such progra m i s CoCoA 5 whic h i s comparabl e t o Singula r an d Macaula y 2 . Th e
textbook b y Kreuze r an d Robbian o [KROO ] doe s a wonderfu l jo b introducin g th e
basics o f Computationa l Commutativ e Algebr a togethe r wit h example s i n CoCoA.
Software is necessarily ephemeral. Whil e the mathematics of solving polynomial
systems continue s t o liv e fo r centuries , th e compute r cod e presente d i n thi s boo k
will becom e obsolet e muc h sooner . I teste d i t al l i n Ma y 2002 , an d i t worke d wel l
at tha t time , o n ou r departmenta l compute r syste m a t U C Berkeley . An d i f yo u
would lik e to find ou t more , eac h o f these program s ha s excellen t documentation .
I a m gratefu l t o th e student s i n m y graduat e course , Math 275: Topics in Ap-
plied Mathematics, fo r listenin g t o my te n lecture s a t hom e i n Berkele y whil e I
first assemble d the m i n th e sprin g o f 2002 . Thei r spontaneou s comment s prove d
to b e extremel y valuabl e fo r improvin g m y performanc e late r o n i n Texas . Afte r
the CBM S conference, th e followin g peopl e provided ver y helpfu l comment s o n my
manuscript: Joh n Dalbec , Jesu s D e Loera , Mik e Develin , Alici a Dickenstein , Ia n
Dinwoodie, Bahma n Engheta , Stephe n Fulling , Kari n Gatermann , Raymon d Hem -
mecke, Serkan Ho§ten, Robert Lewis , Gregorio Malajovich, Pabl o Parrilo, Francisc o
Santos, Fran k Sottile , Set h Sullivant , Cale b Walther, an d Dongshen g Wu .
Special thank s g o t o Ami t Kheta n an d Ruchir a Datt a fo r helpin g m e whil e
in Texa s an d fo r contributin g t o Section s 4. 5 an d 6. 2 respectively . Ruchir a als o
assisted m e in the har d wor k of preparing th e final version o f this book . I t wa s her
help tha t mad e th e rapi d completio n o f this projec t possible .
Last bu t no t least , I wis h t o dedicat e thi s boo k t o th e bes t tea m o f all : m y
daughter Nina , my son Pascal, an d my wife Hyungsook. A million thanks fo r bein g
patient wit h you r pap a an d puttin g u p wit h hi s crazy early-mornin g wor k hours .
Bernd Sturmfels *
Berkeley, Jun e 200 2
A. Capani, G . Niesi, L. Robbiano, CoCoA , a system for doing Computations i n Commutativ e
Algebra, availabl e vi a anonymou s ft p from : http://cocoa.dima.unige.i t
*The autho r wa s supporte d i n par t b y th e U.S . National Scienc e Foundation , grant s #DMS -
0200729 an d #DMS-0138323
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