split a chain by a variable - Maple Help

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Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : ChainTools Subpackage : RegularChains/ChainTools/Cut

RegularChains[ChainTools][Cut] - split a chain by a variable

Calling Sequence

Cut(v, rc, R)

Parameters

v

-

variable of of R

rc

-

regular chain of R

R

-

polynomial ring

out_top

-

unevaluated name

out_pv

-

unevaluated name

out_sub_rc

-

unevaluated name

Description

• 

The command Cut(v, rc, R) returns alg_v,top,pv,sub_rc where alg_v is true if and only if v is an algebraic variable of rc, that is, if there exists a polynomial of rc with v as main variables.

• 

Moreover, top is assigned to the list of polynomials of rc with main variable strictly greater than v, ordered by increasing main variable.

• 

pv is assigned to the polynomial of rc with main variable v. If no such polynomial exists, pv is left unchanged.

• 

sub_rc is the regular chain under the variable v, i.e. composed of the polynomials of rc with main variable strictly lower than v.

• 

This command is part of the RegularChains[ChainTools] package, so it can be used in the form Cut(..) only after executing the command with(RegularChains[ChainTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][Cut](..).

Examples

withRegularChains:

R:=PolynomialRingx,y,z

R:=polynomial_ring

(1)

withChainTools:

rc:=EmptyR

rc:=regular_chain

(2)

rc:=Chainz+1,y+2,x+3,rc,R

rc:=regular_chain

(3)

res:=Cutx,rc,R;Equationsres4,R

res:=true,,x+3,regular_chain

y+2,z+1

(4)

res:=Cuty,rc,R;Equationsres4,R

res:=true,x+3,y+2,regular_chain

z+1

(5)

res:=Cutz,rc,R;Equationsres4,R

res:=true,y+2,x+3,z+1,regular_chain

(6)

See Also

Chain, ChainTools, Empty, Equations, IsAlgebraic, Polynomial, PolynomialRing, RegularChains, Under, Upper


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