Computer Algebra and Symbolic Computation: Mathematical Methods

Cohen Computer Algebra and Symbolic Computation Mathematical Methods Mathematica™, Maple™, and similar software packag...

Author: Joel S. Cohen

167 downloads 1168 Views 6MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Cohen

Computer Algebra and Symbolic Computation Mathematical Methods

Mathematica™, Maple™, and similar software packages provide programs that carry out sophisticated mathematical operations. In this book the author explores the mathematical methods that form the basis for such programs, in particular the application of algorithms to methods such as automatic simplification, polynomial decomposition, and polynomial factorization. Computer Algebra and Symbolic Computation: Mathematical Methods goes beyond the basics of computer algebra—presented in Computer Algebra and Symbolic Computation: Elementary Algorithms—to explore complexity analysis of algorithms and recent developments in the field. This text:

For the student, Mathematical Methods is an essential companion to Elementary Algorithms, illustrating applications of basic ideas. For the professional, Mathematical Methods is a look at new applications of familiar concepts.

ISBN 1-56881-159-4

A K Peters, Ltd.

ì1H pIIR ]9s}B stI NsAsYt >nH $tB >EEH $tB stI 7aPQstR{Z >EH $RYs >EMH %Bt 9Z psYt stI pYsI >EH G$t,j >d(dH Os} >d(xH B $}}j >d(MH

3UHIDFH

[LLL

]Ys} 1U ej8tsk ]Bt{}R BP ]B8}Z VjAs qY$R {Ys} $tBIZ{R st sjB$Y8${ jstZs {sjjI 8sY8s${sj }RZIBT jstZs wB R$8}jk _ND Ys $R ZRI YBZYBZ Y ABB,R B IR{$A Y {Bt{}R -s8}jR stI sjB$Y8R BP {B8}Z sjAs _N $R s R$8}j jstZs Ys {st A sR$jk stRjsI $tB Y RZ{ZR stI B}s$BtR s%s$jsAj $t 8BIt {B8}Z sjAs jstZsR qY$R {Ys} sjRB $t{jZIR s tsj IR{$}$Bt BP Y %sjZs$Bt }B{RR $t {B8}Z sjAs RBPbs w$t{jZI$t sZB8s${ R$8}j$h{s$BtD stI s {sR RZIk bY${Y $t{jZIR st _N }Bs8 Ys BAs$tR Y {Yst BP PB8 BP JZsIs${ -}RR$BtR ZtI Bs$Bt BP {BBI$tsR ]Ys} nU i{ZR$% 7Z{Z BP sY8s${sj e-}RR$BtR qY$R {Ys} $R {Bt{tI b$Y Y $ttsj RZ{Z BP 8sY8s$T {sj -}RR$BtR BY Y {Bt%t$Btsj RZ{Z wAPB %sjZs$BtD stI Y R$8}j$hI RZ{Z wsP %sjZs$Bt stI sZB8s${ R$8}j$h{s$BtD s IR{$AI qY RZ{Z BP sZB8s${sjjk R$8}j$hI -}RR$BtR $R $8}BT st A{sZR sjj sjB$Y8R sRRZ8 Ys Y $t}Z Iss $R $t Y$R PB8 3BZ }$8$$% _N B}sBR w7zQ 5yzQ ] `EK LW LyzQX stI gLzX0`0D Ys stsjk9 stI {BtRZ{ 8sY8s${sj -}RR$BtR s $tBIZ{I qY {Ys} sjRB $t{jZIR s IR{$}$Bt BP PBZ _N B}sT BR w3 BP 7ZAR$Z 7JZt$sj RZAR$Z stI ]Bt{Zt RZAR$ZD bY${Y I}tI Btjk Bt Y RZ{Z BP st -}RR$Bt ]Ys} ;U ej8tsk sY8s${sj VjB$Y8R yt Y$R {Ys}T b IR{$A Y AsR${ }Bs88$t RZ{ZR $t _N stI ZR YR RZ{ZR B IR{$A s tZ8A BP j8tsk sjB$Y8R qY {Ys} $t{jZIR s {sR RZIk bY${Y IR{$AR st sjB$Y8 Ys RBj%R s {jsRR BP hR BI BI$tsk I$&t$sj JZs$BtR ZR$t Y R}ss$Bt BP %s$sAjR {Yt$JZ stI Y 8YBI BP -s{ JZs$BtR b$Y $ts$t Ps{BR ]Ys} xU i{ZR$% VjB$Y8R qY$R {Ys} IR{$AR {ZT R$Bt sR s }Bs88$t {Yt$JZ $t {B8}Z sjAs stI $%R s tZ8A BP -s8}jR Ys $jjZRs $R sI%stsR stI j$8$s$BtR y $t{jZIR s {sR RZIk Ys IR{$AR st j8tsk $ts$Bt sjB$Y8 bY${Y htIR Y st$I$%s$%R PB s j$8$I {jsRR BP PZt{$BtR ZR$t Y j$ts }B}$R BP Y $tsj stI Y RZAR$Z$Bt 8YBI e-tR$BtR BP Y sjB$Y8 B $t{jZI Y j8tsk s$Btsj PZt{$Bt $ts$Bt RB8 $BtB8${ $tsjR j8tsk $ts$Bt Ak }sR stI Bt sjAs${ PZt{$Bt PB8 s IR{$AI $t Y -{$RR ]Ys} EU 7Z{Z BP _BjktB8$sjR stI is$Btsj e-}RT R$BtR qY$R {Ys} $R {Bt{tI b$Y Y sjB$Y8R Ys stsjk9 stI 8sT t$}Zjs }BjktB8$sjR stI s$Btsj -}RR$BtR y $t{jZIR {B8}Zs$Btsj Iht$$BtR PB %s$BZR {jsRRR BP }BjktB8$sjR stI s$Btsj -}RR$BtR Ys s AsRI Bt Y $ttsj RZ{Z BP -}RR$BtR VjB$Y8R AsRI Bt Y }$8$$% B}s$BtR $tBIZ{I $t ]Ys} n s $%t PB I

[LY

3UHIDFH

stI {B^{$t {B8}Zs$Bt {B^{$t {Bjj{$Bt -}stR$Bt stI s$BtsjT $9s$Bt BP sjAs${ -}RR$BtR ]Ys} U e-}Btt$sj stI q$BtB8${ qstRPB8s$BtR qY$R {Ys} $R {Bt{tI b$Y sjB$Y8R Ys 8st$}Zjs -}Btt$sj stI $BtB8${ PZt{$BtR y $t{jZIR sjB$Y8R PB -}Btt$sj -}stR$Bt stI IZ{$Bt $BtB8${ -}stR$Bt stI IZ{$Bt stI s R$8}j$h{s$Bt sjB$Y8 Ys {st %$Pk s js {jsRR BP $BtB8${ $It$$R

0DWKHPDWLFDO 0HWKRGV ]Ys} dU s{,BZtI ]Bt{}R qY$R {Ys} $R s RZ88sk BP Y As{,BZtI 8s$sj PB8 ej8tsk VjB$Y8R Ys }B%$IR s Ps8T bB, PB Y 8sY8s${sj stI {B8}Zs$Btsj I$R{ZRR$BtR $t Y ABB, y $t{jZIR s IR{$}$Bt BP Y 8sY8s${sj }RZIBTjstZs w_ND s A$P I$R{ZRR$Bt BP Y RZ{Z stI }BjktB8$sj RZ{Z BP sjAs${ -T }RR$BtR stI s RZ88sk BP Y AsR${ 8sY8s${sj B}sBR Ys s}}s $t BZ sjB$Y8R ]Ys} 1U ytR is$Btsj WZ8AR stI 3$jIR qY$R {Ys}T $R {Bt{tI b$Y Y tZ8${sj BA`{R Ys s$R $t {B8}Z sjAs $t{jZI$t $tR s$Btsj tZ8AR stI sjAs${ tZ8AR y $t{jZIR eZ{j$I:R sjB$Y8 PB Y sR {B88Bt I$%$RB BP bB $tR Y -tII eZ{j$Ist sjB$Y8 Y ]Y$tR 8s$tI sjB$Y8 stI s R$8}j$h{s$Bt sjB$Y8 Ys stRPB8R st $t%Bj%I s$Y8${ -}RR$Bt b$Y $tR stI Ps{$BtR B s s$Btsj tZ8A $t RstIsI PB8 yt sIT I$$Bt $ $tBIZ{R Y {Bt{} BP s hjI bY${Y IR{$AR $t s tsj bsk Y }B}$R BP tZ8A RkR8R Ys s$R $t {B8}Z sjAs ]Ys} nU VZB8s${ 7$8}j$h{s$Bt VZB8s${ R$8}j$h{s$Bt $R IhtI sR Y {Bjj{$Bt BP sjAs${ stI $BtB8${ R$8}j$h{s$Bt stRPB8s$BtR Ys s s}}j$I B st -}RR$Bt sR }s BP Y %sjZs$Bt }B{RR yt Y$R {Ys} b s, st $tTI}Y jBB, s Y sjAs${ {B8}BT tt BP Y$R }B{RR $% s }{$R Iht$$Bt BP st sZB8s${sjjk R$8}j$hI -}RR$Bt stI IR{$A st w$t%Bj%ID sjB$Y8 Ys stRPB8R 8sYT 8s${sj -}RR$BtR B sZB8s${sjjk R$8}j$hI PB8 VjYBZY sZB8s${ R$8}j$h{s$Bt $R RRt$sj PB Y B}s$Bt BP {B8}Z sjAs RBPbs Y$R $R Y Btjk Is$jI s8t BP Y B}${ $t Y -ABB, j$sZ ]Ys} ;U 7$tj zs$sAj _BjktB8$sjR qY$R {Ys} $R {BtT {tI b$Y sjB$Y8R PB R$tj %s$sAj }BjktB8$sjR b$Y {B^{$tR $t s hjI Vjj sjB$Y8R $t Y$R {Ys} s Zj$8sjk AsRI Bt }BjktB8$sj I$%$R$Bt y $t{jZIR sjB$Y8R PB }BjktB8$sj I$%$R$Bt stI -}stR$Bt eZ{j$I:R sjB$Y8 PB sR {B88Bt I$%$RB {B8}Zs$Bt Y -tII eZ{j$Ist sjB$Y8 stI s }BjktB8$sj %R$Bt BP Y ]Y$tR 8s$tI sjB$Y8 yt sII$$Bt Y AsR${ }BjktB8$sj I$%$R$Bt stI {I sjB$Y8R

3UHIDFH

[Y

s ZRI B $% sjB$Y8R PB tZ8${sj {B8}Zs$BtR $t j8tsk sjT As${ tZ8A hjIR qYR sjB$Y8R s Yt ZRI B I%jB} I$%$R$Bt stI {I sjB$Y8R PB }BjktB8$sjR b$Y sjAs${ tZ8A {B^{$tR qY {Ys} {Bt{jZIR b$Y st sjB$Y8 PB }s$sj Ps{$Bt -}stR$Bt Ys $R AsRI Bt Y -tII eZ{j$Ist sjB$Y8 ]Ys} xU _BjktB8$sj *{B8}BR$$Bt _BjktB8$sj I{B8}BR$T $Bt $R s }B{RR Ys I8$tR $P s }BjktB8$sj {st A }RtI sR s {B8}BR$$Bt BP jBb I }BjktB8$sjR yt Y$R {Ys} b I$R{ZRR RB8 YB${sj sR}{R BP Y I{B8}BR$$Bt }BAj8 stI $% st sjB$Y8 AsRI Bt }BjktB8$sj Ps{B$9s$Bt Ys $Y htIR s I{B8}BR$$Bt B IT 8$tR Ys tB I{B8}BR$$Bt -$RR ]Ys} EU Zj$%s$s _BjktB8$sjR qY$R {Ys} tsj$9R Y I$%$R$Bt stI {I sjB$Y8R B 8Zj$%s$s }BjktB8$sjR b$Y {BPT h{$tR $t st $tsj IB8s$t y $t{jZIR sjB$Y8R PB Y }BjktBT 8$sj I$%$R$Bt B}s$BtR w{ZR$% I$%$R$Bt 8BtB8$sjTAsRI I$%$R$Bt stI }RZIBTI$%$R$BtD }BjktB8$sj -}stR$Bt w$t{jZI$t st s}}j${s$Bt B Y sjAs${ RZAR$Z$Bt }BAj8D stI Y }$8$$% stI RZARZjst sjBT $Y8R PB {I {B8}Zs$Bt ]Ys} U qY iRZjst qY$R {Ys} $tBIZ{R Y RZjst BP bB }BjktB8$sjR bY${Y $R IhtI sR Y I8$tst BP s 8s$- bYBR tT $R I}tI Bt Y {B^{$tR BP Y }BjktB8$sjR G IR{$A s eZ{j$Ist sjB$Y8 stI s RZARZjst sjB$Y8 PB RZjst {B8}Zs$Bt stI ZR Y RZjst B htI }BjktB8$sj js$BtR PB -}j${$ sjAs${ tZ8AR ]Ys} MU _BjktB8$sj 7$8}j$h{s$Bt b$Y 7$I ijs$BtR qY$R {Ys} $t{jZIR st $tBIZ{$Bt B p[ BAt AsR$R {B8}Zs$Bt b$Y st s}}j${s$Bt B Y }BjktB8$sj R$8}j$h{s$Bt }BAj8 qB R$8}j$Pk Y }Rts$Bt b sRRZ8 Ys }BjktB8$sjR Ys% s$Btsj tZ8A {B^{$tR stI ZR Y j-${Bs}Y${sj BI$t R{Y8 PB 8BtB8$sjR ]Ys} U _BjktB8$sj 3s{B$9s$Bt qY Bsj BP Y$R {Ys} $R Y IR{$}$Bt BP s AsR${ %R$Bt BP s 8BIt Ps{B$9s$Bt sjB$Y8 PB R$tj %s$sAj }BjktB8$sjR $t +>?H y $t{jZIR RJZsTP Ps{B$9s$Bt sjT B$Y8R w$t +>?H stI >?HD Bt{,:R {jsRR${sj Ps{B$9s$Bt sjB$Y8 PB >?H j,s8}:R sjB$Y8 PB Ps{B$9s$Bt $t >?H stI s AsR${ %T R$Bt BP Y

Computer Algebra and Symbolic Computation: Mathematical Methods

Computer algebra and symbolic computation: mathematical methods

Computer Algebra and Symbolic Computation: Mathematical Methods