builds a regular differential chain - Maple Help

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DifferentialAlgebra[Tools][PretendRegularDifferentialChain] - builds a regular differential chain

Calling Sequence

PretendRegularDifferentialChain (eqns, R, opts)

Parameters

eqns

-

a list or a set of differential rational fractions

R

-

a differential polynomial ring or ideal

opts (optional)

-

a sequence of options

Description

• 

The function call PretendRegularDifferentialChain (eqns, R) builds a regular differential chain with the numerators of eqns, regarded as differential rational fractions of R, if R is a ring, or its embedding ring if R is an ideal. By default, the built regular differential chain is assumed to hold the attributes: differential, autoreduced, primitive, squarefree, normalized and coherent. For more details on attributes, see DifferentialAlgebra.

• 

It is assumed that eqns already forms a regular differential chain with the above attributes. The list eqns does not need to be sorted.

• 

In principle, the elements of eqns should be differential polynomials with integer numeric coefficients. However, rational differential fractions and expressions involving explicit relational operators, such as p=q and pq are accepted. The rational differential fractions are replaced by their numerators. The expressions p=q are converted into pq. The expressions pq are ignored.

• 

If eqns involves a parameter p, the equations stating that some derivatives of p are zero, are automatically inserted in the regular differential chain, unless p, itself, is the leading derivative of some element of eqns.

• 

If eqns is empty, the returned regular differential chain represents the zero ideal of R.

• 

This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form PretendRegularDifferentialChain(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][PretendRegularDifferentialChain](...).

Examples

withDifferentialAlgebra:withTools:

R:=DifferentialRingderivations=t,blocks=u,s,c

R:=differential_ring

(1)

The function sorts the differential polynomials by increasing rank.

ideal:=PretendRegularDifferentialChainstc,cts,ut2su,R

ideal:=regular_differential_chain

(2)

Equationsideal

su+ut2,stc,cts

(3)

Getattributes,ideal

differential,autoreduced,primitive,squarefree,normalized

(4)

In the next example, the attribute normalized is omitted.

ideal:=PretendRegularDifferentialChaincstc,cts2,ut2ctu,attributes=differential,autoreduced,primitive,pretend=false,R

ideal:=regular_differential_chain

(5)

Equationsideal

su+ut2,stc,cts

(6)

Getattributes,ideal

differential,autoreduced,primitive,squarefree

(7)

See Also

DifferentialAlgebra, Tools, RosenfeldGroebner


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