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Description
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The functionalities of some Maple builtin commands are extended for use on VectorField and OneForm objects.
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The following builtins have been overloaded for this purpose: map, subs, normal, expand, simplify, indets, has, type, hastype
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The map, subs, normal, expand, simplify builtin commands accept a VectorField or a OneForm object and apply their methods onto the components of the object. Then they return a VectorField or a OneForm object with new components.
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Let V be a VectorField (respectively OneForm) object.
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(i) The call type(V, t) returns true if t is any of the following types: module, object, anything, VectorField (respectively OneForm), appliable, and indexable. See examples below.
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(ii) The call type(V,indexable(t)) returns true if the components of V are of type t. See example below.
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(iii) The call type(V, dependent(x)) and type(V, freeof(x)) respectively return true if the components and space coordinates of V contain (respectively don't contain) x. See example below.
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The indets, has, hastype builtin commands accept a VectorField or a OneForm object and apply their methods onto the space coordinate variables and the components of the object.
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Examples
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map, subs
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normal, expand, simplify
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type
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Checking type of the vector field's components, they are functions but not positive integers.
The vector field contains x.
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indets, has, hastype
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The indets of X includes all space variables as well as the indets occurring in the components of X.
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Compatibility
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The VectorField & OneForm Object Overloaded builtins command was introduced in Maple 2020.
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