refine a box - Maple Help

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Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : SemiAlgebraicSetTools Subpackage : RegularChains/SemiAlgebraicSetTools/RefineBox

RegularChains[SemiAlgebraicSetTools][RefineBox] - refine a box

RegularChains[SemiAlgebraicSetTools][RefineListBox] - refine a list of boxes

Calling Sequence

RefineBox(box, precision, R)

RefineListBox(l_boxes, precision, R)

Parameters

R

-

polynomial ring

box

-

box isolating a root

precision

-

positive numeric constant

l_boxes

-

list of boxes isolating roots

Description

• 

The RefineBox command refines a box so its width is smaller or equal to precision. It returns a box isolating the same root as box.

• 

The RefineListBox command refines a list of boxes so their widths are smaller or equal to precision. It returns a list of boxes isolating the same roots as l_boxes. It is more efficient than using map and RefineBox when the boxes isolate roots originating from the same regular chain. Refining a box allows one to refine instantly other boxes which share a common part.

Examples

withRegularChains:

withChainTools:

withSemiAlgebraicSetTools:

R:=PolynomialRingy,x

R:=polynomial_ring

(1)

C:=Chainx22,y1yx,EmptyR,R

C:=regular_chain

(2)

L:=RealRootIsolateC,R

L:=box,box,box,box

(3)

Refine the first box:

rl:=RefineBoxL1,1010,R

rl:=box

(4)

BoxValuesrl,R

y=1,x=2429600399917179869184,759250125536870912

(5)

evalf

y=1.,x=1.414213562,1.414213562

(6)

L:=RealRootIsolateC,R

L:=box,box,box,box

(7)

Refine all boxes at the same time:

rlb:=RefineListBoxL,1010,R

rlb:=box,box,box,box

(8)

mapBoxValues,rlb,R

y=759250125536870912,2429600399917179869184,x=194368031999137438953472,9718401599968719476736,y=2429600399917179869184,759250125536870912,x=9718401599968719476736,194368031999137438953472,y=1,x=194368031999137438953472,9718401599968719476736,y=1,x=9718401599968719476736,194368031999137438953472

(9)

evalf

y=1.414213562,1.414213562,x=1.414213562,1.414213562,y=1.414213562,1.414213562,x=1.414213562,1.414213562,y=1.,x=1.414213562,1.414213562,y=1.,x=1.414213562,1.414213562

(10)

See Also

BoxValues, RealRootIsolate


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