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Description
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The LHPDE object is designed and created to represent a collection of linear homogeneous PDEs (LHPDEs) in both rif-reduced or non-rif-reduced form.
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There are collections of methods that are available for a LHPDE object, including (i) methods for exploring properties of LHPDEs system such as solution dimension, (ii) utility methods for manipulating DEs system (e.g. rif-reducing the DEs system, solving DEs,..), and (iii) exploring relationship between solution spaces of two LHPDE objects. Some Maple existing builtins are extended for allowing LHPDE object.
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All methods of the LHPDE object become available only once a valid LHPDE object is constructed successfully. To construct a LHPDE object, see LieAlgebrasOfVectorFields[LHPDE].
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A LHPDE object is mathematically represented by the minimum of three data attributes: the "DEs system", the "independent variables" and the "dependent variables". These data attributes can be accessed via the GetSystem, GetIndependents and GetDependents methods.
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To represent a LHPDEs system that is in rif-reduced form with respect to a given ranking, a LHPDE object has two additional data attributes: a boolean variable "inRifReducedForm" and the "ranking". These two attributes can be accessed via the IsRifReduced and GetRanking methods.
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After a LHPDE object S is successfully constructed, each method in S can be accessed by either the short form method(S, arguments) or the long form S:-method(S, arguments).
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LHPDE Object Methods
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After a LHPDE object is constructed, the following methods are available:
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The following Maple builtins functions are extended so that they work for a LHPDE object: type, expand, has, hastype, indets, normal, simplify, convert. See LHPDE Object Overloaded Builtins for more detail.
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Examples
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Inserting option `static` gives a list of exports that are available for S as a LHPDE object.
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Basic properties of S can be got:
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For a LHPDE object that is being reduced, we can find more information about the solution space of Q:
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Q and R should regard as same LHPDEs system in the sense that they have same partial differential operator forms.
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We can simplify the dependency of their dependent variables, for example, a new LHPDE object R1 is constructed with minimal dependencies.
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A partial depended LHPDE object R1 has no trouble to be manipulated. For example, solving it..
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