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RegularChains[ChainTools]

  

EqualSaturatedIdeals

  

check if two regular chain generate the same saturated ideal

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

EqualSaturatedIdeals(rc1, rc2, R)

Parameters

rc1

-

regular chain of R

rc2

-

regular chain of R

R

-

polynomial ring

Description

• 

The command EqualSaturatedIdeals(rc1, rc2, R) returns true if and only if the regular chains rc1 and rc2 generate the same saturated ideal.

• 

This command is part of the RegularChains[ChainTools] package, so it can be used in the form EqualSaturatedIdeals(..) 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][EqualSaturatedIdeals](..).

Examples

withRegularChains:

withChainTools:

RPolynomialRingx,y,z

R:=polynomial_ring

(1)

sysx5+y53y1,5y43,20x+yz

sys:=20x+yz,5y43,x5+y53y1

(2)

decTriangularizesys,R,normalized=yes

dec:=regular_chain

(3)

Equationsdec1,R

11474127946569256007468861967138822599454632253404776870051199476222619269004890144761853439484671057123097693465191381050813704562732917125293370932479130541598163953960078201654747916507320573574680356823040x1771260505008202862102854051702189834144507041921400912212854357946960933195335641858396501896935850288388698973423657024874890168951887006119520716403898588447265625000000000000z19+6993494167255643877060419555161219397297718310661681373013610473433161675295215097739765468198629739368658992144459186504824936653303907728642932110182220458984375000000000000000z18+46980330573720043696285723094038459435169014560960809457932826698816864853909365786661752359672134274602580990491031583381442373098978089863389116690573928381886816436810143422403125z17362457794998087226523064237197118238681455387434685379217170814307753153223785029557758914206492139656047158750881706208736371102082285270209948560334845112137055928302241429687500000z16+1825588409831441292570286016853843732976447711290921201282663597873225040956392206905741146687704996955957543164892852708765201681735455663532400560561990184217739346093750000000000000z15+15138417846066725118358222658899878896246722526651227781338839693046020627409354976198946514427454581361714047528896855158315263311055631123529796231583257599303710937500000000000000000z1444394335873903477558622382037619903399605543513019193984850811034401539767435244582975861827087564468519794770271434211676417079225209120663140736918184704321681411620260946061817664157500z13239889463831973885970439654459159240773157947028995584430781544269432684180568707791767576191787113033986469119189293532827387996841920408461551066623181822838810854143891280165251250000000z12+2738339662798997128827712967353520807578712156161195412624338459316853569080754130154719452119622862823530609072130944805722667158059695598771740436061650119196713974446586975000000000000000z1115237133948658997778693395344596342126523231688102858941028295140149607477956051848066457333497202284356641427141996353739796250479018624174619989841534614074349477755996093750000000000000000z10+48563913474106327770615609511108962756349408870293446119857242983280899281287041276597414703953142847110970543541965415369819771789164016371916892583484885932065222266474244223656870580763404750z9+182770901475269211462030828375934181004032581754339209581456763239413822566355167569080400536438012882499416890307268474234594753941991910223913471336544588355841793697886482347774623132375000000z8+309191296130950729973668595368021125635249693248658751381279239017170403224531631090451630403456902301090463541541208661015512101696917723097258264871336817986092045758275049045390250000000000000z76838688396641645490945090868618366582490420637673970853279869471018348887091817749546675847593376908651767451450243404728169565283801174082247345442363224813502338696761842209062500000000000000000z674815682380070752593065205631091355818115420146560706379886171073303776505335730603765529125626467971633284964641482528987570423158923499017031906462266550721041958679333491247172414080955401845651420z5154608045527569292338754337973797843824713701855230758768236174292780150592090630056630234512064066763987236066826571445077192641952424283276680662979283353386614928379571789390957015570270631450000000z4124695385819578642285275287975402015668994502200477065094640515598601115130175167063705343665239193213631330215705606292594773399242228508627801381881595789007869020418417852791444860110175000000000000z366152659857188245320424888024222967738184293737891699176976594293187674688484864881423871033576765065422479234984449961643090211269389726039235842212801812250522818211946896210922615625000000000000000z2+573598714920124956474610718803150703376812978417179178775576117319500000077857129232958889104193427114987500929833686714791341712743162700766075396541379832681132358445310329142895528887477470724804102079717z+239787108649287987286424755607482454864690786827841184696976286133386057573817722098997859322480446751288360706756986017238407677469601203785469989972240351121714956603188344506951151541954650850823956500000,573706397328462800373443098356941129972731612670238843502559973811130963450244507238092671974233552856154884673259569052540685228136645856264668546623956527079908197698003910082737395825366028678734017841152y1771260505008202862102854051702189834144507041921400912212854357946960933195335641858396501896935850288388698973423657024874890168951887006119520716403898588447265625000000000000z19+6993494167255643877060419555161219397297718310661681373013610473433161675295215097739765468198629739368658992144459186504824936653303907728642932110182220458984375000000000000000z18+46980330573720043696285723094038459435169014560960809457932826698816864853909365786661752359672134274602580990491031583381442373098978089863389116690573928381886816436810143422403125z1736245779499808722652306423719711823868145538743468537921717081430775315322378502955775891420649213965604715875088170620873637110208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(4)

dsDahanSchostTransformdec1,R

ds:=regular_chain

(5)

Equationsds,R

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,3125z197500z1530000000000z141209599993250z11858000000000z10+96000000000000000z94866050142720002700z75160960781200000000z61958400000000000000z5102400000000000000000000z43397381727846669567999595z32123365072896045360000000z2589823873280000000000000z61440000000000000000000y1875z16302399995500z12312000000000z111216513874880004050z82211840892800000000z71305600000000000000z6849339791770341311998380z41415574503424181440000000z3884735493120000000000000z2245760000000000000000000z509608055439369331200243,3125z209375z1640000000000z152015999988750z121560000000000z11+192000000000000000z1012165125356800006750z814745602232000000000z76528000000000000000z6409600000000000000000000z516986908639233347839997975z414155767152640302400000000z35898238732800000000000000z21228800000000000000000000z6195303619231982878732441600243

(6)

EqualSaturatedIdealsdec1,ds,R

true

(7)

rcChainz,y,x,EmptyR,R

rc:=regular_chain

(8)

EqualSaturatedIdealsrc,ds,R

false

(9)

See Also

Chain

DahanSchostTransform

Equations

IsIncluded

IsInSaturate

PolynomialRing

RegularChains

Triangularize

 


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