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LHPDE Object Overloaded Builtins

overview of overloaded builtins for LHPDE object.

 

Description

Examples

Compatibility

Description

• 

The functionalities of some Maple builtin commands are extended for use on LHPDE object.

• 

The following builtins have been overloaded for this purpose: normal, expand, simplify, indets, has, type, hastype, convert

• 

The normal, expand, simplify builtin commands accept a LHPDE object and apply their methods onto its DEs system. Then they return a LHPDE object with new DEs system.

• 

Let S be a LHPDE object.

• 

(i) The call type(S, t) returns true if t is any of the following types: module, object, anything, and LHPDE. See examples below.

• 

(ii) The call type(S, dependent(x)) and type(S, freeof(x)) respectively return true if the DEs system, the independent variables, and the dependent variables of S contain (respectively don't contain) x. See example below.

• 

The indets, has, hastype builtin commands accept a LHPDE object and apply their methods onto the DEs system, the independent variables, and the dependent variables of the object.

• 

The convert builtin command can convert a LHPDE object S into a LHPDO object.

• 

These overloaded builtins are associated with the LHPDE object. For more detail, see Overview of the LHPDE object.

Examples

withLieAlgebrasOfVectorFields:

Typesetting:-Settingsuserep=true:

Typesetting:-Suppressux,y:

normal, expand, simplify

SLHPDExx1x2diffux,y,x,x+cosy2+siny2diffux,y,y,y=0

Sxx1x2ux,x+cosy2+siny2uy,y=0,indep=x,y,dep=u

(1)

normalS

cosy2uy,y+siny2uy,yux,xx=0,indep=x,y,dep=u

(2)

expandS

cosy2uy,y+siny2uy,yux,xx=0,indep=x,y,dep=u

(3)

simplifyS

ux,xx+uy,y=0,indep=x,y,dep=u

(4)

type

typeS,LHPDE,typeS,`module`,typeS,object

true

(5)

The LHPDE object contains x

typeS,dependentx

true

(6)

typeS,freeofx

false

(7)

indets, has, hastype

indetsS

x,y,cosy,ux,x,uy,y,ux,uy,siny,u

(8)

hasS,z

false

(9)

hastypeS,scalar

true

(10)

hastypeS,float

false

(11)

convert

convertS,LHPDO

u→xx1x2xxu+cosy2+siny2yyu

(12)

Compatibility

• 

The LHPDE Object Overloaded Builtins command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

LHPDE (Object overview)

LieAlgebrasOfVectorFields[LHPDE]