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Dkunb

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These are questions asked by Dkunb

How to plot vector fields?...

Dkunb 65 Maple 2021
ode differential-equations deplot
March 08 2023
1 1
> 

restart;
> 

with(Physics):with(plots):with(DETools):
> 

sys := {diff(r(t),t)=p(t)/m,
diff(p(t),t)=l^2/(m*r(t)^3)-n*k*r(t)^(n-1),
diff(phi(t),t)=l/(m*r(t)^2)};

{diff(p(t), t) = l^2/(m*r(t)^3)-n*k*r(t)^(n-1), diff(phi(t), t) = l/(m*r(t)^2), diff(r(t), t) = p(t)/m}

 (1)
> 

sys1:=subs({n=1,k=1},sys);

{diff(p(t), t) = l^2/(m*r(t)^3)-1, diff(phi(t), t) = l/(m*r(t)^2), diff(r(t), t) = p(t)/m}

 (2)
> 

conv:=plottools:-transform((a,b)->[a*cos(b),a*sin(b)]):
> 

p1:=DEplot(sys1,[r(t),phi(t)],t=0..30,r=0..10,phi=0..2*Pi,stepsize=0.01);

Error, (in DEtools/DEplot) system must have same number of dependent variables as DE's.

  
> 

plots:-display([conv(p1)],axiscoordinates=polar);

Error, (in conv) invalid argument

  
> 

 


Could you help how to fix the code?

Download DEplot_v1.mw

DEplot for polar coordinates...

Dkunb 65 Maple 2021
differential-equations deplot plotting
March 07 2023
1 1

As2_v2.mw 

What should I fix my code in order to work?

Thanks in advance,

termination issue...

Dkunb 65 Maple 2021
performance integration numeric
December 22 2022
2 3

The loop for HFS _data_2 and SFS_data_2 and the loop for HFS _data_3 and SFS_data_3 do not seem to be terminated. I do not know what it is the issue here. Anyone who can help this?

Negativity_(v12_beta_gamma_mu).mw

Thank you in advance,

matrix index out of range...

Dkunb 65 Maple
matrix
November 23 2022
2 2
> 

restart;
> 

A:= Matrix();

A := Matrix(1, 0, {})

 (1)
> 

i_choices:= [seq(i,i=0..10,1)];

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

 (2)
> 

j_choices:= [seq(j,j=0..10,1)];

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

 (3)
> 

for i in i_choices do:
 for j in j_choices do:
   A[i,j] :=i+j;
   print(A[i,j]);
 od:
od;

Error, Matrix index out of range

  

Download test_Matrix.mw

How to calculate this symbolically?...

Dkunb 65 Maple
simplification summation physics
September 17 2022
0 4

I want to check whether the last expression is zero symbolically in maple. I am trying to learn how to calculate symbolically in Maple. Any suggestion would be very appreciated.


> 

restart;
> 

with(Physics);
with(Physics[Vectors]);

[`*`, `.`, Annihilation, AntiCommutator, Antisymmetrize, Assume, Bra, Bracket, Check, Christoffel, Coefficients, Commutator, CompactDisplay, Coordinates, Creation, D_, Dagger, Decompose, Define, Dgamma, Einstein, EnergyMomentum, Expand, ExteriorDerivative, Factor, FeynmanDiagrams, FeynmanIntegral, Fundiff, Geodesics, GrassmannParity, Gtaylor, Intc, Inverse, Ket, KillingVectors, KroneckerDelta, LeviCivita, Library, LieBracket, LieDerivative, Normal, NumericalRelativity, Parameters, PerformOnAnticommutativeSystem, Projector, Psigma, Redefine, Ricci, Riemann, Setup, Simplify, SortProducts, SpaceTimeVector, StandardModel, SubstituteTensor, SubstituteTensorIndices, SumOverRepeatedIndices, Symmetrize, TensorArray, Tetrads, ThreePlusOne, ToContravariant, ToCovariant, ToFieldComponents, ToSuperfields, Trace, TransformCoordinates, Vectors, Weyl, `^`, dAlembertian, d_, diff, g_, gamma_]

  

[`&x`, `+`, `.`, ChangeBasis, ChangeCoordinates, Component, Curl, DirectionalDiff, Divergence, Gradient, Identify, Laplacian, Nabla, Norm, Setup, diff]

 (1)
> 

 

> 

 

> 

 
> 

H[s]:=sum(Norm(p_[n])^2/2/m+U(q_[n]),n=1..s)+(1/2)*sum(sum(V(q_[i]-q_[j]),j=i..s),i=1..s);

sum((1/2)*Physics:-Vectors:-Norm(p_[n])^2/m+U(q_[n]), n = 1 .. s)+(1/2)*(sum(sum(V(q_[i]-q_[j]), j = i .. s), i = 1 .. s))

 (2)
> 

H[N-s]:=sum(Norm(p_[n])^2/2/m+U(q_[n]),n=s+1..N)+(1/2)*sum(sum(V(q_[i]-q_[j]),j=s+1..N),i=s+1..N);

sum((1/2)*Physics:-Vectors:-Norm(p_[n])^2/m+U(q_[n]), n = s+1 .. N)+(1/2)*(sum(sum(V(q_[i]-q_[j]), j = s+1 .. N), i = s+1 .. N))

 (3)
> 

 

 

Download Ch3.mw
 

 

 

 

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