LHPDO Object Overloaded Builtins - Maple Programming Help

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LHPDO Object Overloaded Builtins

overview of overloaded builtins for LHPDO object.

 

Description

Examples

Compatibility

Description

• 

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

• 

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

• 

The normal, expand, simplify builtin commands accept a LHPDO object and apply their methods onto the coefficients of the differential operator. They return an LHPDO object with the new coefficients.

• 

Let Delta be a LHPDO object.

• 

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

• 

(ii) The calls type(Delta, dependent(x)) and type(Delta, freeof(x)) respectively return true if the differential operator or the independent variables of Delta contain (respectively don't contain) x. See example below.

• 

The indets, has, hastype builtin commands accept a LHPDO object and apply their methods onto the differential operator and the independent variables of the object.

• 

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

Examples

withLieAlgebrasOfVectorFields:

Construct an LHPDO object from some differential expressions...

ΔLHPDOxx1diffux,t,xx2diffux,t,xdiffvx,t,t,cosa2+sina2diffux,t,t+diffvx,t,x

Δu,v→tv+xx1x2xu,cosa2+sina2tu+xv

(1)

normal, expand, simplify

normalΔ

u,v→xxutv,cosa2tu+sina2tu+xv

(2)

expandΔ

u,v→xxutv,cosa2tu+sina2tu+xv

(3)

simplifyΔ,trig

u,v→xxutv,xv+tu

(4)

type

typeΔ,LHPDO,typeΔ,object,typeΔ,`module`,typeΔ,appliable

true,true,true,true

(5)

The LHPDO object contains x

typeΔ,dependentx

true

(6)

typeΔ,freeofx

false

(7)

But the object does not contain the dummy "dependent variable" names...

typeΔ,dependentu,v

false

(8)

indets, has, hastype

indetsΔ

a,t,x,cosa,sina

(9)

hasΔ,v

false

(10)

hastypeΔ,scalar

true

(11)

hastypeΔ,float

false

(12)

Compatibility

• 

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

• 

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

See Also

LHPDO (Object overview)

LieAlgebrasOfVectorFields[LHPDO]