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plots using only single implicit functions

by: Mahardika Mathematics 35 Maple 2016
animation implicit plotting
March 29 2023
1  5

Creating Graph Equation of An Apple in Cartesian Space using single Implicit Function only run by Maple software

Enjoy...

Please click the link below to see full equation on Maple file:

2._Apel_3D_A.mw

 

Creating Graph Equation of A Candle on Cartesian Plane using single Implicit Function only run by Maple software

Enjoy...

3D_Candle.mw

Sea_Shells.mw

 

 

 

Today I'm very greatfull to have Inspiration to create Graph Equation of 3D Candle in Cartesian Space using single 3D Implicit Function only, run by Maple software.

Enjoy... 

Candle_1.mw

 

Today I got an inspiration to create graph equation of "Petrol Truck" using only with Single Implicit Equation in Cartesian space run by Maple Software

Maple software is amazing...

Enjoy...

 

CREATING 3D GRAPH EQUATION OF BACTERIOPHAGE USING ONLY WITH SINGLE IMPLICIT EQAUTION IN CARTESIAN SPACE RUN BY MAPLE SOFTWARE

MAPLE SOFTWARE IS AMAZING...

ENJOY...

 

GRAPH EQUATION OF A FEATHER

AND THE EQUATION IS:

ENJOY...

I like this Equation and post it because it is so beautiful...

Click this link below to see full equation and download the Maple file: 

Bulu_Angsa_3.mw

 

GRAPH EQUATION OF "383" CREATED BY DHIMAS MAHARDIKA

ENJOY...

> 

with(plots):

DHIMAS MAHARDIKA EQUATION

> 

plots:-implicitplot(15-8.*cos(y)^(79/2)-32.*cos(y)^(37/2)+96.*cos(y)^(33/2)-96.*cos(y)^(29/2)+4.*cos(x)^(61/2)+4.*cos(x)^(31/2)-12.*cos(x)^(27/2)+12.*cos(x)^(23/2)+24.*cos(y)^29-48.*cos(y)^27+16.*cos(y)^8-64.*cos(y)^6+96.*cos(y)^4-4.*cos(x)^(19/2)-6.*cos(x)^19-4.*cos(x)^(57/2)+32.*cos(y)^(25/2)+24.*cos(y)^25+8.*cos(y)^(75/2)-cos(x)^38+cos(y)^50-64.*cos(y)^2+4.*cos(x)^2-6.*cos(x)^4+4.*cos(x)^6-cos(x)^8+12.*cos(x)^21-6.*cos(x)^23, x = -15 .. 15, y = -15 .. 15, numpoints = 50000, thickness = 4, colour = blue)

 
> 

NULL

Download 383.mw

 

Drawing Eifel Tower using Implicit Equation in Cartesian Space 

How can I handle this error?...

Asked by: OLOWE RUTH 5
syntax differential-equations
March 22 2023
1  4

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

Non zero Christoffel display ...

Asked by: albivaldmaple 20
tensor physics christoffel
March 08 2023
2  1

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

restart; with(Physics)

Physics:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

 (1)

Physics:-Setup(spacetimeindices, dimension = 2, signature = "++")

[dimension = 2, signature = `+ +`, spacetimeindices = greek]

 (2)

Physics:-Coordinates(X)

{X}

 (3)

ds2 := Physics:-`^`(dx1, 2)+Physics:-`*`(Physics:-`^`(sin(x1), 2), Physics:-`^`(dx2, 2))

dx1^2+sin(x1)^2*dx2^2

 (4)

NULL

Physics:-Setup(metric = ds2)

[metric = {(1, 1) = 1, (2, 2) = sin(x1)^2}]

 (5)

NULL

NULL

g_[]

g[mu, nu] = (Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 2) = sin(x1)^2}, storage = triangular[upper], shape = [symmetric]))

 (6)

Physics:-Christoffel[`~k`, i, j]

Physics:-Christoffel[`~k`, i, j]

 (7)

Physics:-Christoffel[`~1`, 2, 2]

-sin(x1)*cos(x1)

 (8)

Physics:-Christoffel[`~2`, 1, 2]

cos(x1)/sin(x1)

 (9)

Physics:-Christoffel[`~1`, 1, 1]

0

 (10)

Download Approfondimento_1_-_Calcolo_Sfera_2D.mw

Lorentz tansformation leaves Minkowski metric inv...

Asked by: albivaldmaple 20
February 04 2023
2  5

Hello everybody

I would like to check, with Spacetime Tensors computation , if  a transfomation is a Lorentz transformation , i.e that leavs Minkosky metric invariant 

For esample a boost  or axis rotation transformation

Some could help me ? ( Maple 2016)

Thank's a lot

Any comment, idea or innovation to calculate this ...

Asked by: mehdibgh 240
integration
January 14 2023
0  3

Any comment, idea or innovation to calculate this parametric integral?

Note M, II, JJ are arbitrary positive integers (0<M, II, JJ<11).

F must be a function of Pm at the final!

``

> 

restart
> 

M := 3:
> 

JJ := 5
> 

II := 5
> 

with(ArrayTools):
> 

W := RandomArray(II, JJ, M):
> 

V := ArrayTools:-RandomArray(II, JJ, M):
> 

w := add(add(add(W[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

v := add(add(add(V[i, j, m]*LegendreP(i-1, x)*LegendreP(j-1, y)*p[m], i = 1 .. II), j = 1 .. JJ), m = 1 .. M):
> 

L := add(add((LegendreP(i-1, x)*LegendreP(j-1, y))^2, i = 1 .. II), j = 1 .. JJ):
> 

H := 1+tanh(w-v)
> 

F := int(H*L, [y = -1 .. 1, x = -1 .. 1])

Warning,  computation interrupted

  
> 

``
> 

``

Download integralproblem.mw

Don't know where the error is from...

Asked by: kencom1 110
pde numeric pdsolve
January 08 2023
1  5

Good day everyone,

I have been having problems with a system of PDE solution using `numeric`.

It's giving me the error code "Error, (in pdsolve/numeric/par_hyp) input system is too far from a 'standard' form (see ?pdsolve,numeric for more detail)" and I have checked to the best of my ability for the error but could not see anything.

The code is attached below.

Please, anyone with useful information should help. Thanks

Numeric.mw

Solve a system of nonlinear algebraic equations...

Asked by: moh111 20
solve
October 30 2022
1  5

How can these eight equations q[0]...q[7] be solved for the eight unknowns a1[0]...a1[7] and with the lowest CPU time

11.mw

Transplots not working for PDE...

Asked by: kencom1 110
syntax transform plotting
October 23 2022
0  2

Good day everyone,

I am trying to rotate the plots of pde solution using transplot, but it is giving me errors. Anyone with better suggestions should help. The code is attached below. Thanks

Transplot_not_working.mw

Please help with this DTM-Pade CODE...

Asked by: Syed Asadullah Shah 15
solve syntax homework
October 11 2022
0  12

DTM_Pade_for_A_and_B.mw

> 

restart; Digits := 10; m := 2; F[0] := 0; M := 1; F[1] := 1; F[2] := (1/2)*A; T[0] := 0; T[1] := B; for k from 0 to m+2 do F[k+3] := (M*(k+1)*F[k+1]+sum((k-r+1)*(r+1)*F[r+1]*F[k-r+1], r = 0 .. k)-(sum((k-r+1)*(k-r+2)*F[r]*F[k-r+2], r = 0 .. k)))*factorial(k)/factorial(k+3); T[k+1] := (2*(sum((k-r+1)*F[k-r+1], r = 0 .. k))+(2*(k+2))*(k+1)*F(k+2))*factorial(k)/factorial(k+1) end do; f := 0; t := 0; for k from 0 to m do f := f+F[k]*x^k; t := t+T[k]*x^k end do; print(f); print(t); with(numapprox); pade(t, x, [2, 2]); pade(diff(f, x), x, [2, 2]); solve({limit(pade*(t, x, [2, 2]), x = infinity) = 0., limit(pade(diff(f, x), x, [2, 2]), x = infinity) = 0.}, [A, B])

x+(1/2)*A*x^2

  

(2+4*(table( [( 0 ) = 0, ( 1 ) = 1, ( 2 ) = (1/2)*A, ( 3 ) = 1/3, ( 4 ) = (1/12)*A, ( 5 ) = 1/60+(1/120)*A^2, ( 6 ) = (1/180)*A, ( 7 ) = 1/840+(1/5040)*A^2 ] ))(k+2))*x+(1+A+6*(table( [( 0 ) = 0, ( 1 ) = 1, ( 2 ) = (1/2)*A, ( 3 ) = 1/3, ( 4 ) = (1/12)*A, ( 5 ) = 1/60+(1/120)*A^2, ( 6 ) = (1/180)*A, ( 7 ) = 1/840+(1/5040)*A^2 ] ))(k+2))*x^2

  

Error, (in testeq) invalid arguments

  
> 

NULL

Download DTM_Pade_for_A_and_B.mw

use union, intersection and minus A and B...

Asked by: minhhieuh2003 135
intersection realrange minus
September 19 2022
1  2

I want to use union, intersection and minus to find. Help me

What is the convenient way to export a large symbo...

Asked by: mehdibgh 240
matrix matlab export
September 09 2022
0  6

What is the best and accurate way to export a large symbolic matrix (200*300) from Maple to Matlab? The Marix have a lot of variables, symbols and operators such as diiff, int, ....

Here is a simple example:

NULL

> 

restart
> 

NULL
> 

A := Matrix(2, 6, {(1, 1) = x*y*z, (1, 2) = (1/2)*tau[2], (1, 3) = sin(x*y*z), (1, 4) = ln(x*y*z), (1, 5) = tau[1]*exp(x*y*z), (1, 6) = sin(x+y)+cos(x+y), (2, 1) = x^2+1, (2, 2) = x^2+1/sin(x*y*z), (2, 3) = 2*exp(y), (2, 4) = tau[1], (2, 5) = diff(f(x, y, z), x), (2, 6) = int(f(x, y, z), x)})

A := 1/sin(protected)

 (1)
> 

``
> 

CodeGeneration[Matlab](codegen[makeproc](A, [x, y, tau[1], tau[2]]))

Error, (in codegen/makeproc) optional arguments must be equations [x, y, tau[1], tau[2]]

  
> 

``
> 

``
> 

``
> 

``
> 

``
> 

``

Download export.mw

Why this procedure does not work to get the numeri...

Asked by: mehdibgh 240
table procedure
September 05 2022
0  4

Where is the problem within this procedure which I can not get the numerical values of V[1] , V[2], ...

> 

restart
> 

A := Matrix([[2*t, 2, 3], [4, 5*t, 6], [7, 8*t, 9]])

A := Matrix(3, 3, {(1, 1) = 2*t, (1, 2) = 2, (1, 3) = 3, (2, 1) = 4, (2, 2) = 5*t, (2, 3) = 6, (3, 1) = 7, (3, 2) = 8*t, (3, 3) = 9})

 (1)
> 

B := LinearAlgebra:-Transpose(Matrix([t, 2*t, 3*t]))

B := Matrix(3, 1, {(1, 1) = t, (2, 1) = 2*t, (3, 1) = 3*t})

 (2)
> 

``
> 

test:=proc(n)
  local s,t,M,V;
  s:=1:
  for t from 1 to n do
    M:=A+A^(-1);
    V[s]:=(M.B):
    s:=s+1:
  end do;
  V;
end proc:
> 

``
> 

test(4)

V

 (3)
> 

V[1]

V[1]

 (4)
> 

``
> 

``

Download ProcPropl.mw

Where is the problem in my loop which increases th...

Asked by: mehdibgh 240
performance integration memory
September 01 2022
0  6

In part of my program, I have a loop that the iterative calculations are performed there. During running the program when it comes to the loop the memory usage become full in a short period of time and I face the memory shortage. Since my program is so long and huge, I only can show the loop part of it here, you may look at where is the problem of high memory usage in loop and how to deal with it. Any comment will be appreciated.

I again note that, this segment can not be run independently since it is a part of big program. I put it just to see and mmake comment if any.

> 

M := 3; Nm := 1
> 

w0 := Matrix(M+Nm, 1)
> 

wd0 := Matrix(M+Nm, 1)
> 

taim := 1
> 

F0 := convert([seq(Quadrature(Quadrature(simplify(add(add(W[i, j, 4, r]*LegendreP(i, 1)*LegendreP(j, 0), i = 0 .. II), j = 0 .. JJ)), `&zeta;__1` = -1 .. 1, method = romberg[3]), `&eta;__1` = -1 .. 1, method = romberg[3]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)
> 

T := 1/(2*Pi*`&omega;__km`[M][2])
> 

dt := (1/10)*T

0.1123479896110e-4

 (1)
> 

for i to M do tau[i](t) := tau[i] end do
> 

for i to Nm do p[i](t) := p[i] end do
> 

`&alpha;__N` := .5; `&beta;__N` := .25; a__0 := 1/(`&beta;__N`*dt^2); a__1 := `&alpha;__N`/(`&beta;__N`*dt); a__2 := 1/(`&beta;__N`*dt); a__3 := 1/(2*`&beta;__N`)-1; a__4 := `&alpha;__N`/`&beta;__N`-1; a__5 := dt*(`&alpha;__N`/(2*`&beta;__N`)-1); a__6 := dt*(1-`&alpha;__N`); a__7 := `&alpha;__N`*dt
> 

q := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

dq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

ddq := Matrix(1 .. M+Nm, 1 .. floor(taim/dt)+1)
> 

q(1 .. M+Nm, 1) := w0
> 

dq(1 .. M+Nm, 1) := wd0
> 

for i to M do tau[i] := q(i, 1) end do
> 

for i to Nm do p[i] := q(M+i, 1) end do
> 

ddq(1 .. M+Nm, 1) := 1/ML.(diff((diff(sin(`&omega;__b`*t__0), t__0))*LinearAlgebra:-Transpose(F0), t__0)-CL.dq(1 .. M+Nm, 1 .. 1)-KL.q(1 .. M+Nm, 1 .. 1)-eqMNL)
> 

t__0 := dt
> 

V := LinearAlgebra:-Transpose(convert([seq(Tau[i], i = 1 .. M), seq(P[i], i = 1 .. Nm)], Matrix))
> 

Qn__2 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))
> 

Qn__3 := LinearAlgebra:-Transpose(Matrix(1, M+Nm))

External force

 
> 

`&omega;__b` := 25

> 

``

> 

F := diff((diff(sin(`&omega;__b`*t), t))*LinearAlgebra:-Transpose(convert(F0, Matrix)), t)

> 

``
> 

s := 1
> 

k__d := 100000
> 

with(Student[NumericalAnalysis]); dt
> 

``

Loop

 
> 

for t from t__0 by dt to taim do EQ := KL.V+a__0*ML.V+a__1*CL.V-ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))-CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))-F-Qn__2-Qn__3; G := Matrix(M+Nm, proc (i, j) options operator, arrow; (diff(EQ[i], V[j, 1]))[1] end proc); G1 := 1/G; if t = t__0 then X[1] := 1/(CL*a__1+ML*a__0+KL).(F+ML.(a__0*q(1 .. M+Nm, s .. s)+a__2*dq(1 .. M+Nm, s .. s)+a__3*ddq(1 .. M+Nm, s .. s))+CL.(a__1*q(1 .. M+Nm, s .. s)+a__4*dq(1 .. M+Nm, s .. s)+a__5*ddq(1 .. M+Nm, s .. s))) else X[1] := q(1 .. M+Nm, s .. s) end if; for k to 11 do X[k+1] := eval(V-G1.EQ, Equate(V, X[k])) end do; q(1 .. M+Nm, s+1 .. s+1) := X[k]; ddq(1 .. M+Nm, s+1 .. s+1) := a__0*(q(1 .. M+Nm, s+1 .. s+1)-q(1 .. M+Nm, s .. s))-a__2*dq(1 .. M+Nm, s .. s)-a__3*ddq(1 .. M+Nm, s .. s); dq(1 .. M+Nm, s+1 .. s+1) := dq(1 .. M+Nm, s .. s)+a__6*ddq(1 .. M+Nm, s .. s)+a__7*ddq(1 .. M+Nm, s+1 .. s+1); Wxy2 := add(add(add(h*W[i, j, 2, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Wxy3 := add(add(add(h*W[i, j, 3, o]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`)*q[o, s+1], i = 0 .. II), j = 0 .. JJ), o = 1 .. M); Plt := plots:-implicitplot(Wxy2-Wxy3, `&zeta;__2` = -1 .. 1, `&eta;__2` = -1 .. 1, color = red, thickness = 2, gridrefine = 3); j := 111111; Hvs2 := 1; for i while i <= j do Pnt[i] := op([1, i], Plt); if Wxy2-Wxy3 = 0 then j := 0 elif convert(Pnt[i], string)[1] = "C" then j := 0 else a__e[i] := (1/2)*abs(max(Column(Pnt[i], 1))-min(Column(Pnt[i], 1))); if a__e[i] = 0 then a__e[i] = 0.1e-5 end if; b__e[i] := (1/2)*abs(max(Column(Pnt[i], 2))-min(Column(Pnt[i], 2))); if b__e[i] = 0 then b__e[i] = 0.1e-5 end if; xc[i] := (max(Column(Pnt[i], 1))+min(Column(Pnt[i], 1)))*(1/2); yc[i] := (max(Column(Pnt[i], 2))+min(Column(Pnt[i], 2)))*(1/2); Hv2[i] := ((`&zeta;__2`-xc[i])/a__e[i])^2+((`&eta;__2`-yc[i])/b__e[i])^2-1; Hvs2 := Hv2[i]*Hvs2 end if end do; Qn__2 := LinearAlgebra:-Transpose(convert([(1/2)*k__d*Grid:-Seq(Quadrature(Quadrature(Heaviside(-Hvs2)*abs(Wxy2-Wxy3)*add(add(W[i, j, 2, r]*LegendreP(i, `&zeta;__2`)*LegendreP(j, `&eta;__2`), i = 0 .. II), j = 0 .. JJ), `&zeta;__2` = -1 .. 1, method = romberg[5]), `&eta;__2` = -1 .. 1, method = romberg[5]), r = 1 .. M), seq(0, n = 1 .. Nm)], Matrix)); Qn__3 := -Qn__2; s := s+1 end do

``

Download HighMemUseProb.mw

Rotate graph on x and y components...

Asked by: kencom1 110
plotting
August 30 2022
0  3

Good day everyone, 

Can I plot the graph of the sheet attached below such that x will be on the vertical component and y will be on the horizontal component? Can this be done on Maple? Anyone with useful information should please help.

plot_graph.mw

Why extracting a n*1 matrix from n*m matrix gives...

Asked by: mehdibgh 240
matrix vector indexing
August 24 2022
0  1

I am trying to do the following computation. I  extracted n*1 matrix from n*n matrix which unbelievably gives vector?

How I can do the following multiplication without using convert command? Or how to extract n*1 matrix (not vector) from n*n matrix without using convert?

> 

``
> 

restart
> 

``
> 

``
> 

A := Matrix(4, 4, {(1, 1) = m[1, 1], (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = m[2, 1], (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = m[3, 1], (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = m[4, 1], (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

A := Matrix(4, 4, {(1, 1) = 0, (1, 2) = m[1, 2], (1, 3) = m[1, 3], (1, 4) = m[1, 4], (2, 1) = 0, (2, 2) = m[2, 2], (2, 3) = m[2, 3], (2, 4) = m[2, 4], (3, 1) = 0, (3, 2) = m[3, 2], (3, 3) = m[3, 3], (3, 4) = m[3, 4], (4, 1) = 0, (4, 2) = m[4, 2], (4, 3) = m[4, 3], (4, 4) = m[4, 4]})

 (1)
> 

A(1 .. 4, 1) := Matrix(4, 1):
> 

A

Matrix([[0, m[1, 2], m[1, 3], m[1, 4]], [0, m[2, 2], m[2, 3], m[2, 4]], [0, m[3, 2], m[3, 3], m[3, 4]], [0, m[4, 2], m[4, 3], m[4, 4]]])

 (2)
> 

B := A(1 .. 4, 2)

B := Vector(4, {(1) = m[1, 2], (2) = m[2, 2], (3) = m[3, 2], (4) = m[4, 2]})

 (3)
> 

A.B

4

 (4)
> 

F := Matrix(4, 1, {(1, 1) = 0.4279668887e-7, (2, 1) = -0.3901148183e-7, (3, 1) = 0.3900685346e-7, (4, 1) = 0.})
> 

Typesetting:-delayDotProduct(A, B)-F

Error, (in rtable/Sum) invalid input: dimensions do not match: Vector[column](1 .. 4) cannot be added to Matrix(1 .. 4, 1 .. 1)

  
> 

A.convert(B, Matrix)-F

Matrix(4, 1, {(1, 1) = m[1, 2]*m[2, 2]+m[1, 3]*m[3, 2]+m[1, 4]*m[4, 2]-0.4279668887e-7, (2, 1) = m[2, 2]^2+m[2, 3]*m[3, 2]+m[2, 4]*m[4, 2]+0.3901148183e-7, (3, 1) = m[3, 2]*m[2, 2]+m[3, 3]*m[3, 2]+m[3, 4]*m[4, 2]-0.3900685346e-7, (4, 1) = m[2, 2]*m[4, 2]+m[3, 2]*m[4, 3]+m[4, 2]*m[4, 4]})

 (5)

``

Download soalzarb.mw

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