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Calling Sequence
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OneForm( components = compList, space = varList)
OneForm( dExpr, space = varList)
OneForm( listOfPairs, space = varList )
OneForm( 0, space = varList)
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Parameters
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compList
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a list of scalar expressions [theta1, theta2,...,thetan] the components of the 1-form.
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varList
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a list of names [x1, x2, ... ,xn], the coordinates of space
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DExpr
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expression of the form theta1*d[x1] + theta2*d[x2] + ... + thetan*d[xn]
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listOfPairs
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a list of ordered pairs [[theta1,x1], [theta2,x2], ..., [thetan,xn]] of component values and corresponding space coordinate
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Description
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The command OneForm(...) is a constructor method for creating a OneForm object. Once a valid OneForm object has been created, it has access to various methods which allow it to be manipulated and its contents queried. see Overview of OneForm object for more detail.
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A 1-form is an expression of the form living on a space with coordinates . The are referred to as components, and are referred to as (coordinates of) space.
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The OneForm command first validates the user input arguments and then constructs a 1-form object named OneForm. A valid OneForm object consists of two data attributes: components and space variables .
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In the first calling sequence, both arguments components = compList, space=varList are required. These two lists must be of the same length.
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The second calling sequence is a textual representation of the usual appearance of a 1-form. The space = varList argument is optional; if present, its specification of the space [x1, x2,..., xn] implied by dExpr.
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In the third calling sequence, the space =varList argument is optional; if present, its specification of the space overrides the space [x1, x2,..., xn] implied by listOfPairs.
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The fourth calling sequence is a special constructor for the zero 1-form on the specified space; the space = varList argument is required.
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This command can be used in the form OneForm(...) only after executing the command with(LieAlgebrasOfVectorFields), but can always be used by executing LieAlgebrasOfVectorFields:-OneForm(...).
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Examples
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>
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First calling sequence:
>
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Second calling sequence:
Third calling sequence, 1-form specified by ordered pairs:
>
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Fourth calling sequence:
>
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The second calling sequence is especially useful as a sparse form entry, where only a few components are nonzero:
>
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Although the coordinates y,z are not visible in the printed form of this 1-form, they are present in the OneForm object:
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