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 Topics FrontPage SandBox SandBoxGroebnerBasis HomogeneousDistributedMultivariatePolynomial <-- You are here. fricas)show HomogeneousDistributedMultivariatePolynomial HomogeneousDistributedMultivariatePolynomial(vl: List(Symbol),R: Ring) is a domain constructor Abbreviation for HomogeneousDistributedMultivariatePolynomial is HDMP This constructor is not exposed in this frame. ------------------------------- Operations -------------------------------- ?*? : (%,R) -> % ?*? : (R,%) -> % ?*? : (%,%) -> % ?*? : (Integer,%) -> % ?*? : (PositiveInteger,%) -> % ?+? : (%,%) -> % ?-? : (%,%) -> % -? : % -> % ?=? : (%,%) -> Boolean 1 : () -> % 0 : () -> % ?^? : (%,PositiveInteger) -> % coefficients : % -> List(R) coerce : R -> % coerce : Integer -> % coerce : % -> OutputForm eval : (%,%,%) -> % eval : (%,Equation(%)) -> % ground : % -> R ground? : % -> Boolean hash : % -> SingleInteger latex : % -> String leadingCoefficient : % -> R leadingMonomial : % -> % map : ((R -> R),%) -> % monomial? : % -> Boolean monomials : % -> List(%) one? : % -> Boolean recip : % -> Union(%,"failed") reductum : % -> % reorder : (%,List(Integer)) -> % retract : % -> R sample : () -> % zero? : % -> Boolean ?~=? : (%,%) -> Boolean ?*? : (Fraction(Integer),%) -> % if R has ALGEBRA(FRAC(INT)) ?*? : (%,Fraction(Integer)) -> % if R has ALGEBRA(FRAC(INT)) ?*? : (NonNegativeInteger,%) -> % ?/? : (%,R) -> % if R has FIELD D : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % D : (%,OrderedVariableList(vl),NonNegativeInteger) -> % D : (%,List(OrderedVariableList(vl))) -> % D : (%,OrderedVariableList(vl)) -> % ?^? : (%,NonNegativeInteger) -> % associates? : (%,%) -> Boolean if $has ATVCWC and R has INTDOM or R has ENTIRER binomThmExpt : (%,%,NonNegativeInteger) -> % if$ has COMRING characteristic : () -> NonNegativeInteger charthRoot : % -> Union(%,"failed") if $has CHARNZ and R has PFECAT or R has CHARNZ coefficient : (%,HomogeneousDirectProduct(#(vl),NonNegativeInteger)) -> R coefficient : (%,OrderedVariableList(vl),NonNegativeInteger) -> % coefficient : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % coerce : % -> % if$ has ATVCWC and R has INTDOM or R has GCDDOM coerce : OrderedVariableList(vl) -> % coerce : Fraction(Integer) -> % if R has ALGEBRA(FRAC(INT)) or R has RETRACT(FRAC(INT)) conditionP : Matrix(%) -> Union(Vector(%),"failed") if $has CHARNZ and R has PFECAT content : (%,OrderedVariableList(vl)) -> % if R has GCDDOM content : % -> R if R has GCDDOM convert : % -> InputForm if R has KONVERT(INFORM) and OrderedVariableList(vl) has KONVERT(INFORM) convert : % -> Pattern(Integer) if R has KONVERT(PATTERN(INT)) and OrderedVariableList(vl) has KONVERT(PATTERN(INT)) convert : % -> Pattern(Float) if R has KONVERT(PATTERN(FLOAT)) and OrderedVariableList(vl) has KONVERT(PATTERN(FLOAT)) degree : % -> HomogeneousDirectProduct(#(vl),NonNegativeInteger) degree : (%,OrderedVariableList(vl)) -> NonNegativeInteger degree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) differentiate : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % differentiate : (%,OrderedVariableList(vl),NonNegativeInteger) -> % differentiate : (%,List(OrderedVariableList(vl))) -> % differentiate : (%,OrderedVariableList(vl)) -> % discriminant : (%,OrderedVariableList(vl)) -> % if R has COMRING eval : (%,List(OrderedVariableList(vl)),List(%)) -> % eval : (%,OrderedVariableList(vl),%) -> % eval : (%,List(OrderedVariableList(vl)),List(R)) -> % eval : (%,OrderedVariableList(vl),R) -> % eval : (%,List(%),List(%)) -> % eval : (%,List(Equation(%))) -> % exquo : (%,%) -> Union(%,"failed") if$ has ATVCWC and R has INTDOM or R has ENTIRER exquo : (%,R) -> Union(%,"failed") if R has ENTIRER factor : % -> Factored(%) if R has PFECAT factorPolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT factorSquareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT gcd : (%,%) -> % if R has GCDDOM gcd : List(%) -> % if R has GCDDOM gcdPolynomial : (SparseUnivariatePolynomial(%),SparseUnivariatePolynomial(%)) -> SparseUnivariatePolynomial(%) if R has GCDDOM hashUpdate! : (HashState,%) -> HashState isExpt : % -> Union(Record(var: OrderedVariableList(vl),exponent: NonNegativeInteger),"failed") isPlus : % -> Union(List(%),"failed") isTimes : % -> Union(List(%),"failed") lcm : (%,%) -> % if R has GCDDOM lcm : List(%) -> % if R has GCDDOM lcmCoef : (%,%) -> Record(llcm_res: %,coeff1: %,coeff2: %) if R has GCDDOM mainVariable : % -> Union(OrderedVariableList(vl),"failed") mapExponents : ((HomogeneousDirectProduct(#(vl),NonNegativeInteger) -> HomogeneousDirectProduct(#(vl),NonNegativeInteger)),%) -> % minimumDegree : (%,List(OrderedVariableList(vl))) -> List(NonNegativeInteger) minimumDegree : (%,OrderedVariableList(vl)) -> NonNegativeInteger minimumDegree : % -> HomogeneousDirectProduct(#(vl),NonNegativeInteger) monicDivide : (%,%,OrderedVariableList(vl)) -> Record(quotient: %,remainder: %) monomial : (R,HomogeneousDirectProduct(#(vl),NonNegativeInteger)) -> % monomial : (%,OrderedVariableList(vl),NonNegativeInteger) -> % monomial : (%,List(OrderedVariableList(vl)),List(NonNegativeInteger)) -> % multivariate : (SparseUnivariatePolynomial(%),OrderedVariableList(vl)) -> % multivariate : (SparseUnivariatePolynomial(R),OrderedVariableList(vl)) -> % numberOfMonomials : % -> NonNegativeInteger patternMatch : (%,Pattern(Integer),PatternMatchResult(Integer,%)) -> PatternMatchResult(Integer,%) if R has PATMAB(INT) and OrderedVariableList(vl) has PATMAB(INT) patternMatch : (%,Pattern(Float),PatternMatchResult(Float,%)) -> PatternMatchResult(Float,%) if R has PATMAB(FLOAT) and OrderedVariableList(vl) has PATMAB(FLOAT) pomopo! : (%,R,HomogeneousDirectProduct(#(vl),NonNegativeInteger),%) -> % prime? : % -> Boolean if R has PFECAT primitiveMonomials : % -> List(%) primitivePart : (%,OrderedVariableList(vl)) -> % if R has GCDDOM primitivePart : % -> % if R has GCDDOM reducedSystem : Matrix(%) -> Matrix(Integer) if R has LINEXP(INT) reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(Integer),vec: Vector(Integer)) if R has LINEXP(INT) reducedSystem : (Matrix(%),Vector(%)) -> Record(mat: Matrix(R),vec: Vector(R)) reducedSystem : Matrix(%) -> Matrix(R) resultant : (%,%,OrderedVariableList(vl)) -> % if R has COMRING retract : % -> OrderedVariableList(vl) retract : % -> Integer if R has RETRACT(INT) retract : % -> Fraction(Integer) if R has RETRACT(FRAC(INT)) retractIfCan : % -> Union(OrderedVariableList(vl),"failed") retractIfCan : % -> Union(Integer,"failed") if R has RETRACT(INT) retractIfCan : % -> Union(Fraction(Integer),"failed") if R has RETRACT(FRAC(INT)) retractIfCan : % -> Union(R,"failed") smaller? : (%,%) -> Boolean if R has COMPAR solveLinearPolynomialEquation : (List(SparseUnivariatePolynomial(%)),SparseUnivariatePolynomial(%)) -> Union(List(SparseUnivariatePolynomial(%)),"failed") if R has PFECAT squareFree : % -> Factored(%) if R has GCDDOM squareFreePart : % -> % if R has GCDDOM squareFreePolynomial : SparseUnivariatePolynomial(%) -> Factored(SparseUnivariatePolynomial(%)) if R has PFECAT subtractIfCan : (%,%) -> Union(%,"failed") totalDegree : % -> NonNegativeInteger totalDegree : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger totalDegreeSorted : (%,List(OrderedVariableList(vl))) -> NonNegativeInteger unit? : % -> Boolean if $has ATVCWC and R has INTDOM or R has ENTIRER unitCanonical : % -> % if$ has ATVCWC and R has INTDOM or R has ENTIRER unitNormal : % -> Record(unit: %,canonical: %,associate: %) if \$ has ATVCWC and R has INTDOM or R has ENTIRER univariate : % -> SparseUnivariatePolynomial(R) univariate : (%,OrderedVariableList(vl)) -> SparseUnivariatePolynomial(%) variables : % -> List(OrderedVariableList(vl))

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