Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

How do I calculate the intersection curve between a plane and a drop?
The "drop" is defined in the following way:

R1 := 3.;R2 := 1.0;DR := 4;g := R2 + DR;

f1 := h -> sqrt(R1^2 - h^2);
f2 := h -> sqrt(g^2 - h^2);
f3 := h -> (1 - h/g)*f1(h*R1/g) + h*f2(h)/g;
f4 := h -> sqrt(1/2*g - 1/2*h);
f5 := h -> (1 - h/g)*f3(h) + h*f4(h)/g;
gg := h -> piecewise(h < 0, f1(h), 0 <= h, f5(h));#Radius depending on the z-position h
cir := (h, phi, R) -> <sin(phi)*R, cos(phi)*R, h>; # a circle at the hight h with radius R
#The plane is placed inside the drop.
n := (x, y, z) -> <x, y, z>/sqrt(x^2 + y^2 + z^2);

# the following lines show, how it looks like:
with(plots);
with(plottools);
dro1 := plot3d(cir(h, phi, gg(h)), h = -R1 .. g, phi = 0 .. 2*Pi, scaling = constrained, orientation = [-60, 72, 0]);
plotDropWithPlane := (x, y, z) -> display(dro1, arrow(Vector([0, 0, 0]), 2*R1*n(x, y, z), 0.2, 0.4, 0.1, cylindrical_arrow, fringe = blue, color = "Green"), implicitplot3d(x*x1 + y*y1 + z*z1 = 0, x1 = -R1 .. R1, y1 = -R1 .. R1, z1 = -R1 .. g, color = blue));
plotDropWithPlane(3, 1, 2);

#I'm searching a function like
fintersect:=theta-><"?,?,?>"

Any idea how to solve?

Best regards,

Andreas

unprotect(D); f := proc (x, y) options operator, arrow; (295849/5841396)*x^2-(29441/324522)*y*x+(33995/216348)*y^2-(5989/14751)*x+(3635/4917)*y+1 end proc; 295849 2 29441 33995 2 5989 f := (x, y) -> ------- x - ------ y x + ------ y - ----- x 5841396 324522 216348 14751 3635 + ---- y + 1 4917 coeffs(f(x, y)); -5989 3635 295849 33995 -29441 1, -----, ----, -------, ------, ------ 14751 4917 5841396 216348 324522 A, B, C, D, E, F := %; -5989 295849 33995 -29441 3635 A, B, C, D, E, F := 1, -----, -------, ------, ------, ---- 14751 5841396 216348 324522 4917

Is there any way we can get maple to tell us which variable we are recursively assigning? 

I would like to simplify

sin(4*pi*w)/sin(2*pi*w) 

The answer I am looking for is 2*cos(2*pi*w).

Does anyone have an idea how to do this is Maple? Some earlier version of Maple I used could do this, 

simplify( sin(4*pi*w)/sin(2*pi*w) ) =  2*cos(2*pi*w)

There a plenty of different trigonometric representations for the answer, so my hypothesis is that I should somehow tell to Maple which I am looking for. 

For example

Gives

Which is better, but still not the answer I am looking for

Best Regards,

P

 

 

 

RootOf(_Z^2*beta*h[1]-alpha*l[1]*l[2], label = _L2)


 

with(VectorCalculus)

pde := Laplacian(u(r, t), 'cylindrical'[r, theta, z]) = diff(u(r, t), t)

iv := {u(1, t) = 0, u(4, t) = 0, u(r, 0) = r}

dsol := pdsolve(pde, iv, numeric):-value(output = listprocedure)

sd := rhs(dsol[3])

proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (18446746697122892894)  ] ) ] ) INFO := table( [( "extrabcs" ) = [0], ( "totalwidth" ) = 6, ( "spacevar" ) = r, ( "dependson" ) = [{1}], ( "solmatrix" ) = Matrix(21, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0}, datatype = float[8], order = C_order), ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, xi; _s1 := 4*h^2; _s2 := -(h^2+k)/(h^2*k); mat[3] := 1; mat[6*n-3] := 1; for xi from 2 to n-1 do mat[6*xi-3] := _s2; mat[6*xi-4] := -(h-2*x[xi])/(_s1*x[xi]); mat[6*xi-2] := (h+2*x[xi])/(_s1*x[xi]) end do end proc, ( "leftwidth" ) = 1, ( "solmat_i1" ) = 0, ( "eqnords" ) = [[2, 1]], ( "allocspace" ) = 21, ( "method" ) = theta, ( "theta" ) = 1/2, ( "solmat_i2" ) = 0, ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "depords" ) = [[2, 1]], ( "rightwidth" ) = 0, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "spacepts" ) = 21, ( "indepvars" ) = [r, t], ( "minspcpoints" ) = 4, ( "startup_only" ) = false, ( "eqndep" ) = [1], ( "depdords" ) = [[[2, 1]]], ( "adjusted" ) = false, ( "norigdepvars" ) = 1, ( "solvec4" ) = 0, ( "explicit" ) = false, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "pts", r ) = [1, 4], ( "spaceidx" ) = 1, ( "solmat_v" ) = Vector(126, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 6, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0}, datatype = float[8], order = C_order))]), ( "maxords" ) = [2, 1], ( "solvec5" ) = 0, ( "fdepvars" ) = [u(r, t)], ( "spacestep" ) = .150000000000000, ( "banded" ) = true, ( "PDEs" ) = [(diff(u(r, t), r)+r*(diff(diff(u(r, t), r), r)))/r-(diff(u(r, t), t))], ( "erroraccum" ) = true, ( "autonomous" ) = true, ( "solmat_ne" ) = 0, ( "inputargs" ) = [(diff(u(r, t), r)+r*(diff(diff(u(r, t), r), r)))/r = diff(u(r, t), t), {u(1, t) = 0, u(4, t) = 0, u(r, 0) = r}], ( "multidep" ) = [false, false], ( "initialized" ) = false, ( "BCS", 1 ) = {[[1, 0, 1], b[1, 0, 1]], [[1, 0, 4], b[1, 0, 4]]}, ( "matrixhf" ) = true, ( "ICS" ) = [r], ( "timeadaptive" ) = false, ( "solspace" ) = Vector(21, {(1) = 1.0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 4.0}, datatype = float[8]), ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, _s5, _s6, xi; _s3 := -2*k; _s4 := -4*h^2; _s5 := -h*k; _s6 := 4*h^2*k; vec[1] := 0; vec[n] := 0; for xi from 2 to n-1 do _s1 := -vp[xi-1]+vp[xi+1]; _s2 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := (_s2*_s3*x[xi]+_s4*vp[xi]*x[xi]+_s1*_s5)/(_s6*x[xi]) end do end proc, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "timeidx" ) = 2, ( "depvars" ) = [u], ( "bandwidth" ) = [1, 2], ( "depshift" ) = [1], ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "timevar" ) = t, ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "timestep" ) = .150000000000000, ( "spaceadaptive" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "IBC" ) = b, ( "solmat_is" ) = 0, ( "errorest" ) = false, ( "mixed" ) = false, ( "vectorhf" ) = true, ( "linear" ) = true, ( "t0" ) = 0, ( "periodic" ) = false ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2:
", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2:
", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "2nd"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc

(1)

eval(diff(sd(r, t), r), [r = 2, t = 4])

(D[1](sd))(2, 4)

(2)

subs(r = 2, t = 4, diff(sd(r, t), r))

diff(sd(2, 4), 2)

(3)

 Using numerical methods, I cannot calculate the derivative of sd with respect to r at r = 2 and t = 4.

Oliveira.

``


 

Download Derivative-numerical.mw

Does anyone know how to enter in the pdsolve function Dirichlet conditions and Neumann values?

Oliveira.

I am reading the help page for "time" and it says that it will display the time elapsed since the maple kernel was loaded, but I just want output that is the value of the time and date displayed on my computer at the point the input in the command line is exrcuted. How do I do this? 

Hi,

I am struggling with one task involving solve and plot commands. I would appreciate if I could get some help. What I need to do is as follows:

1. Define alpha between 0 and 1.

2. Solve an equation f(x,alpha) =0 for x by taking different values of alpha.

3. Of all values of x obtained in step 2, choose the value of x between 0 and 1 and discard all others. I have technically shown that there will be exactly one value that is acceptable and all other values of x can be discarded.

4. For different values of alpha and correspondingly selected values of x in step 3, plot and display function g(x,alpha) with function value on the vertical axis and alpha on the horizontal axis.

Regards,

Omkar

 

solve({-infinity < a , a < -1, -1 < b ,  b < 0});

 

Hi, 

does anyone remember of a recent question (maybe a post) about a bouncing ball over a hilly ground?
I can't put the finger on it.

TIA

f(x) := piecewise(0 < x, x^(3/2)*sin(1/x), x = 0, 0, undefined);
plot(f(x));

gives me the following error:

Error, (in plot) incorrect first argument piecewise(0 < x, (HFloat(2.739493386336394e-116)+HFloat(2.739493386336394e-116)*I)*x^(3/2), x = 0, 0, undefined)

I just want to see the function plot. With Wolfram Alpha this is no deal at all!
 

I used the implicit function to draw two images, how to display only the intersection of two images? Or, how do I draw the x^2+y^2+z^2=1 image under x+y+z=0 condition? Code show as above.Thank you.

 

Is it because I have handed subs a multiset or is it because I used the "``" things in the code producing my set? I seemed to remember algsubs and subs working perfectly well regardless of the dimensions of the argument in previous times i have needed it.

 

 

 

abCaseSet := {[`0<a<1`, `0<b<1`], [`0<a<1`, `b=-1`], [`0<a<1`, `b=0`], [`0<a<1`, `b=1`], [`0<a<1`, `1<b<&infin;`], [`0<a<1`, -`1<b<0`], [`0<a<1`, -`&infin;<b<-1`], [`a=-1`, `0<b<1`], [`a=-1`, `b=-1`], [`a=-1`, `b=0`], [`a=-1`, `b=1`], [`a=-1`, `1<b<&infin;`], [`a=-1`, -`1<b<0`], [`a=-1`, -`&infin;<b<-1`], [`a=0`, `0<b<1`], [`a=0`, `b=-1`], [`a=0`, `b=0`], [`a=0`, `b=1`], [`a=0`, `1<b<&infin;`], [`a=0`, -`1<b<0`], [`a=0`, -`&infin;<b<-1`], [`a=1`, `0<b<1`], [`a=1`, `b=-1`], [`a=1`, `b=0`], [`a=1`, `b=1`], [`a=1`, `1<b<&infin;`], [`a=1`, -`1<b<0`], [`a=1`, -`&infin;<b<-1`], [`1<a<&infin;`, `0<b<1`], [`1<a<&infin;`, `b=-1`], [`1<a<&infin;`, `b=0`], [`1<a<&infin;`, `b=1`], [`1<a<&infin;`, `1<b<&infin;`], [`1<a<&infin;`, -`1<b<0`], [`1<a<&infin;`, -`&infin;<b<-1`], [-`1<a<0`, `0<b<1`], [-`1<a<0`, `b=-1`], [-`1<a<0`, `b=0`], [-`1<a<0`, `b=1`], [-`1<a<0`, `1<b<&infin;`], [-`1<a<0`, -`1<b<0`], [-`1<a<0`, -`&infin;<b<-1`], [-`&infin;<a<-1`, `0<b<1`], [-`&infin;<a<-1`, `b=-1`], [-`&infin;<a<-1`, `b=0`], [-`&infin;<a<-1`, `b=1`], [-`&infin;<a<-1`, `1<b<&infin;`], [-`&infin;<a<-1`, -`1<b<0`], [-`&infin;<a<-1`, -`&infin;<b<-1`]}

{[`0<a<1`, `0<b<1`], [`0<a<1`, `b=-1`], [`0<a<1`, `b=0`], [`0<a<1`, `b=1`], [`0<a<1`, `1<b<&infin;`], [`0<a<1`, -`1<b<0`], [`0<a<1`, -`&infin;<b<-1`], [`a=-1`, `0<b<1`], [`a=-1`, `b=-1`], [`a=-1`, `b=0`], [`a=-1`, `b=1`], [`a=-1`, `1<b<&infin;`], [`a=-1`, -`1<b<0`], [`a=-1`, -`&infin;<b<-1`], [`a=0`, `0<b<1`], [`a=0`, `b=-1`], [`a=0`, `b=0`], [`a=0`, `b=1`], [`a=0`, `1<b<&infin;`], [`a=0`, -`1<b<0`], [`a=0`, -`&infin;<b<-1`], [`a=1`, `0<b<1`], [`a=1`, `b=-1`], [`a=1`, `b=0`], [`a=1`, `b=1`], [`a=1`, `1<b<&infin;`], [`a=1`, -`1<b<0`], [`a=1`, -`&infin;<b<-1`], [`1<a<&infin;`, `0<b<1`], [`1<a<&infin;`, `b=-1`], [`1<a<&infin;`, `b=0`], [`1<a<&infin;`, `b=1`], [`1<a<&infin;`, `1<b<&infin;`], [`1<a<&infin;`, -`1<b<0`], [`1<a<&infin;`, -`&infin;<b<-1`], [-`1<a<0`, `0<b<1`], [-`1<a<0`, `b=-1`], [-`1<a<0`, `b=0`], [-`1<a<0`, `b=1`], [-`1<a<0`, `1<b<&infin;`], [-`1<a<0`, -`1<b<0`], [-`1<a<0`, -`&infin;<b<-1`], [-`&infin;<a<-1`, `0<b<1`], [-`&infin;<a<-1`, `b=-1`], [-`&infin;<a<-1`, `b=0`], [-`&infin;<a<-1`, `b=1`], [-`&infin;<a<-1`, `1<b<&infin;`], [-`&infin;<a<-1`, -`1<b<0`], [-`&infin;<a<-1`, -`&infin;<b<-1`]}

(1)

map(subs, {[`0<a<1`, `0<b<1`], [`0<a<1`, `b=-1`], [`0<a<1`, `b=0`], [`0<a<1`, `b=1`], [`0<a<1`, `1<b<&infin;`], [`0<a<1`, -`1<b<0`], [`0<a<1`, -`&infin;<b<-1`], [`a=-1`, `0<b<1`], [`a=-1`, `b=-1`], [`a=-1`, `b=0`], [`a=-1`, `b=1`], [`a=-1`, `1<b<&infin;`], [`a=-1`, -`1<b<0`], [`a=-1`, -`&infin;<b<-1`], [`a=0`, `0<b<1`], [`a=0`, `b=-1`], [`a=0`, `b=0`], [`a=0`, `b=1`], [`a=0`, `1<b<&infin;`], [`a=0`, -`1<b<0`], [`a=0`, -`&infin;<b<-1`], [`a=1`, `0<b<1`], [`a=1`, `b=-1`], [`a=1`, `b=0`], [`a=1`, `b=1`], [`a=1`, `1<b<&infin;`], [`a=1`, -`1<b<0`], [`a=1`, -`&infin;<b<-1`], [`1<a<&infin;`, `0<b<1`], [`1<a<&infin;`, `b=-1`], [`1<a<&infin;`, `b=0`], [`1<a<&infin;`, `b=1`], [`1<a<&infin;`, `1<b<&infin;`], [`1<a<&infin;`, -`1<b<0`], [`1<a<&infin;`, -`&infin;<b<-1`], [-`1<a<0`, `0<b<1`], [-`1<a<0`, `b=-1`], [-`1<a<0`, `b=0`], [-`1<a<0`, `b=1`], [-`1<a<0`, `1<b<&infin;`], [-`1<a<0`, -`1<b<0`], [-`1<a<0`, -`&infin;<b<-1`], [-`&infin;<a<-1`, `0<b<1`], [-`&infin;<a<-1`, `b=-1`], [-`&infin;<a<-1`, `b=0`], [-`&infin;<a<-1`, `b=1`], [-`&infin;<a<-1`, `1<b<&infin;`], [-`&infin;<a<-1`, -`1<b<0`], [-`&infin;<a<-1`, -`&infin;<b<-1`]}, a = A)

Error, invalid input: subs received [`0<a<1`, `0<b<1`], which is not valid for its 1st argument

 

``


 

Download subsQuestionMP.mw

 

Why Maple returns -1/x as singular solution below when this solution can be obtained from the general solution when constant of integration is zero?

restart;

ode:=2*y(x)+2*x*y(x)^2+(2*x+2*x^2*y(x))*diff(y(x),x) = 0;
dsolve(ode,singsol=false);

2*y(x)+2*x*y(x)^2+(2*x+2*x^2*y(x))*(diff(y(x), x)) = 0

y(x) = (-1-_C1)/x, y(x) = (-1+_C1)/x

sol:=[dsolve(ode,singsol=essential)];

[y(x) = -1/x, y(x) = (-1-_C1)/x, y(x) = (-1+_C1)/x]

subs(_C1=0,sol)

[y(x) = -1/x, y(x) = -1/x, y(x) = -1/x]

 


Download essential.mw

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