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$\mathrm{with}\left(\mathrm{LieAlgebrasOfVectorFields}\right)\:$

List of methods available for a OneForm object is available via the static exports of the object:
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$\mathrm{exports}\left(\mathrm{OneForm}\,\mathrm{static}\right)$

${\mathrm{GetComponents}}{,}{\mathrm{GetSpace}}{,}{\mathrm{AreSameSpace}}{,}{\mathrm{dchange}}{,}{\mathrm{DChange}}{,}{\mathrm{`=`}}{,}{\mathrm{`+`}}{,}{\mathrm{``}}{,}{\mathrm{`*`}}{,}{\mathrm{?[]}}{,}{\mathrm{map}}{,}{\mathrm{subs}}{,}{\mathrm{normal}}{,}{\mathrm{expand}}{,}{\mathrm{simplify}}{,}{\mathrm{indets}}{,}{\mathrm{has}}{,}{\mathrm{hastype}}{,}{\mathrm{type}}{,}{\mathrm{ModuleType}}{,}{\mathrm{ModulePrint}}{,}{\mathrm{ModuleCopy}}$
 (1) 
Construction by direct specification...
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$\mathrm{\omega}\u2254\mathrm{OneForm}\left(xyd\left[x\right]{y}^{2}d\left[y\right]\right)$

${\mathrm{\omega}}{\u2254}{x}{}{y}{}{\mathrm{dx}}{}{{y}}^{{2}}{}{\mathrm{dy}}$
 (2) 
Construction with Differential...
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$\mathrm{df}\u2254\mathrm{Differential}\left({x}^{2}+{y}^{2}\right)$

${\mathrm{df}}{\u2254}{2}{}{x}{}{\mathrm{dx}}{+}{2}{}{y}{}{\mathrm{dy}}$
 (3) 
A OneForm is of type OneForm...
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$\mathrm{type}\left(\mathrm{\omega}\,\mathrm{OneForm}\right)$

Extract data that make up a OneForm...
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$\mathrm{GetSpace}\left(\mathrm{\omega}\right)$

$\left[{x}{\,}{y}\right]$
 (5) 
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$\mathrm{GetComponents}\left(\mathrm{\omega}\right)$

$\left[{x}{}{y}{\,}{}{{y}}^{{2}}\right]$
 (6) 
Overloaded Maple operators...
Component extraction...
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$\mathrm{\omega}\left[x\right]$

Scalar multiplication and 1form addition:
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$2\mathrm{\omega}+y\mathrm{df}$

${4}{}{x}{}{y}{}{\mathrm{dx}}$
 (8) 
A OneForm object acts as an operator (via contraction) on a VectorField object
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$X\u2254\mathrm{VectorField}\left(y\mathrm{D}\left[x\right]+x\mathrm{D}\left[y\right]\right)$

${X}{\u2254}{}{y}{}\frac{{\textstyle {\partial}}}{{\textstyle {\partial}}{x}}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}{+}{x}{}\frac{{\textstyle {\partial}}}{{\textstyle {\partial}}{y}}\phantom{\rule[0.0ex]{0.4em}{0.0ex}}$
 (9) 
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$\mathrm{\omega}\left(X\right)$

${}{2}{}{x}{}{{y}}^{{2}}$
 (10) 
Overloaded Maple functions work as expected...
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$\mathrm{has}\left(\mathrm{\omega}\,x\right)$

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$\mathrm{hastype}\left(\mathrm{\omega}\,\mathrm{trig}\right)$
