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Question: Trouble with NABLA operator? MAPLE 12

Question:Trouble with NABLA operator? MAPLE 12

tsunamiBTP 292 Maple
vector-calculus
April 08 2012
0

See attached.  I am not sure but I think eq #4 is the same as the HESSIAN operator.  Why can I not get MAPLE to express this in the form of a matrix with the NABLA command? Note the discrepancy of NABLA with theDELoperator as well shown by eq's 5 & 6.

Am I missing some command to get NABLA to carry out the correct operation or am I not interpreting what NABLA actually is?

regards

with(VectorCalculus);

[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, Compatibility, ConvertVector, CrossProd, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProd, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, Tangent, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]

 (1)

 

SetCoordinates('cartesian'[x[1], x[2], x[3]])

cartesian[x[1], x[2], x[3]]

 (2)

F := VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(x[1]^3, x[2]^3), x[3]^3), VectorCalculus:-`*`(x[1]^2, VectorCalculus:-`+`(x[2], x[3]))), VectorCalculus:-`*`(x[2]^2, VectorCalculus:-`+`(x[1], x[3]))), VectorCalculus:-`*`(x[3]^2, VectorCalculus:-`+`(x[1], x[2]))), VectorCalculus:-`*`(VectorCalculus:-`*`(x[1], x[2]), x[3]))

x[1]^3+x[2]^3+x[3]^3+x[1]^2*(x[2]+x[3])+x[2]^2*(x[1]+x[3])+x[3]^2*(x[1]+x[2])+x[1]*x[2]*x[3]

 (3)

Hessian(F)(=)Matrix([[6*x[1]+2*x[2]+2*x[3], 2*x[1]+2*x[2]+x[3], 2*x[1]+2*x[3]+x[2]], [2*x[1]+2*x[2]+x[3], 6*x[2]+2*x[1]+2*x[3], 2*x[2]+2*x[3]+x[1]], [2*x[1]+2*x[3]+x[2], 2*x[2]+2*x[3]+x[1], 6*x[3]+2*x[1]+2*x[2]]])

LA_Main:-VectorScalarMultiply,

Vector[column]([[Nabla*(3*x[1]^2+2*x[1]*(x[2]+x[3])+x[2]^2+x[3]^2+x[2]*x[3])], [Nabla*(3*x[2]^2+x[1]^2+2*x[2]*(x[1]+x[3])+x[3]^2+x[1]*x[3])], [Nabla*(3*x[3]^2+x[1]^2+x[2]^2+2*x[3]*(x[1]+x[2])+x[1]*x[2])]], [

 (4)

VectorCalculus:-`*`(`VectorCalculus:-Nabla`, VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`+`(VectorCalculus:-`*`(3, x[2]^2), x[1]^2), VectorCalculus:-`*`(VectorCalculus:-`*`(2, x[2]), VectorCalculus:-`+`(x[1], x[3]))), x[3]^2), VectorCalculus:-`*`(x[1], x[3])))

`VectorCalculus:-Nabla`*(3*x[2]^2+x[1]^2+2*x[2]*(x[1]+x[3])+x[3]^2+x[1]*x[3])

 (5)

Nabla(3*x[1]^2+2*x[1]*(x[2]+x[3])+x[2]^2+x[3]^2+x[2]*x[3])

Vector[column]([[6*x[1]+2*x[2]+2*x[3]], [2*x[1]+2*x[2]+x[3]], [2*x[1]+2*x[3]+x[2]]], [

 (6)

``

 

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