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Question: How to calculate this symbolically?

Question:How to calculate this symbolically?

Dkunb 35 Maple
simplification summation physics incomplete-question
September 17 2022
2

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.


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restart;
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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)
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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)
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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)
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