, y], [x_, y_]), z, z_, z_1))1]], points)))), z_ := z_1), y_ :+ i), x_ :+ h), size := DIM(points), arrow_pts := VECTOR([pointsr, pointsr + SUBST(v, [x, y, z], pointsr)], r, 1, size), arrows := VECTOR([ARROW_3(arrow_ptsr, 1/20, 0)], r, 1, size)) UNI_VECT_FIELD_2D(v, x, y, x0, y0, x1, y1, n, m, h, k):=PROG(IF(DIM(v) 2 DIM(VARIABLES(v)) > 2, RETURN "Not a 2D Vector Field"), h := (x1 - x0)/n, k := (y1 - y0)/m, VECTOR(VECTOR(ARROW_2([x0 + hr, y0 + ks; x0 + hr + SUBST(v1, [x, y], [x0 + hr, y0 + ks]), y0 + ks + SUBST(v2, vars, [x0 + hr, y0 + ks])], 1/20, 0), r, 0, n), s, 0, m)) UNI_VECT_FIELD_3D(v, x, y, z, x0, y0, z0, x1, y1, z1, n, m, l, i, j, k):=PROG(IF(DIM(v) 3 DIM(VARIABLES(v)) > 3, RETURN "Not a 3D Vector Field"), i := (x1 - x0)/n, j := (y1 - y0)/m, k := (z1 - z0)/l, VECTOR(VECTOR(VECTOR([ARROW_3([x0 + ir, y0 + js, z0 + kt; x0 + ir + SUBST(v1, [x, y, z], [x0 + ir, y0 + js, z0 + kt]), y0 + js + SUBST(v2, [x, y, z], [x0 + ir, y0 + js, z0 + kt]), z0 + kt + SUBST(v3, [x, y, z], [x0 + ir, y0 + js, z0 + kt])], 1/20, 0)], r, 0, n), s, 0, m), t, 0, l)) ARROW:= ARROWF:= EQU_VECT_FIELD:= FEE:= VECTOR_FIELD:= arrow_pts:= arrows:=[[24/25, 6085984/1776729; 48/25, 1484113/471838; 2076388/1104413, 5978951/1875985; 48/25, 1484113/471838; 48/25, 1484113/471838; 1744673/936025, 8045737/2569149; 48/25, 1484113/471838; 48/25, 1484113/471838], [24/25, 15603923/5460120; 48/25, 7613887/2426506; 1744673/936025, 2417704/767157; 48/25, 7613887/2426506; 48/25, 7613887/2426506; 2076388/1104413, 237767/76796; 48/25, 7613887/2426506; 48/25, 7613887/2426506], [24/25, 1824856/6430211; 48/25, 704874/1250233; 1744673/936025, 1039591/1800136; 48/25, 704874/1250233; 48/25, 704874/1250233; 2076388/1104413, 2994048/5734831; 48/25, 704874/1250233; 48/25, 704874/1250233], [24/25, - 1824856/6430211; 48/25, - 704874/1250233; 2076388/1104413, - 2994048/5734831; 48/25, - 704874/1250233; 48/25, - 704874/1250233; 1744673/936025, - 1039591/1800136; 48/25, - 704874/1250233; 48/25, - 704874/1250233], [24/25, - 15603923/5460120; 48/25, - 7613887/2426506; 2076388/1104413, - 237767/76796; 48/25, - 7613887/2426506; 48/25, - 7613887/2426506; 1744673/936025, - 2417704/767157; 48/25, - 7613887/2426506; 48/25, - 7613887/2426506], [24/25, - 6085984/1776729; 48/25, - 1484113/471838; 1744673/936025, - 8045737/2569149; 48/25, - 1484113/471838; 48/25, - 1484113/471838; 2076388/1104413, - 5978951/1875985; 48/25, - 1484113/471838; 48/25, - 1484113/471838], [9/10, 2193481/610552; 9/5, 1613717/511199; 1241667/702466, 874817/272996; 9/5, 1613717/511199; 9/5, 1613717/511199; 1193465/684948, 2238807/710159; 9/5, 1613717/511199; 9/5, 1613717/511199], [9/10, 1446989/537801; 9/5, 11121494/3557221; 1873377/1075160, 8669881/2769362; 9/5, 11121494/3557221; 9/5, 11121494/3557221; 1376751/778889, 2574525/836243; 9/5, 11121494/3557221; 9/5, 11121494/3557221], [9/10, 760341/1685800; 9/5, 5842327/6587233; 1363443/782501, 2483553/2787055; 9/5, 5842327/6587233; 9/5, 5842327/6587233; 2987279/1690036, 1351032/1610017; 9/5, 5842327/6587233; 9/5, 5842327/6587233], [9/10, - 760341/1685800; 9/5, - 5842327/6587233; 2987279/1690036, - 1351032/1610017; 9/5, - 5842327/6587233; 9/5, - 5842327/6587233; 1363443/782501, - 2483553/2787055; 9/5, - 5842327/6587233; 9/5, - 5842327/6587233], [9/10, - 1446989/537801; 9/5, - 11121494/3557221; 1376751/778889, - 2574525/836243; 9/5, - 11121494/3557221; 9/5, - 11121494/3557221; 1873377/1075160, - 8669881/2769362; 9/5, - 11121494/3557221; 9/5, - 11121494/3557221], [9/10, - 2193481/610552; 9/5, - 1613717/511199; 1193465/684948, - 2238807/710159; 9/5, - 1613717/511199; 9/5, - 1613717/511199; 1241667/702466, - 874817/272996; 9/5, - 1613717/511199; 9/5, - 1613717/511199], [21/25, 10115033/2722677; 42/25, 1195878/376949; 2560656/1548475, 1636057/507478; 42/25, 1195878/376949; 42/25, 1195878/376949; 7186954/4430001, 2481972/781625; 42/25, 1195878/376949; 42/25, 1195878/376949], [21/25, 2124734/827363; 42/25, 1552045/498943; 12808984/7895391, 1496063/481392; 42/25, 1552045/498943; 42/25, 1552045/498943; 1307606/790733, 16610159/5429420; 42/25, 1552045/498943; 42/25, 1552045/498943], [21/25, 1880499/3278912; 42/25, 3997874/3582005; 3251533/2004228, 984759/884605; 42/25, 3997874/3582005; 42/25, 3997874/3582005; 4957644/2997977, 1194412/1121807; 42/25, 3997874/3582005; 42/25, 3997874/3582005], [21/25, - 1880499/3278912; 42/25, - 3997874/3582005; 4957644/2997977, - 1194412/1121807; 42/25, - 3997874/3582005; 42/25, - 3997874/3582005; 3251533/2004228, - 984759/884605; 42/25, - 3997874/3582005; 42/25, - 3997874/3582005], [21/25, - 2124734/827363; 42/25, - 1552045/498943; 1307606/790733, - 16610159/5429420; 42/25, - 1552045/498943; 42/25, - 1552045/498943; 12808984/7895391, - 1496063/481392; 42/25, - 1552045/498943; 42/25, - 1552045/498943], [21/25, - 10115033/2722677; 42/25, - 1195878/376949; 7186954/4430001, - 2481972/781625; 42/25, - 1195878/376949; 42/25, - 1195878/376949; 2560656/1548475, - 1636057/507478; 42/25, - 1195878/376949; 42/25, - 1195878/376949], [39/50, 2157361/565091; 39/25, 2336008/731845; 3718959/2416376, 1223060/376819; 39/25, 2336008/731845; 39/25, 2336008/731845; 1183536/787483, 1705047/532708; 39/25, 2336008/731845; 39/25, 2336008/731845], [39/50, 2596891/1053308; 39/25, 4934005/1596124; 1183536/787483, 1463951/474928; 39/25, 4934005/1596124; 39/25, 4934005/1596124; 5638599/3663653, 1065244/350705; 39/25, 4934005/1596124; 39/25, 4934005/1596124], [39/50, 1091324/1614073; 39/25, 1102861/847110; 1183536/787483, 1121281/867101; 39/25, 1102861/847110; 39/25, 1102861/847110; 3079079/2000617, 317851/254667; 39/25, 1102861/847110; 39/25, 1102861/847110], [39/50, - 1091324/1614073; 39/25, - 1102861/847110; 3079079/2000617, - 317851/254667; 39/25, - 1102861/847110; 39/25, - 1102861/847110; 1183536/787483, - 1121281/867101; 39/25, - 1102861/847110; 39/25, - 1102861/847110], [39/50, - 2596891/1053308; 39/25, - 4934005/1596124; 5638599/3663653, - 1065244/350705; 39/25, - 4934005/1596124; 39/25, - 4934005/1596124; 1183536/787483, - 1463951/474928; 39/25, - 4934005/1596124; 39/25, - 4934005/1596124], [39/50, - 2157361/565091; 39/25, - 2336008/731845; 1183536/787483, - 1705047/532708; 39/25, - 2336008/731845; 39/25, - 2336008/731845; 3718959/2416376, - 1223060/376819; 39/25, - 2336008/731845; 39/25, - 2336008/731845], [18/25, 799091/204445; 36/25, 1394335/433749; 1672295/1174337, 1391416/425497; 36/25, 1394335/433749; 36/25, 1394335/433749; 402571/290882, 4094989/1268377; 36/25, 1394335/433749; 36/25, 1394335/433749], [18/25, 1201782/506099; 36/25, 369852/120529; 11869362/8576335, 2110931/691053; 36/25, 369852/120529; 36/25, 369852/120529; 2036923/1430390, 1130939/375342; 36/25, 369852/120529; 36/25, 369852/120529], [18/25, 1518721/1980095; 36/25, 1251119/856363; 402571/290882, 2430919/1679909; 36/25, 1251119/856363; 36/25, 1251119/856363; 1672295/1174337, 3234577/2301396; 36/25, 1251119/856363; 36/25, 1251119/856363], [18/25, - 1518721/1980095; 36/25, - 1251119/856363; 1672295/1174337, - 3234577/2301396; 36/25, - 1251119/856363; 36/25, - 1251119/856363; 402571/290882, - 2430919/1679909; 36/25, - 1251119/856363; 36/25, - 1251119/856363], [18/25, - 1201782/506099; 36/25, - 369852/120529; 2036923/1430390, - 1130939/375342; 36/25, - 369852/120529; 36/25, - 369852/120529; 11869362/8576335, - 2110931/691053; 36/25, - 369852/120529; 36/25, - 369852/120529], [18/25, - 799091/204445; 36/25, - 1394335/433749; 402571/290882, - 4094989/1268377; 36/25, - 1394335/433749; 36/25, - 1394335/433749; 1672295/1174337, - 1391416/425497; 36/25, - 1394335/433749; 36/25, - 1394335/433749], [33/50, 7306705/1830534; 33/25, 1496013/461689; 1622653/1239909, 11402195/3458438; 33/25, 1496013/461689; 33/25, 1496013/461689; 11175601/8832283, 2889106/886551; 33/25, 1496013/461689; 33/25, 1496013/461689], [33/50, 1390261/606673; 33/25, 1456770/478747; 2221263/1755505, 1706035/564096; 33/25, 1456770/478747; 33/25, 1456770/478747; 1861457/1422385, 937505/313939; 33/25, 1456770/478747; 33/25, 1456770/478747], [33/50, 5183051/6097868; 33/25, 1507777/941629; 1289641/1019227, 3584191/2264559; 33/25, 1507777/941629; 33/25, 1507777/941629; 2583232/1973911, 1137496/736421; 33/25, 1507777/941629; 33/25, 1507777/941629], [33/50, - 5183051/6097868; 33/25, - 1507777/941629; 2583232/1973911, - 1137496/736421; 33/25, - 1507777/941629; 33/25, - 1507777/941629; 1289641/1019227, - 3584191/2264559; 33/25, - 1507777/941629; 33/25, - 1507777/941629], [33/50, - 1390261/606673; 33/25, - 1456770/478747; 1861457/1422385, - 937505/313939; 33/25, - 1456770/478747; 33/25, - 1456770/478747; 2221263/1755505, - 1706035/564096; 33/25, - 1456770/478747; 33/25, - 1456770/478747], [33/50, - 7306705/1830534; 33/25, - 1496013/461689; 11175601/8832283, - 2889106/886551; 33/25, - 1496013/461689; 33/25, - 1496013/461689; 1622653/1239909, - 11402195/3458438; 33/25, - 1496013/461689; 33/25, - 1496013/461689], [3/5, 4014556/986647; 6/5, 1136236/347591; 2218025/1859053, 1061902/319253; 6/5, 1136236/347591; 6/5, 1136236/347591; 3805535/3318088, 1248373/379264; 6/5, 1136236/347591; 6/5, 1136236/347591], [3/5, 2791288/1260575; 6/5, 3799748/1260575; 3805535/3318088, 7687079/2569539; 6/5, 3799748/1260575; 6/5, 3799748/1260575; 2218025/1859053, 2102177/710921; 6/5, 3799748/1260575; 6/5, 3799748/1260575], [3/5, 1944679/2097152; 6/5, 1257293/727897; 3805535/3318088, 4700021/2757232; 6/5, 1257293/727897; 6/5, 1257293/727897; 2218025/1859053, 1261387/755333; 6/5, 1257293/727897; 6/5, 1257293/727897], [3/5, - 1944679/2097152; 6/5, - 1257293/727897; 2218025/1859053, - 1261387/755333; 6/5, - 1257293/727897; 6/5, - 1257293/727897; 3805535/3318088, - 4700021/2757232; 6/5, - 1257293/727897; 6/5, - 1257293/727897], [3/5, - 2791288/1260575; 6/5, - 3799748/1260575; 2218025/1859053, - 2102177/710921; 6/5, - 3799748/1260575; 6/5, - 3799748/1260575; 3805535/3318088, - 7687079/2569539; 6/5, - 3799748/1260575; 6/5, - 3799748/1260575], [3/5, - 4014556/986647; 6/5, - 1136236/347591; 3805535/3318088, - 1248373/379264; 6/5, - 1136236/347591; 6/5, - 1136236/347591; 2218025/1859053, - 1061902/319253; 6/5, - 1136236/347591; 6/5, - 1136236/347591], [27/50, 2754369/664993; 27/25, 1690100/512107; 370993/344374, 123499/36778; 27/25, 1690100/512107; 27/25, 1690100/512107; 2092047/2033674, 1452067/436478; 27/25, 1690100/512107; 27/25, 1690100/512107], [27/50, 3798137/1773808; 27/25, 6040259/2024963; 1294121/1258012, 2253362/762197; 27/25, 6040259/2024963; 27/25, 6040259/2024963; 2280731/2117087, 1168827/399568; 27/25, 6040259/2024963; 27/25, 6040259/2024963], [27/50, 1333929/1333450; 27/25, 13346860/7245757; 6041537/5872964, 5433433/2992754; 27/25, 13346860/7245757; 27/25, 13346860/7245757; 906305/841277, 3312795/1856581; 27/25, 13346860/7245757; 27/25, 13346860/7245757], [27/50, - 1333929/1333450; 27/25, - 13346860/7245757; 906305/841277, - 3312795/1856581; 27/25, - 13346860/7245757; 27/25, - 13346860/7245757; 6041537/5872964, - 5433433/2992754; 27/25, - 13346860/7245757; 27/25, - 13346860/7245757], [27/50, - 3798137/1773808; 27/25, - 6040259/2024963; 2280731/2117087, - 1168827/399568; 27/25, - 6040259/2024963; 27/25, - 6040259/2024963; 1294121/1258012, - 2253362/762197; 27/25, - 6040259/2024963; 27/25, - 6040259/2024963], [27/50, - 2754369/664993; 27/25, - 1690100/512107; 2092047/2033674, - 1452067/436478; 27/25, - 1690100/512107; 27/25, - 1690100/512107; 370993/344374, - 123499/36778; 27/25, - 1690100/512107; 27/25, - 1690100/512107], [12/25, 4271722/1014243; 24/25, 4991872/1497053; 1381632/1437217, 303085/89348; 24/25, 4991872/1497053; 24/25, 4991872/1497053; 9711034/10663551, 8550885/2541523; 24/25, 4991872/1497053; 24/25, 4991872/1497053], [12/25, 2594799/1252648; 24/25, 1533343/520003; 674418/740569, 3293554/1128427; 24/25, 1533343/520003; 24/25, 1533343/520003; 2623597/2729148, 2137822/739475; 24/25, 1533343/520003; 24/25, 1533343/520003], [12/25, 8913446/8329221; 24/25, 1873835/962219; 1314509/1443444, 1140201/594659; 24/25, 1873835/962219; 24/25, 1873835/962219; 4695958/4884883, 2222323/1176025; 24/25, 1873835/962219; 24/25, 1873835/962219], [12/25, - 8913446/8329221; 24/25, - 1873835/962219; 4695958/4884883, - 2222323/1176025; 24/25, - 1873835/962219; 24/25, - 1873835/962219; 1314509/1443444, - 1140201/594659; 24/25, - 1873835/962219; 24/25, - 1873835/962219], [12/25, - 2594799/1252648; 24/25, - 1533343/520003; 2623597/2729148, - 2137822/739475; 24/25, - 1533343/520003; 24/25, - 1533343/520003; 674418/740569, - 3293554/1128427; 24/25, - 1533343/520003; 24/25, - 1533343/520003], [12/25, - 4271722/1014243; 24/25, - 4991872/1497053; 9711034/10663551, - 8550885/2541523; 24/25, - 4991872/1497053; 24/25, - 4991872/1497053; 1381632/1437217, - 303085/89348; 24/25, - 4991872/1497053; 24/25, - 4991872/1497053], [21/50, 4100961/958405; 21/25, 3600993/1068094; 1214017/1436370, 1366891/398636; 21/25, 3600993/1068094; 21/25, 3600993/1068094; 1269613/1601425, 1327495/389904; 21/25, 3600993/1068094; 21/25, 3600993/1068094], [21/50, 395495/197329; 21/25, 4341236/1490929; 2600267/3279844, 6197190/2152913; 21/25, 4341236/1490929; 21/25, 4341236/1490929; 941477/1113913, 2421433/848356; 21/25, 4341236/1490929; 21/25, 4341236/1490929], [21/50, 1156769/1017073; 21/25, 2032111/993758; 2326717/2934802, 1736918/863441; 21/25, 2032111/993758; 21/25, 2032111/993758; 477132/564521, 364562/183439; 21/25, 2032111/993758; 21/25, 2032111/993758], [21/50, - 1156769/1017073; 21/25, - 2032111/993758; 477132/564521, - 364562/183439; 21/25, - 2032111/993758; 21/25, - 2032111/993758; 2326717/2934802, - 1736918/863441; 21/25, - 2032111/993758; 21/25, - 2032111/993758], [21/50, - 395495/197329; 21/25, - 4341236/1490929; 941477/1113913, - 2421433/848356; 21/25, - 4341236/1490929; 21/25, - 4341236/1490929; 2600267/3279844, - 6197190/2152913; 21/25, - 4341236/1490929; 21/25, - 4341236/1490929], [21/50, - 4100961/958405; 21/25, - 3600993/1068094; 1269613/1601425, - 1327495/389904; 21/25, - 3600993/1068094; 21/25, - 3600993/1068094; 1214017/1436370, - 1366891/398636; 21/25, - 3600993/1068094; 21/25, - 3600993/1068094], [9/25, 1734386/399249; 18/25, 1484585/435213; 2801925/3843877, 1770198/510407; 18/25, 1484585/435213; 18/25, 1484585/435213; 884709/1310548, 1477990/428723; 18/25, 1484585/435213; 18/25, 1484585/435213], [9/25, - 1734386/399249; 18/25, - 1484585/435213; 884709/1310548, - 1477990/428723; 18/25, - 1484585/435213; 18/25, - 1484585/435213; 2801925/3843877, - 1770198/510407; 18/25, - 1484585/435213; 18/25, - 1484585/435213], [3/10, 2500301/567258; 3/5, 4422909/1280608; 4205133/6865099, 9715656/2767903; 3/5, 4422909/1280608; 3/5, 4422909/1280608; 1188812/2132543, 2043473/585054; 3/5, 4422909/1280608; 3/5, 4422909/1280608], [3/10, - 2500301/567258; 3/5, - 4422909/1280608; 1188812/2132543, - 2043473/585054; 3/5, - 4422909/1280608; 3/5, - 4422909/1280608; 4205133/6865099, - 9715656/2767903; 3/5, - 4422909/1280608; 3/5, - 4422909/1280608], [- 3/10, 2500301/567258; - 3/5, 4422909/1280608; - 1188812/2132543, 2043473/585054; - 3/5, 4422909/1280608; - 3/5, 4422909/1280608; - 4205133/6865099, 9715656/2767903; - 3/5, 4422909/1280608; - 3/5, 4422909/1280608], [- 3/10, - 2500301/567258; - 3/5, - 4422909/1280608; - 4205133/6865099, - 9715656/2767903; - 3/5, - 4422909/1280608; - 3/5, - 4422909/1280608; - 1188812/2132543, - 2043473/585054; - 3/5, - 4422909/1280608; - 3/5, - 4422909/1280608], [- 9/25, 1734386/399249; - 18/25, 1484585/435213; - 884709/1310548, 1477990/428723; - 18/25, 1484585/435213; - 18/25, 1484585/435213; - 2801925/3843877, 1770198/510407; - 18/25, 1484585/435213; - 18/25, 1484585/435213], [- 9/25, - 1734386/399249; - 18/25, - 1484585/435213; - 2801925/3843877, - 1770198/510407; - 18/25, - 1484585/435213; - 18/25, - 1484585/435213; - 884709/1310548, - 1477990/428723; - 18/25, - 1484585/435213; - 18/25, - 1484585/435213], [- 21/50, 4100961/958405; - 21/25, 3600993/1068094; - 1269613/1601425, 1327495/389904; - 21/25, 3600993/1068094; - 21/25, 3600993/1068094; - 1214017/1436370, 1366891/398636; - 21/25, 3600993/1068094; - 21/25, 3600993/1068094], [- 21/50, 395495/197329; - 21/25, 4341236/1490929; - 941477/1113913, 2421433/848356; - 21/25, 4341236/1490929; - 21/25, 4341236/1490929; - 2600267/3279844, 6197190/2152913; - 21/25, 4341236/1490929; - 21/25, 4341236/1490929], [- 21/50, 1156769/1017073; - 21/25, 2032111/993758; - 477132/564521, 364562/183439; - 21/25, 2032111/993758; - 21/25, 2032111/993758; - 2326717/2934802, 1736918/863441; - 21/25, 2032111/993758; - 21/25, 2032111/993758], [- 21/50, - 1156769/1017073; - 21/25, - 2032111/993758; - 2326717/2934802, - 1736918/863441; - 21/25, - 2032111/993758; - 21/25, - 2032111/993758; - 477132/564521, - 364562/183439; - 21/25, - 2032111/993758; - 21/25, - 2032111/993758], [- 21/50, - 395495/197329; - 21/25, - 4341236/1490929; - 2600267/3279844, - 6197190/2152913; - 21/25, - 4341236/1490929; - 21/25, - 4341236/1490929; - 941477/1113913, - 2421433/848356; - 21/25, - 4341236/1490929; - 21/25, - 4341236/1490929], [- 21/50, - 4100961/958405; - 21/25, - 3600993/1068094; - 1214017/1436370, - 1366891/398636; - 21/25, - 3600993/1068094; - 21/25, - 3600993/1068094; - 1269613/1601425, - 1327495/389904; - 21/25, - 3600993/1068094; - 21/25, - 3600993/1068094], [- 12/25, 4271722/1014243; - 24/25, 4991872/1497053; - 9711034/10663551, 8550885/2541523; - 24/25, 4991872/1497053; - 24/25, 4991872/1497053; - 1381632/1437217, 303085/89348; - 24/25, 4991872/1497053; - 24/25, 4991872/1497053], [- 12/25, 2594799/1252648; - 24/25, 1533343/520003; - 2623597/2729148, 2137822/739475; - 24/25, 1533343/520003; - 24/25, 1533343/520003; - 674418/740569, 3293554/1128427; - 24/25, 1533343/520003; - 24/25, 1533343/520003], [- 12/25, 8913446/8329221; - 24/25, 1873835/962219; - 4695958/4884883, 2222323/1176025; - 24/25, 1873835/962219; - 24/25, 1873835/962219; - 1314509/1443444, 1140201/594659; - 24/25, 1873835/962219; - 24/25, 1873835/962219], [- 12/25, - 8913446/8329221; - 24/25, - 1873835/962219; - 1314509/1443444, - 1140201/594659; - 24/25, - 1873835/962219; - 24/25, - 1873835/962219; - 4695958/4884883, - 2222323/1176025; - 24/25, - 1873835/962219; - 24/25, - 1873835/962219], [- 12/25, - 2594799/1252648; - 24/25, - 1533343/520003; - 674418/740569, - 3293554/1128427; - 24/25, - 1533343/520003; - 24/25, - 1533343/520003; - 2623597/2729148, - 2137822/739475; - 24/25, - 1533343/520003; - 24/25, - 1533343/520003], [- 12/25, - 4271722/1014243; - 24/25, - 4991872/1497053; - 1381632/1437217, - 303085/89348; - 24/25, - 4991872/1497053; - 24/25, - 4991872/1497053; - 9711034/10663551, - 8550885/2541523; - 24/25, - 4991872/1497053; - 24/25, - 4991872/1497053], [- 27/50, 2754369/664993; - 27/25, 1690100/512107; - 2092047/2033674, 1452067/436478; - 27/25, 1690100/512107; - 27/25, 1690100/512107; - 370993/344374, 123499/36778; - 27/25, 1690100/512107; - 27/25, 1690100/512107], [- 27/50, 3798137/1773808; - 27/25, 6040259/2024963; - 2280731/2117087, 1168827/399568; - 27/25, 6040259/2024963; - 27/25, 6040259/2024963; - 1294121/1258012, 2253362/762197; - 27/25, 6040259/2024963; - 27/25, 6040259/2024963], [- 27/50, 1333929/1333450; - 27/25, 13346860/7245757; - 906305/841277, 3312795/1856581; - 27/25, 13346860/7245757; - 27/25, 13346860/7245757; - 6041537/5872964, 5433433/2992754; - 27/25, 13346860/7245757; - 27/25, 13346860/7245757], [- 27/50, - 1333929/1333450; - 27/25, - 13346860/7245757; - 6041537/5872964, - 5433433/2992754; - 27/25, - 13346860/7245757; - 27/25, - 13346860/7245757; - 906305/841277, - 3312795/1856581; - 27/25, - 13346860/7245757; - 27/25, - 13346860/7245757], [- 27/50, - 3798137/1773808; - 27/25, - 6040259/2024963; - 1294121/1258012, - 2253362/762197; - 27/25, - 6040259/2024963; - 27/25, - 6040259/2024963; - 2280731/2117087, - 1168827/399568; - 27/25, - 6040259/2024963; - 27/25, - 6040259/2024963], [- 27/50, - 2754369/664993; - 27/25, - 1690100/512107; - 370993/344374, - 123499/36778; - 27/25, - 1690100/512107; - 27/25, - 1690100/512107; - 2092047/2033674, - 1452067/436478; - 27/25, - 1690100/512107; - 27/25, - 1690100/512107], [- 3/5, 4014556/986647; - 6/5, 1136236/347591; - 3805535/3318088, 1248373/379264; - 6/5, 1136236/347591; - 6/5, 1136236/347591; - 2218025/1859053, 1061902/319253; - 6/5, 1136236/347591; - 6/5, 1136236/347591], [- 3/5, 2791288/1260575; - 6/5, 3799748/1260575; - 2218025/1859053, 2102177/710921; - 6/5, 3799748/1260575; - 6/5, 3799748/1260575; - 3805535/3318088, 7687079/2569539; - 6/5, 3799748/1260575; - 6/5, 3799748/1260575], [- 3/5, 1944679/2097152; - 6/5, 1257293/727897; - 2218025/1859053, 1261387/755333; - 6/5, 1257293/727897; - 6/5, 1257293/727897; - 3805535/3318088, 4700021/2757232; - 6/5, 1257293/727897; - 6/5, 1257293/727897], [- 3/5, - 1944679/2097152; - 6/5, - 1257293/727897; - 3805535/3318088, - 4700021/2757232; - 6/5, - 1257293/727897; - 6/5, - 1257293/727897; - 2218025/1859053, - 1261387/755333; - 6/5, - 1257293/727897; - 6/5, - 1257293/727897], [- 3/5, - 2791288/1260575; - 6/5, - 3799748/1260575; - 3805535/3318088, - 7687079/2569539; - 6/5, - 3799748/1260575; - 6/5, - 3799748/1260575; - 2218025/1859053, - 2102177/710921; - 6/5, - 3799748/1260575; - 6/5, - 3799748/1260575], [- 3/5, - 4014556/986647; - 6/5, - 1136236/347591; - 2218025/1859053, - 1061902/319253; - 6/5, - 1136236/347591; - 6/5, - 1136236/347591; - 3805535/3318088, - 1248373/379264; - 6/5, - 1136236/347591; - 6/5, - 1136236/347591], [- 33/50, 7306705/1830534; - 33/25, 1496013/461689; - 11175601/8832283, 2889106/886551; - 33/25, 1496013/461689; - 33/25, 1496013/461689; - 1622653/1239909, 11402195/3458438; - 33/25, 1496013/461689; - 33/25, 1496013/461689], [- 33/50, 1390261/606673; - 33/25, 1456770/478747; - 1861457/1422385, 937505/313939; - 33/25, 1456770/478747; - 33/25, 1456770/478747; - 2221263/1755505, 1706035/564096; - 33/25, 1456770/478747; - 33/25, 1456770/478747], [- 33/50, 5183051/6097868; - 33/25, 1507777/941629; - 2583232/1973911, 1137496/736421; - 33/25, 1507777/941629; - 33/25, 1507777/941629; - 1289641/1019227, 3584191/2264559; - 33/25, 1507777/941629; - 33/25, 1507777/941629], [- 33/50, - 5183051/6097868; - 33/25, - 1507777/941629; - 1289641/1019227, - 3584191/2264559; - 33/25, - 1507777/941629; - 33/25, - 1507777/941629; - 2583232/1973911, - 1137496/736421; - 33/25, - 1507777/941629; - 33/25, - 1507777/941629], [- 33/50, - 1390261/606673; - 33/25, - 1456770/478747; - 2221263/1755505, - 1706035/564096; - 33/25, - 1456770/478747; - 33/25, - 1456770/478747; - 1861457/1422385, - 937505/313939; - 33/25, - 1456770/478747; - 33/25, - 1456770/478747], [- 33/50, - 7306705/1830534; - 33/25, - 1496013/461689; - 1622653/1239909, - 11402195/3458438; - 33/25, - 1496013/461689; - 33/25, - 1496013/461689; - 11175601/8832283, - 2889106/886551; - 33/25, - 1496013/461689; - 33/25, - 1496013/461689], [- 18/25, 799091/204445; - 36/25, 1394335/433749; - 402571/290882, 4094989/1268377; - 36/25, 1394335/433749; - 36/25, 1394335/433749; - 1672295/1174337, 1391416/425497; - 36/25, 1394335/433749; - 36/25, 1394335/433749], [- 18/25, 1201782/506099; - 36/25, 369852/120529; - 2036923/1430390, 1130939/375342; - 36/25, 369852/120529; - 36/25, 369852/120529; - 11869362/8576335, 2110931/691053; - 36/25, 369852/120529; - 36/25, 369852/120529], [- 18/25, 1518721/1980095; - 36/25, 1251119/856363; - 1672295/1174337, 3234577/2301396; - 36/25, 1251119/856363; - 36/25, 1251119/856363; - 402571/290882, 2430919/1679909; - 36/25, 1251119/856363; - 36/25, 1251119/856363], [- 18/25, - 1518721/1980095; - 36/25, - 1251119/856363; - 402571/290882, - 2430919/1679909; - 36/25, - 1251119/856363; - 36/25, - 1251119/856363; - 1672295/1174337, - 3234577/2301396; - 36/25, - 1251119/856363; - 36/25, - 1251119/856363], [- 18/25, - 1201782/506099; - 36/25, - 369852/120529; - 11869362/8576335, - 2110931/691053; - 36/25, - 369852/120529; - 36/25, - 369852/120529; - 2036923/1430390, - 1130939/375342; - 36/25, - 369852/120529; - 36/25, - 369852/120529], [- 18/25, - 799091/204445; - 36/25, - 1394335/433749; - 1672295/1174337, - 1391416/425497; - 36/25, - 1394335/433749; - 36/25, - 1394335/433749; - 402571/290882, - 4094989/1268377; - 36/25, - 1394335/433749; - 36/25, - 1394335/433749], [- 39/50, 2157361/565091; - 39/25, 2336008/731845; - 1183536/787483, 1705047/532708; - 39/25, 2336008/731845; - 39/25, 2336008/731845; - 3718959/2416376, 1223060/376819; - 39/25, 2336008/731845; - 39/25, 2336008/731845], [- 39/50, 2596891/1053308; - 39/25, 4934005/1596124; - 5638599/3663653, 1065244/350705; - 39/25, 4934005/1596124; - 39/25, 4934005/1596124; - 1183536/787483, 1463951/474928; - 39/25, 4934005/1596124; - 39/25, 4934005/1596124], [- 39/50, 1091324/1614073; - 39/25, 1102861/847110; - 3079079/2000617, 317851/254667; - 39/25, 1102861/847110; - 39/25, 1102861/847110; - 1183536/787483, 1121281/867101; - 39/25, 1102861/847110; - 39/25, 1102861/847110], [- 39/50, - 1091324/1614073; - 39/25, - 1102861/847110; - 1183536/787483, - 1121281/867101; - 39/25, - 1102861/847110; - 39/25, - 1102861/847110; - 3079079/2000617, - 317851/254667; - 39/25, - 1102861/847110; - 39/25, - 1102861/847110], [- 39/50, - 2596891/1053308; - 39/25, - 4934005/1596124; - 1183536/787483, - 1463951/474928; - 39/25, - 4934005/1596124; - 39/25, - 4934005/1596124; - 5638599/3663653, - 1065244/350705; - 39/25, - 4934005/1596124; - 39/25, - 4934005/1596124], [- 39/50, - 2157361/565091; - 39/25, - 2336008/731845; - 3718959/2416376, - 1223060/376819; - 39/25, - 2336008/731845; - 39/25, - 2336008/731845; - 1183536/787483, - 1705047/532708; - 39/25, - 2336008/731845; - 39/25, - 2336008/731845], [- 21/25, 10115033/2722677; - 42/25, 1195878/376949; - 7186954/4430001, 2481972/781625; - 42/25, 1195878/376949; - 42/25, 1195878/376949; - 2560656/1548475, 1636057/507478; - 42/25, 1195878/376949; - 42/25, 1195878/376949], [- 21/25, 2124734/827363; - 42/25, 1552045/498943; - 1307606/790733, 16610159/5429420; - 42/25, 1552045/498943; - 42/25, 1552045/498943; - 12808984/7895391, 1496063/481392; - 42/25, 1552045/498943; - 42/25, 1552045/498943], [- 21/25, 1880499/3278912; - 42/25, 3997874/3582005; - 4957644/2997977, 1194412/1121807; - 42/25, 3997874/3582005; - 42/25, 3997874/3582005; - 3251533/2004228, 984759/884605; - 42/25, 3997874/3582005; - 42/25, 3997874/3582005], [- 21/25, - 1880499/3278912; - 42/25, - 3997874/3582005; - 3251533/2004228, - 984759/884605; - 42/25, - 3997874/3582005; - 42/25, - 3997874/3582005; - 4957644/2997977, - 1194412/1121807; - 42/25, - 3997874/3582005; - 42/25, - 3997874/3582005], [- 21/25, - 2124734/827363; - 42/25, - 1552045/498943; - 12808984/7895391, - 1496063/481392; - 42/25, - 1552045/498943; - 42/25, - 1552045/498943; - 1307606/790733, - 16610159/5429420; - 42/25, - 1552045/498943; - 42/25, - 1552045/498943], [- 21/25, - 10115033/2722677; - 42/25, - 1195878/376949; - 2560656/1548475, - 1636057/507478; - 42/25, - 1195878/376949; - 42/25, - 1195878/376949; - 7186954/4430001, - 2481972/781625; - 42/25, - 1195878/376949; - 42/25, - 1195878/376949], [- 9/10, 2193481/610552; - 9/5, 1613717/511199; - 1193465/684948, 2238807/710159; - 9/5, 1613717/511199; - 9/5, 1613717/511199; - 1241667/702466, 874817/272996; - 9/5, 1613717/511199; - 9/5, 1613717/511199], [- 9/10, 1446989/537801; - 9/5, 11121494/3557221; - 1376751/778889, 2574525/836243; - 9/5, 11121494/3557221; - 9/5, 11121494/3557221; - 1873377/1075160, 8669881/2769362; - 9/5, 11121494/3557221; - 9/5, 11121494/3557221], [- 9/10, 760341/1685800; - 9/5, 5842327/6587233; - 2987279/1690036, 1351032/1610017; - 9/5, 5842327/6587233; - 9/5, 5842327/6587233; - 1363443/782501, 2483553/2787055; - 9/5, 5842327/6587233; - 9/5, 5842327/6587233], [- 9/10, - 760341/1685800; - 9/5, - 5842327/6587233; - 1363443/782501, - 2483553/2787055; - 9/5, - 5842327/6587233; - 9/5, - 5842327/6587233; - 2987279/1690036, - 1351032/1610017; - 9/5, - 5842327/6587233; - 9/5, - 5842327/6587233], [- 9/10, - 1446989/537801; - 9/5, - 11121494/3557221; - 1873377/1075160, - 8669881/2769362; - 9/5, - 11121494/3557221; - 9/5, - 11121494/3557221; - 1376751/778889, - 2574525/836243; - 9/5, - 11121494/3557221; - 9/5, - 11121494/3557221], [- 9/10, - 2193481/610552; - 9/5, - 1613717/511199; - 1241667/702466, - 874817/272996; - 9/5, - 1613717/511199; - 9/5, - 1613717/511199; - 1193465/684948, - 2238807/710159; - 9/5, - 1613717/511199; - 9/5, - 1613717/511199], [- 24/25, 6085984/1776729; - 48/25, 1484113/471838; - 1744673/936025, 8045737/2569149; - 48/25, 1484113/471838; - 48/25, 1484113/471838; - 2076388/1104413, 5978951/1875985; - 48/25, 1484113/471838; - 48/25, 1484113/471838], [- 24/25, 15603923/5460120; - 48/25, 7613887/2426506; - 2076388/1104413, 237767/76796; - 48/25, 7613887/2426506; - 48/25, 7613887/2426506; - 1744673/936025, 2417704/767157; - 48/25, 7613887/2426506; - 48/25, 7613887/2426506], [- 24/25, 1824856/6430211; - 48/25, 704874/1250233; - 2076388/1104413, 2994048/5734831; - 48/25, 704874/1250233; - 48/25, 704874/1250233; - 1744673/936025, 1039591/1800136; - 48/25, 704874/1250233; - 48/25, 704874/1250233], [- 24/25, - 1824856/6430211; - 48/25, - 704874/1250233; - 1744673/936025, - 1039591/1800136; - 48/25, - 704874/1250233; - 48/25, - 704874/1250233; - 2076388/1104413, - 2994048/5734831; - 48/25, - 704874/1250233; - 48/25, - 704874/1250233], [- 24/25, - 15603923/5460120; - 48/25, - 7613887/2426506; - 1744673/936025, - 2417704/767157; - 48/25, - 7613887/2426506; - 48/25, - 7613887/2426506; - 2076388/1104413, - 237767/76796; - 48/25, - 7613887/2426506; - 48/25, - 7613887/2426506], [- 24/25, - 6085984/1776729; - 48/25, - 1484113/471838; - 2076388/1104413, - 5978951/1875985; - 48/25, - 1484113/471838; - 48/25, - 1484113/471838; - 1744673/936025, - 8045737/2569149; - 48/25, - 1484113/471838; - 48/25, - 1484113/471838]] contour:= count:= counter:= f_:= f_1:= fixedbarbs:= h:=0 hCross:=APPROX(2790322580645161/1000000000000000) inc:= k:=0 points:=APPEND([[x_, y_, y_1, f_, f_1]], points) propbarbs:=1/20 size:= slidebarbs:= vCross:=APPROX(12416666666666667/5000000000000000) vars:=[x, y] x0:= x1:= xCross:=APPROX(- 23999999999999999/10000000000000000) x_:=-2 y0:= y1:= yCross:=APPROX(- 23999999999999999/10000000000000000) y_:=[] y_1:=12/5 z0:= z1:= zCross:=APPROX(- 23999999999999999/10000000000000000) z_:= z_1:= CTextObj  {\rtf1\ansi\ansicpg1252\deff0\deflang2057{\fonttbl{\f0\fnil\fcharset0 Arial;}{\f1\fnil\fcharset2 DfW5 Printer;}} {\colortbl ;\red0\green0\blue128;\red0\green0\blue0;\red255\green0\blue0;\red0\green128\blue0;\red0\green0\blue255;} \viewkind4\uc1\pard\qc\cf1\b\fs40 2D and 3D Vector Fields\cf0\b0\fs24 \par \cf2\fs32 Terence Etchells\cf3 \par \fs24 School of Computing and Mathematical Sciences \par Liverpool John Moores University, UK\cf0 \par \pard\b [Revised by Mike Kawai, 04/04/2006]\b0 \par \par \fs20 This dfw file includes some functions from \cf4 Peter Schofields\cf0 \cf5 Arrows.dfw\cf0 file. \par \par Normally, we author the command below in the Algebra Window and then \par open a 2D Plot Window (then in the \b Window\b0 pull-down menu, select \par \b Tile Vertically\b0 to split the screen). \par Perform the following steps BEFORE you attempt to plot the vector field: \par \par 1. In the 2D Plot Window, select the \ul\b O\ulnone ptions \b0 pull-down menu and select \par \ul\b D\ulnone isplay. \b0 Click on the \b Points\b0 tab and set \b Connected\b0 to \b Yes\b0 and \par \b Size\b0 to\b Small\b0 . Click on "\b OK\b0 ". [Note that each time an Option is \par manipulated, the \ul\b O\ulnone ptions \b0 pull-down menu closes and we must re-open \par it each time. Sorry for the inconvenience.] \par \par 2. Select the \ul\b O\ulnone ptions \b0 pull-down menu again. Locate the item \par \b Change Plot Colors.\b0 If there is a check mark in front of this item, then \par click on it to REMOVE it. If there is no check mark there, then ignore \par this step. \par \par 3. Select the \ul\b O\ulnone ptions \b0 pull-down menu again. Select \par \b Appro\ul x\ulnone imate Before Plotting\b0 . [It's a good idea to check the \ul\b O\ulnone ptions \par \b0 menu one last time before you Plot. The option \b Change Plot Colors\b0 \par should NOT have a check mark in front of it, and the option \par \b Appro\ul x\ulnone imate Before Plotting\b0 SHOULD have a check mark in front of it. \par \ul\fs24 \ulnone \par \cf5\f1\fs32 \par \fs24 UNI_VECT_FIELD_2D(v, x, y, x0, y0, x1, y1, n, m)\cf0 \par \f0 \par \fs20 This function plots the 2D vector field v at uniformly selected points within the rectangle whose lower left corner is at (x0,y0) and upper right corner is (x1,y1). x and y are the variables in the vector field; n is the number of horizontal intervals; m the number of vertical intervals. \par \par e.g. highlight the function below, open a 2 D plot window and plot \par \f1 \par } {\rtf1\ansi\ansicpg1252\deff0\deflang1033{\fonttbl{\f0\fnil\fcharset2 DfW5 Printer;}} \viewkind4\uc1\pard\f0\fs24 This example plots the radial field \par F(x,y) := \par over the domain [-4,4] x [-4,4]. \par We plot 16 rows and 16 columns of vectors. \par } CExpnObj8*ZUser,UNI_VECT_FIELD_2D([x,y],x,y,-4,-4,4,4,16,16) CDispOleObj[f CDispItem0ࡱ>   !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~Root EntryF!cXOle CONTENTS2CompObjj F$Picture (Device Independent Bitmap) StaticDib9q| DdLp6Bit Rate      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~BM2B(