Contents

• Contents
• The Gröbner Basis package
  • *grobner$-$debug*
  • *buchberger$-$merge$-$pairs*
  • *gebauer$-$moeller$-$merge$-$pairs*
  • *grobner$-$function*
  • select$-$grobner$-$algorithm
  • grobner
  • debug$-$cgb
  • spoly
  • grobner$-$primitive$-$part
  • grobner$-$content
  • normal$-$form
  • buchberger
  • grobner$-$op
  • buchberger$-$sort$-$pairs
  • mock$-$spoly
  • buchberger$-$merge$-$pairs$-$use$-$mock$-$spoly
  • buchberger$-$merge$-$pairs$-$smallest$-$lcm
  • buchberger$-$merge$-$pairs$-$use$-$smallest$-$degree
  • buchberger$-$merge$-$pairs$-$use$-$smallest$-$length
  • buchberger$-$merge$-$pairs$-$use$-$smallest$-$coefficient$-$length
  • buchberger$-$set$-$pair$-$heuristic
  • criterion$-$1
  • criterion$-$2
  • normalize$-$poly
  • normalize$-$basis
  • reduction
  • reduced$-$grobner
  • monom$-$depends$-$p
  • term$-$depends$-$p
  • poly$-$depends$-$p
  • ring$-$intersection
  • elimination$-$ideal
  • ideal$-$intersection
  • poly$-$contract
  • poly$-$lcm
  • grobner$-$gcd
  • grobner$-$equal
  • grobner$-$subsetp
  • grobner$-$member
  • ideal$-$equal
  • ideal$-$subsetp
  • ideal$-$member
  • ideal$-$saturation$-$1
  • add$-$variables
  • extend$-$polynomials
  • saturation$-$extension
  • polysaturation$-$extension
  • saturation$-$extension$-$1
  • ideal$-$polysaturation$-$1
  • ideal$-$saturation
  • ideal$-$polysaturation
  • buchberger$-$criterion
  • grobner$-$test
  • minimization
  • add$-$minimized
  • colon$-$ideal
  • colon$-$ideal$-$1
  • pseudo$-$divide
  • gebauer$-$moeller
  • update
  • gebauer$-$moeller$-$merge$-$pairs$-$use$-$mock$-$spoly
  • gebauer$-$moeller$-$merge$-$pairs$-$smallest$-$lcm
  • gebauer$-$moeller$-$merge$-$pairs$-$use$-$smallest$-$degree
  • gebauer$-$moeller$-$merge$-$pairs$-$use$-$smallest$-$length
  • gebauer$-$moeller$-$merge$-$pairs$-$use$-$smallest$-$coefficient$-$length
  • gebauer$-$moeller$-$set$-$pair$-$heuristic
  • spoly$-$sugar
  • spoly$-$with$-$sugar
  • normal$-$form$-$with$-$sugar
  • buchberger$-$with$-$sugar
  • buchberger$-$with$-$sugar$-$merge$-$pairs
  • buchberger$-$with$-$sugar$-$sort$-$pairs
  • criterion$-$1$-$with$-$sugar
  • criterion$-$2$-$with$-$sugar
  • gebauer$-$moeller$-$with$-$sugar
  • update$-$with$-$sugar
  • gebauer$-$moeller$-$with$-$sugar$-$merge$-$pairs
  • grobner$-$primitive$-$part$-$with$-$sugar
• The String Interface to the Gröbner Basis package
  • string$-$normal$-$form
  • string$-$grobner
  • string$-$elimination$-$ideal
  • string$-$ideal$-$intersection
  • string$-$poly$-$lcm
  • string$-$ideal$-$saturation$-$1
  • string$-$ideal$-$polysaturation$-$1
  • string$-$ideal$-$saturation
  • string$-$ideal$-$polysaturation
  • string$-$colon$-$ideal
  • string$-$read$-$poly
  • poly$-$rational$-$to$-$integer
  • read$-$vars
• The Comprehensive Gröbner basis package
  • *colored$-$poly$-$debug*
  • debug$-$cgb
  • make$-$colored$-$poly
  • make$-$colored$-$poly$-$list
  • color$-$poly$-$list
  • color$-$poly
  • colored$-$poly$-$to$-$poly
  • colored$-$poly$-$print
  • colored$-$poly$-$print$-$list
  • determine
  • determine$-$1
  • determine$-$white$-$term
  • cond$-$system$-$print
  • cond$-$print
  • add$-$pairs
  • cond$-$part
  • cond$-$hm
  • delete$-$green$-$polys
  • grobner$-$system
  • reorder$-$pairs
  • colored$-$criterion$-$1
  • colored$-$criterion$-$2
  • cond$-$normal$-$form
  • cond$-$spoly
  • cond$-$lm
  • cond$-$lc
  • colored$-$term$-$times$-$poly
  • colored$-$scalar$-$times$-$poly
  • colored$-$term*
  • color*
  • color+
  • color$-$
  • colored$-$poly+
  • colored$-$poly$-$
  • colored$-$term$-$uminus
  • colored$-$minus$-$poly
  • string$-$grobner$-$system
  • string$-$cond
  • string$-$cover
  • saturate$-$cover
  • saturate$-$cond
  • string$-$determine
  • tidy$-$grobner$-$system
  • tidy$-$pair
  • tidy$-$cond
  • colored$-$reduction
  • green$-$reduce$-$colored$-$poly
  • green$-$reduce$-$colored$-$list
  • cond$-$system$-$green$-$reduce
  • parse$-$to$-$colored$-$poly$-$list
  • red$-$reduction
• The Coefficient Ring package
  • ring
  • *ring$-$of$-$integers*
  • *field$-$of$-$rationals*
  • field$-$modulo$-$prime
  • *coefficient$-$ring*
• The Division Package
  • divide
  • poly$-$exact$-$divide
• The Dynamical Systems package
  • poly$-$scalar$-$composition
  • poly$-$composition
  • poly$-$dynamic$-$power
  • poly$-$scalar$-$evaluate
  • poly$-$evaluate
  • factorial
  • poly$-$scalar$-$diff
  • poly$-$diff
  • standard$-$vector
  • scalar$-$partial
  • partial
  • determinant
  • minor
  • drop$-$row
  • drop$-$column
  • drop$-$elt
  • matrix$-$
  • scalar$-$times$-$matrix
  • monom$-$times$-$matrix
  • term$-$times$-$matrix
  • poly$-$list$-$
  • scalar$-$times$-$poly$-$list
  • monom$-$times$-$poly$-$list
  • term$-$times$-$poly$-$list
  • characteristic$-$combination
  • characteristic$-$combination$-$poly$-$list
  • characteristic$-$matrix
  • characteristic$-$polynomial
  • identity$-$matrix
  • print$-$matrix
  • jacobi$-$matrix
  • jacobian
• The Geometric Theorem Prover package
  • *prover$-$order*
  • csym
  • real$-$identical$-$points
  • identical$-$points
  • perpendicular
  • parallel
  • collinear
  • equidistant
  • euclidean$-$distance
  • midpoint
  • translate$-$statements
  • translate$-$assumptions
  • translate$-$conclusions
  • translate$-$theorem
  • prove$-$theorem
• The Monomial Order Package
  • lex$>$
  • total$-$degree
  • grlex$>$
  • grevlex$>$
  • revlex$>$
  • invlex$>$
  • elimination$-$order
  • elimination$-$order$-$1
• The Polynomial Package
  • scalar$-$times$-$poly
  • term$-$times$-$poly
  • monom$-$times$-$poly
  • minus$-$poly
  • sort$-$poly
  • poly+
  • poly$-$
  • poly*
  • poly$-$op
  • poly$-$expt
  • poly$-$mexpt
  • poly$-$constant$-$p
  • poly$-$extend
  • poly$-$extend$-$end
  • poly$-$zerop
  • lt
  • lm
  • lc
• The Parser Package
  • parse
  • alist$-$form
  • alist$-$form$-$1
  • powers
  • parse$-$to$-$alist
  • parse$-$string$-$to$-$alist
  • parse$-$to$-$sorted$-$alist
  • parse$-$string$-$to$-$sorted$-$alist
  • sort$-$poly$-$1
  • sort$-$poly
  • poly$-$eval$-$1
  • poly$-$eval
  • monom$-$basis
  • convert$-$number
  • $poly+
  • $poly$-$
  • $minus$-$poly
  • $poly*
  • $poly/
  • $poly$-$expt
• Other packages
  • makelist$-$1
  • makelist
  • sum
  • list$-$of
  • list$-$of$-$1
  • union$-$of
  • union$-$of$-$1
  • set$-$of
  • set$-$of$-$1
  • select
  • monom/
  • monom*
  • nmonom*
  • monom$-$divides$-$p
  • monom$-$divisible$-$by$-$p
  • monom$-$rel$-$prime
  • monom$-$equal
  • monom$-$lcm
  • monom$-$gcd
  • poly$-$gcd
  • poly$-$pseudo$-$divide
  • poly$-$pseudo$-$remainder
  • mdeg
  • lcoeff
  • lrest
  • lpart
  • poly$-$primitive$-$part
  • poly$-$content
  • poly$-$with$-$sugar$-$poly
  • poly$-$with$-$sugar$-$sugar
  • poly$-$with$-$sugar$-$tail
  • (setf poly$-$with$-$sugar$-$poly)
  • (setf poly$-$with$-$sugar$-$sugar)
  • (setf poly$-$with$-$sugar$-$tail)
  • monom$-$sugar
  • coefficient$-$sugar
  • term$-$sugar
  • poly$-$add$-$sugar
  • scalar$-$times$-$poly$-$with$-$sugar
  • term$-$times$-$poly$-$with$-$sugar
  • monom$-$times$-$poly$-$with$-$sugar
  • minus$-$poly$-$with$-$sugar
  • poly$-$with$-$sugar+
  • poly$-$with$-$sugar$-$
  • poly$-$with$-$sugar$-$op
  • poly$-$with$-$sugar$-$nreverse
  • poly$-$with$-$sugar$-$append
  • poly$-$with$-$sugar$-$zerop
  • poly$-$with$-$sugar$-$lm
  • poly$-$with$-$sugar$-$lc
  • poly$-$with$-$sugar$-$lt
  • poly$-$print
  • poly$-$print$-$1
  • poly$-$print$-$2
  • print$-$term
  • print$-$monom
  • num
  • denom
  • rat$-$simplify$-$2
  • rat$-$simplify
  • rat+
  • rat$-$
  • rat*
  • rat/
  • scalar$-$times$-$rat
  • scalar$-$div$-$rat
  • rat$-$zerop
  • rat$-$uminus
  • rat$-$expt
  • rat$-$constant
  • rat$-$to$-$poly
  • ratpoly+
  • ratpoly$-$
  • ratpoly$-$uminus
  • ratpoly*
  • scalar$-$times$-$ratpoly
  • rat$-$times$-$ratpoly
  • ratpoly$-$divide
  • ratpoly$-$remainder
  • ratpoly$-$gcd
  • ratpoly$-$diff
  • ratpoly$-$square$-$free
  • ratpoly$-$normalize
  • ratpoly$-$resultant
  • deg
  • lead
  • ratpoly$-$discriminant
  • ratpoly$-$print
  • poly$-$to$-$ratpoly
  • poly$-$to$-$poly1
  • poly1$-$to$-$ratpoly
  • ratpoly$-$to$-$poly1
  • poly1$-$to$-$poly
  • ratpoly$-$to$-$poly
  • poly$-$resultant
  • term*
  • term/
  • monom$-$times$-$term
  • term$-$divides$-$p
  • term$-$monom
  • term$-$coefficient
  • (setf term$-$monom)
  • (setf term$-$coefficient)
  • xgcd
• All examples produced by the all-examples utility