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janhardo

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12 years, 107 days
B. Ed math
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These are answers submitted by janhardo

The model llm is too small to answer thi...

janhardo 1007
October 02 2026
1 0

Apparently, the LLM model is simply too small to be able to reason this out?

Download torus-clairaut-worksheet_29-9-2...

janhardo 1007
September 29 2026
1 1

Download torus-clairaut-worksheet_29-9-2026.mw
torus-clairaut-worksheet-VERSION_B_29-9-2026.mw

I used the geom3d package It's ...

janhardo 1007
August 29 2026
3 3

I used the geom3d package 

restart:
with(geom3d):

# Twee vlakken
plane(P1, 2*x-y+z=3, [x,y,z]): plane(P2, x+2*y-z=-1, [x,y,z]):

# Punten op P1
point(A, 1, 0, 1): point(B, 0, 0, 3):

# Punten op P2
point(C, 0, 0, 1): point(E, 1, 0, 2):

draw([P1(color=blue,transparency=0.35,style=surface),
      P2(color=green,transparency=0.35,style=surface),
      A(color=red,symbol=solidsphere,symbolsize=18),
      B(color=red,symbol=solidsphere,symbolsize=18),
      C(color=red,symbol=solidsphere,symbolsize=18),
      E(color=red,symbol=solidsphere,symbolsize=18)],
      view=[-4..4,-4..4,-4..6],axes=boxed,labels=[x,y,z],
      scaling=constrained,orientation=[60,65]);

It's complicated to make a Geom3D package completely easy to use.
I've asked for outside help to point me in the right direction.

@Angelo Melino ...

janhardo 1007
August 27 2026
0 7

@Angelo Melino 

@Ronan weinburger_-module_-maple_pr...

janhardo 1007
August 15 2026
0 28

@Ronan 
A start module 
weinburger_-module_-maple_primesDEF_15-8-2026.mw

  The integral outcome...

janhardo 1007
August 10 2026
2 4

  The integral outcome

 for 0< a <Pi

restart: with(codegen): F := proc(x,y)...

janhardo 1007
August 08 2026
3 3 
restart:
with(codegen):

F := proc(x,y)
    x*y^2
end proc:

G_forward := GRADIENT(F, mode=forward):

G_forward;
                           G_forward


G_forward(2,3);
                             9, 12

 

foo := proc(params) local b,c,d; b := ...

janhardo 1007
August 05 2026
0 9 
foo := proc(params)
local b,c,d;

b := rhs(params[1]);
c := rhs(params[2]);
d := rhs(params[3]);

print(b,c,d);

end proc;

foo([b = 2, c = 3, d = 4]);
foo([b = 2, c = 3, d = 4]);
                            2, 3, 4

                            2, 3, 4

Once the procedure has finished, these local variables are no longer in use.
No global assignments were made.

Therefore, the second call is exactly the same as the first:

 

in this format : as fiirst order re...

janhardo 1007
August 02 2026
0 0

in this format : as fiirst order recurrence equation

 Alfred_F 590After series opti...

janhardo 1007
July 29 2026
1 0

 Alfred_F 590
After series option in dsolve  : order= 10 as example 

restart;

infolevel[dsolve] := 5:

ode := (1+f(x))*diff(f(x),x$2)=1+x:
ics := {f(0)=1,D(f)(0)=0}:

T := time():

sol := dsolve(ics union {ode}, f(x));

time()-T;

Does the AI in Maple itself provide bet...

janhardo 1007
July 25 2026
0 2


Does the AI in Maple itself provide better answers than when using AI outside of Maple?

How_can_I_define_a_Tensor_equation_mprim...

janhardo 1007
July 19 2026
1 0

I've been tinkering with the tensor a bit


 

experiment with different conditions for...

janhardo 1007
July 16 2026
1 17

experiment with different conditions for heated rod ( easy experiment, because there can be a lot more involved)   )

heat_pde_procedure_mprimes_16-7-2026.mw

  > ....

janhardo 1007
July 08 2026
0 3

use display command with ; 
The code was otherwise to large for uploading to the mprime server 
 

> 

 

 

 
> 

restart:
with(plots):
with(plottools):

interface(imaginaryunit = J):

printf("\n"):
printf("=============================================================\n"):
printf("      FARADAY-LENZ-LORENTZ: DIDACTIC 3D SIMULATION\n"):
printf("=============================================================\n\n"):

printf("External magnetic field:\n"):
printf("   black arrows point downward: B_ext = -B k\n\n"):

printf("Induced magnetic field:\n"):
printf("   magenta arrows point upward: B_ind = +B_ind k\n\n"):

printf("This shows Lenz's law visually:\n"):
printf("the induced magnetic field opposes the increasing external flux.\n\n"):

printf("Blue rails       = parabolic conducting rails\n"):
printf("Red rod          = moving conducting rod\n"):
printf("Cyan surface     = enclosed flux area\n"):
printf("Black arrows     = external magnetic field downward\n"):
printf("Magenta arrows   = induced counter-field upward\n"):
printf("Yellow arrows    = induced current direction\n"):
printf("Green arrow      = Lorentz force on the rod\n\n"):

printf("=============================================================\n\n"):


# ============================================================
# 1. Parameters
# ============================================================

ParmValues := 0.5, 0.5, 1, 1, 2:

# B    = magnetic field strength
# r    = resistance per unit length
# m    = rod mass
# x__0 = initial position
# v__0 = initial velocity


# ============================================================
# 2. Geometry
# ============================================================

T := x -> (4/3)*x^(3/2):


# ============================================================
# 3. Equation of motion
# ============================================================

ode :=
    m*diff(x(t), t) + B^2*T(x(t))/r
    =
    m*v__0 + B^2*T(x__0)/r:

ics := x(0) = x__0:


# ============================================================
# 4. Numerical solution
# ============================================================

Sol := dsolve(
    {ode, ics},
    numeric,
    parameters = [B, r, m, x__0, v__0]
):

Sol(parameters = [ParmValues]):

B, r, m, x__0, v__0 := ParmValues:


# ============================================================
# 5. Clear external magnetic field arrows
# ============================================================

# Black arrows:
# start high, end low
# direction = downward = -z direction

ExternalBArrow := proc(a, b)
    return arrow(
        [a, b, 1.80],
        [a, b, 0.35],
        0.09,
        0.28,
        0.10,
        color = black
    ):
end proc:

DispExternalB := display(
    seq(
        seq(
            ExternalBArrow(a, b),
            a = 0 .. 5, 0.75
        ),
        b = -3.5 .. 3.5, 0.75
    )
):


# ============================================================
# 6. Clear induced magnetic counter-field arrows
# ============================================================

# Magenta arrows:
# start low, end high
# direction = upward = +z direction
#
# Their height depends on the induced current I.

InducedBArrow := proc(a, b, h)
    return arrow(
        [a, b, 0.05],
        [a, b, 0.05 + h],
        0.08,
        0.25,
        0.09,
        color = magenta
    ):
end proc:


# ============================================================
# 7. Rails
# ============================================================

RailTop := spacecurve(
    [s, sqrt(s), 0],
    s = 0 .. 5,
    color = blue,
    thickness = 6
):

RailBottom := spacecurve(
    [s, -sqrt(s), 0],
    s = 0 .. 5,
    color = blue,
    thickness = 6
):

DispWire := display([RailTop, RailBottom]):


# ============================================================
# 8. Animation loop
# ============================================================

i := 0:

for tau from 0 by 0.025 to 4 do

    vals := Sol(tau):

    X := rhs(vals[2]):

    V :=
        (
            m*v__0
            + B^2*T(x__0)/r
            - B^2*T(X)/r
        )/m:

    L := 2*sqrt(X):

    DiffT := L*V:

    Flux := B*T(X):

    EMF := B*DiffT:

    R := r*L:

    I := EMF/R:

    LorentzForce := I*B*L:

    Accel := -LorentzForce/m:

    JoulePower := I^2*R:

    InducedHeight := min(1.25, 0.35 + 0.70*abs(I)):

    Rod := spacecurve(
        [X, u, 0],
        u = -sqrt(X) .. sqrt(X),
        color = red,
        thickness = 9
    ):

    AreaPatch := plot3d(
        [s, q*sqrt(s), 0],
        s = 0 .. X,
        q = -1 .. 1,
        color = cyan,
        transparency = 0.65
    ):

    # Induced field only inside the enclosed loop
    DispInducedB := display(
        seq(
            seq(
                InducedBArrow(s, q*sqrt(s), InducedHeight),
                s = 0.30 .. X, 0.65
            ),
            q = -0.70 .. 0.70, 0.35
        )
    ):

    # Current direction:
    # for external B downward and increasing flux,
    # induced current is counterclockwise when viewed from +z.

    CurrentBottom := arrow(
        [0.20*X, -sqrt(0.20*X), 0.18],
        [0.60*X, -sqrt(0.60*X), 0.18],
        0.09,
        0.28,
        0.10,
        color = yellow
    ):

    CurrentRod := arrow(
        [X, -0.65*sqrt(X), 0.18],
        [X,  0.65*sqrt(X), 0.18],
        0.09,
        0.28,
        0.10,
        color = yellow
    ):

    CurrentTop := arrow(
        [0.85*X, sqrt(0.85*X), 0.18],
        [0.45*X, sqrt(0.45*X), 0.18],
        0.09,
        0.28,
        0.10,
        color = yellow
    ):

    DispCurrent := display(
        [CurrentBottom, CurrentRod, CurrentTop]
    ):

    # Lorentz force opposes motion, therefore points left
    ForceArrow := arrow(
        [X, 0, 0.55],
        [X - min(1.20, 0.35 + 0.35*abs(LorentzForce)), 0, 0.55],
        0.10,
        0.30,
        0.11,
        color = green
    ):

    i := i + 1:

    Disp[i] := display(
        [
            DispExternalB,
            DispInducedB,
            DispWire,
            AreaPatch,
            Rod,
            DispCurrent,
            ForceArrow
        ],
        axes = normal,
        labels = ["x", "y", "z"],
        scaling = constrained,
        orientation = [60, 68],
        view = [0 .. 5, -3.8 .. 3.8, -0.2 .. 2.0],
        size = [1100, 850],
        caption = typeset(
            "BLACK: B_ext downward  |  MAGENTA: B_ind upward  |  t=%1, x=%2, v=%3, EMF=%4, I=%5, F_L=%6",
            evalf(tau, 3),
            evalf(X, 4),
            evalf(V, 4),
            evalf(EMF, 4),
            evalf(I, 4),
            evalf(LorentzForce, 4)
        ),
        captionfont = [Courier, bold, 14]
    ):

end do:


# ============================================================
# 9. Display larger animation
# ============================================================

display(
    seq(Disp[j], j = 1 .. i),
    insequence,
    axes = normal,
    labels = ["x", "y", "z"],
    scaling = constrained,
    orientation = [60, 68],
    size = [1100, 850],
    title = typeset(
        "Lenz's law: induced magenta field points opposite to increasing external black flux"
    ),
    titlefont = [Courier, bold, 16]
):


=============================================================
      FARADAY-LENZ-LORENTZ: DIDACTIC 3D SIMULATION
=============================================================

External magnetic field:
   black arrows point downward: B_ext = -B k

Induced magnetic field:
   magenta arrows point upward: B_ind = +B_ind k

This shows Lenz's law visually:
the induced magnetic field opposes the increasing external flux.

Blue rails       = parabolic conducting rails
Red rod          = moving conducting rod
Cyan surface     = enclosed flux area
Black arrows     = external magnetic field downward
Magenta arrows   = induced counter-field upward
Yellow arrows    = induced current direction
Green arrow      = Lorentz force on the rod

=============================================================
 

  
> 

 

Download conducting_rod_in_magnetisch_veld_mprimesVersie_A_8-7-2026.mw

@KIRAN SAJJAN Cannot upload now, so...

janhardo 1007
July 06 2026
0 2

@KIRAN SAJJAN 
no shooting method is used

 

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