RegularChains[SemiAlgebraicSetTools] - Maple Programming 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

  

RefineListBox

  

refine a list of boxes

 

Calling Sequence

Parameters

Description

Examples

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:

RPolynomialRingy,x

Rpolynomial_ring

(1)

CChainx22x1,y2yx,EmptyR,R

Cregular_chain

(2)

LRealRootIsolateC,R

Lbox,box,box,box,box,box

(3)

mapBoxValues,L,R

y=4634132768,14829091048576,x=14829111048576,741455524288,y=1048575524288,1048577524288,x=14829111048576,741455524288,y=1,x=1,y=2,x=1,y=14828991048576,741461524288,x=741455524288,14829111048576,y=524285262144,524291262144,x=741455524288,14829111048576

(4)

Refine the first box:

rbRefineBoxL1,105,R

rbbox

(5)

BoxValuesrb,R

y=4634132768,14829091048576,x=14829111048576,741455524288

(6)

rlbRefineListBoxL,104,R

rlbbox,box,box,box,box,box

(7)

mapBoxValues,rlb,R

y=524285262144,524291262144,x=741455524288,14829111048576,y=14828991048576,741461524288,x=741455524288,14829111048576,y=2,x=1,y=1,x=1,y=1048575524288,1048577524288,x=14829111048576,741455524288,y=4634132768,14829091048576,x=14829111048576,741455524288

(8)

rbRefineBoxL1,120,R

rbbox

(9)

BoxValuesrb,R

y=4634132768,14829091048576,x=14829111048576,741455524288

(10)

rlbRefineListBoxL,120,R

rlbbox,box,box,box,box,box

(11)

mapBoxValues,rlb,R

y=524285262144,524291262144,x=741455524288,14829111048576,y=14828991048576,741461524288,x=741455524288,14829111048576,y=2,x=1,y=1,x=1,y=1048575524288,1048577524288,x=14829111048576,741455524288,y=4634132768,14829091048576,x=14829111048576,741455524288

(12)

See Also

BoxValues

RealRootIsolate