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VectorCalculus[eval] - evaluation for Vectors
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Calling Sequence
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eval(v, t=a)
eval(v, eqns)
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Parameters
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v
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Vector(algebraic); Vector or algebraic expression
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t
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name; usually a name but may be a general expression
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a
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expression
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eqns
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list or set; list or set of equations
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Description
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The eval(v, eqns) command is an extension of the top-level eval command which correctly evaluates free Vectors , rooted Vectors, position Vectors, and VectorFields for the VectorCalculus package. If v is not a Vector, the arguments are passed to the top level eval command.
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If v is a rooted Vector then both the root point or origin and the components, corresponding to the coefficients of the basis vectors, are evaluted.
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If v is a VectorField, then the components are evaluated and a VectorField is returned. To properly evalute a VectorField at a point use evalVF.
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If v is a free Vector or a position Vector, then the components are evaluated. The type of the Vector does not change.
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Examples
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>
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Evaluating free Vectors
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![Vector[column]([[1], [1], [1]], ["x", "y", "z"])](/support/helpjp/helpview.aspx?si=4983/file03415/math136.png)
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![v1 := Vector(`<,>`(x, y^2, z^3), coords = cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4983/file03415/math140.png)
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![v1 := Vector[column]([[x], [y^2], [z^3]], ["x", "y", "z"])](/support/helpjp/helpview.aspx?si=4983/file03415/math143.png)
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![eval(v1, [x = 1, y = 2, z = 3])](/support/helpjp/helpview.aspx?si=4983/file03415/math147.png)
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![Vector[column]([[1], [4], [27]], ["x", "y", "z"])](/support/helpjp/helpview.aspx?si=4983/file03415/math150.png)
| (3) |
Evaluating rooted Vectors: both the root point and the components are evaluated.
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![v2 := RootedVector(point = [u, Pi], [u, v], polar[r, t])](/support/helpjp/helpview.aspx?si=4983/file03415/math156.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math159.png)
| (4) |
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![eval(v2, [u = 1, v = 2])](/support/helpjp/helpview.aspx?si=4983/file03415/math163.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math166.png)
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![GetRootPoint(eval(v2, [u = 1, v = 2]))](/support/helpjp/helpview.aspx?si=4983/file03415/math170.png)
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![Vector[column]([[1], [Pi]], ["r", "t"])](/support/helpjp/helpview.aspx?si=4983/file03415/math173.png)
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If the components have no variables then the root point is evaluated.
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![v3 := RootedVector(point = [s, t], [1, 2], parabolic[u, v])](/support/helpjp/helpview.aspx?si=4983/file03415/math179.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math182.png)
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![eval(v3, [s = 1, t = Pi])](/support/helpjp/helpview.aspx?si=4983/file03415/math186.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math189.png)
| (8) |
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![Vector[column]([[1], [Pi]], ["u", "v"])](/support/helpjp/helpview.aspx?si=4983/file03415/math196.png)
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If the root point has no variables then the components are evaluated.
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![v4 := RootedVector(point = [1, (1/4)*Pi, (1/4)*Pi], [u, v, w], spherical[r, p, t])](/support/helpjp/helpview.aspx?si=4983/file03415/math202.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math205.png)
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![eval(v4, [u = 1, v = -1, w = 1])](/support/helpjp/helpview.aspx?si=4983/file03415/math209.png)
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](/support/helpjp/helpview.aspx?si=4983/file03415/math212.png)
| (11) |
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*Pi], [(1/4)*Pi]], ["r", "p", "t"])](/support/helpjp/helpview.aspx?si=4983/file03415/math219.png)
| (12) |
Evaluating position Vectors
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![pv1 := PositionVector([t, t], polar)](/support/helpjp/helpview.aspx?si=4983/file03415/math225.png)
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], [t*sin(t)]])](/support/helpjp/helpview.aspx?si=4983/file03415/math228.png)
| (13) |
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], [3*sin(3)]])](/support/helpjp/helpview.aspx?si=4983/file03415/math235.png)
| (14) |
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![pv2 := PositionVector([t, v/sqrt(1+t^2), v*t/sqrt(1+t^2)], cartesian[x, y, z])](/support/helpjp/helpview.aspx?si=4983/file03415/math239.png)
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^(1/2)], [v*t/(1+t^2)^(1/2)]])](/support/helpjp/helpview.aspx?si=4983/file03415/math242.png)
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![eval(pv2, [t = 3, v = 4])](/support/helpjp/helpview.aspx?si=4983/file03415/math246.png)
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*10^(1/2)], [(6/5)*10^(1/2)]])](/support/helpjp/helpview.aspx?si=4983/file03415/math249.png)
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Evaluating VectorFields: eval evaluates the components and returns a VectorField.
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![vf := VectorField(`<,>`(1/r^2, 0, 0), spherical[r, p, t])](/support/helpjp/helpview.aspx?si=4983/file03415/math257.png)
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![vf := Vector[column]([[1/r^2], [0], [0]], ["r", "p", "t"], "field")](/support/helpjp/helpview.aspx?si=4983/file03415/math260.png)
| (17) |
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![Vector[column]([[1], [0], [0]], ["r", "p", "t"], "field")](/support/helpjp/helpview.aspx?si=4983/file03415/math267.png)
| (18) |
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![vectorfield, coords = spherical[r, p, t]](/support/helpjp/helpview.aspx?si=4983/file03415/math274.png)
| (19) |
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