returns the element of minimal rank in a list - Maple Help

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DifferentialAlgebra[Tools][RankElement] - returns the element of minimal rank in a list

Calling Sequence

RankElement(minmax, L, R, pos, opts)

Parameters

minmax

-

the keyword min or max

L

-

a non-empty list or a set of differential polynomials

R

-

a differential polynomial ring or ideal

pos(optional)

-

a name

opts(optional)

-

a sequence of options

Description

• 

The function call RankElement(<min, max>, L, R, pos) returns the element of minimal or maximal rank  occurring in the list L. Ranks are compared with respect to the ranking of R, or its embedding polynomial ring, if R is an ideal. If pos is present, it is assigned the index of the element in L.

• 

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

Examples

withDifferentialAlgebra&colon;withTools&colon;

R:=DifferentialRingderivations&equals;x&comma;y&comma;blocks&equals;v&comma;u&comma;p&comma;parameters&equals;p

R:=differential_ring

(1)

L:=ux24u&comma;ux&comma;yvyu&plus;p&comma;vx&comma;xux&colon;

RankElementmin&comma;L&comma;R&comma;&apos;pos&apos;

ux24u

(2)

Lpos

ux24u

(3)

RankElementmax&comma;L&comma;R&comma;&apos;pos&apos;

vx&comma;xux

(4)

Lpos

vx&comma;xux

(5)

The following command returns the lowest dependent variable of R,

RankElementmin&comma;Getderivatives&comma;R&comma;R

p

(6)

The following command returns the highest dependent variable of R,

RankElementmax&comma;Getderivatives&comma;R&comma;R

vx&comma;y

(7)

See Also

DifferentialAlgebra, LeadingRank, SortByRank


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