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fricas
A := SparseUnivariatePolynomial( Integer)

\label{eq1}\hbox{\axiomType{SparseUnivariatePolynomial}\ } (\hbox{\axiomType{Integer}\ })(1)
Type: Type
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1::A

\label{eq2}1(2)
Type: SparseUnivariatePolynomial?(Integer)
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x := monomial(1,1)$A

\label{eq3}?(3)
Type: SparseUnivariatePolynomial?(Integer)
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y:= x*2

\label{eq4}2 \  ?(4)
Type: SparseUnivariatePolynomial?(Integer)
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a := y*y*y +y*y +y

\label{eq5}{8 \ {{?}^{3}}}+{4 \ {{?}^{2}}}+{2 \  ?}(5)
Type: SparseUnivariatePolynomial?(Integer)
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reductum a

\label{eq6}{4 \ {{?}^{2}}}+{2 \  ?}(6)
Type: SparseUnivariatePolynomial?(Integer)
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monomials a

\label{eq7}\left[{8 \ {{?}^{3}}}, \:{4 \ {{?}^{2}}}, \:{2 \  ?}\right](7)
Type: List(SparseUnivariatePolynomial?(Integer))
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primitiveMonomials a

\label{eq8}\left[{{?}^{3}}, \:{{?}^{2}}, \: ? \right](8)
Type: List(SparseUnivariatePolynomial?(Integer))
fricas
)show List
List(S: Type) is a domain constructor Abbreviation for List is LIST This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- append : (%,%) -> % children : % -> List(%) concat : (%,S) -> % concat : List(%) -> % concat : (S,%) -> % concat : (%,%) -> % concat! : (%,S) -> % concat! : (%,%) -> % cons : (S,%) -> % construct : List(S) -> % copy : % -> % cycleEntry : % -> % cycleTail : % -> % cyclic? : % -> Boolean delete : (%,Integer) -> % delete! : (%,Integer) -> % distance : (%,%) -> Integer elt : (%,Integer,S) -> S ?.? : (%,Integer) -> S ?.last : (%,last) -> S ?.rest : (%,rest) -> % ?.first : (%,first) -> S ?.value : (%,value) -> S empty : () -> % empty? : % -> Boolean entries : % -> List(S) eq? : (%,%) -> Boolean explicitlyFinite? : % -> Boolean first : % -> S index? : (Integer,%) -> Boolean indices : % -> List(Integer) insert : (S,%,Integer) -> % insert : (%,%,Integer) -> % insert! : (S,%,Integer) -> % insert! : (%,%,Integer) -> % last : % -> S leaf? : % -> Boolean leaves : % -> List(S) list : S -> % map : (((S,S) -> S),%,%) -> % map : ((S -> S),%) -> % new : (NonNegativeInteger,S) -> % nil : () -> % nodes : % -> List(%) null : % -> Boolean possiblyInfinite? : % -> Boolean qelt : (%,Integer) -> S rest : % -> % reverse : % -> % sample : () -> % second : % -> S tail : % -> % third : % -> S value : % -> S #? : % -> NonNegativeInteger if $ has ATFINAG ?<? : (%,%) -> Boolean if S has ORDSET ?<=? : (%,%) -> Boolean if S has ORDSET ?=? : (%,%) -> Boolean if $ has ATFINAG and S has BASTYPE or S has SETCAT ?>? : (%,%) -> Boolean if S has ORDSET ?>=? : (%,%) -> Boolean if S has ORDSET OMwrite : % -> String if S has OM OMwrite : (%,Boolean) -> String if S has OM OMwrite : (OpenMathDevice,%) -> Void if S has OM OMwrite : (OpenMathDevice,%,Boolean) -> Void if S has OM any? : ((S -> Boolean),%) -> Boolean if $ has ATFINAG child? : (%,%) -> Boolean if S has SETCAT coerce : % -> OutputForm if S has KOERCE(OUTFORM) convert : % -> InputForm if S has KONVERT(INFORM) copyInto! : (%,%,Integer) -> % if $ has ATSHMUT count : (S,%) -> NonNegativeInteger if $ has ATFINAG and S has BASTYPE count : ((S -> Boolean),%) -> NonNegativeInteger if $ has ATFINAG cycleLength : % -> NonNegativeInteger cycleSplit! : % -> % if $ has ATSHMUT delete : (%,UniversalSegment(Integer)) -> % delete! : (%,UniversalSegment(Integer)) -> % ?.? : (%,UniversalSegment(Integer)) -> % entry? : (S,%) -> Boolean if $ has ATFINAG and S has SETCAT eval : (%,List(S),List(S)) -> % if S has EVALAB(S) and S has SETCAT eval : (%,S,S) -> % if S has EVALAB(S) and S has SETCAT eval : (%,Equation(S)) -> % if S has EVALAB(S) and S has SETCAT eval : (%,List(Equation(S))) -> % if S has EVALAB(S) and S has SETCAT every? : ((S -> Boolean),%) -> Boolean if $ has ATFINAG fill! : (%,S) -> % if $ has ATSHMUT find : ((S -> Boolean),%) -> Union(S,"failed") first : (%,NonNegativeInteger) -> % hash : % -> SingleInteger if S has SETCAT hashUpdate! : (HashState,%) -> HashState if S has SETCAT last : (%,NonNegativeInteger) -> % latex : % -> String if S has SETCAT less? : (%,NonNegativeInteger) -> Boolean map! : ((S -> S),%) -> % if $ has ATSHMUT max : (%,%) -> % if S has ORDSET maxIndex : % -> Integer if Integer has ORDSET member? : (S,%) -> Boolean if $ has ATFINAG and S has BASTYPE members : % -> List(S) if $ has ATFINAG merge : (((S,S) -> Boolean),%,%) -> % merge : (%,%) -> % if S has ORDSET merge! : (((S,S) -> Boolean),%,%) -> % merge! : (%,%) -> % if S has ORDSET min : (%,%) -> % if S has ORDSET minIndex : % -> Integer if Integer has ORDSET more? : (%,NonNegativeInteger) -> Boolean node? : (%,%) -> Boolean if S has SETCAT parts : % -> List(S) if $ has ATFINAG position : ((S -> Boolean),%) -> Integer position : (S,%) -> Integer if S has BASTYPE position : (S,%,Integer) -> Integer if S has BASTYPE qsetelt! : (%,Integer,S) -> S if $ has ATSHMUT reduce : (((S,S) -> S),%,S,S) -> S if $ has ATFINAG and S has BASTYPE reduce : (((S,S) -> S),%,S) -> S if $ has ATFINAG reduce : (((S,S) -> S),%) -> S if $ has ATFINAG remove : (S,%) -> % if $ has ATFINAG and S has BASTYPE remove : ((S -> Boolean),%) -> % if $ has ATFINAG remove! : ((S -> Boolean),%) -> % remove! : (S,%) -> % if S has SETCAT removeDuplicates : % -> % if $ has ATFINAG and S has BASTYPE removeDuplicates! : % -> % if S has SETCAT rest : (%,NonNegativeInteger) -> % reverse! : % -> % if $ has ATSHMUT select : ((S -> Boolean),%) -> % if $ has ATFINAG select! : ((S -> Boolean),%) -> % setDifference : (%,%) -> % if S has BASTYPE setIntersection : (%,%) -> % if S has BASTYPE setUnion : (%,%) -> % if S has BASTYPE setchildren! : (%,List(%)) -> % if $ has ATSHMUT setelt : (%,Integer,S) -> S if $ has ATSHMUT setelt : (%,UniversalSegment(Integer),S) -> S if $ has ATSHMUT setelt : (%,last,S) -> S if $ has ATSHMUT setelt : (%,rest,%) -> % if $ has ATSHMUT setelt : (%,first,S) -> S if $ has ATSHMUT setelt : (%,value,S) -> S if $ has ATSHMUT setfirst! : (%,S) -> S if $ has ATSHMUT setlast! : (%,S) -> S if $ has ATSHMUT setrest! : (%,%) -> % if $ has ATSHMUT setvalue! : (%,S) -> S if $ has ATSHMUT size? : (%,NonNegativeInteger) -> Boolean smaller? : (%,%) -> Boolean if S has ORDSET sort : (((S,S) -> Boolean),%) -> % sort : % -> % if S has ORDSET sort! : (((S,S) -> Boolean),%) -> % if $ has ATSHMUT sort! : % -> % if $ has ATSHMUT and S has ORDSET sorted? : (((S,S) -> Boolean),%) -> Boolean sorted? : % -> Boolean if S has ORDSET split! : (%,Integer) -> % if $ has ATSHMUT swap! : (%,Integer,Integer) -> Void if $ has ATSHMUT ?~=? : (%,%) -> Boolean if $ has ATFINAG and S has BASTYPE or S has SETCAT




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