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Coming Soon! (Or you can provide them!) Please insert comments after each problem. Original quizzes on SandBoxPolynomials#quizzes

fricas
)clear all
All user variables and function definitions have been cleared.
fricas
)set mess bot on
variables (2*x+1/x)$DMP([x], EXPR INT) Function Selection for * Arguments: (PI,VARIABLE(x)) -> no appropriate * found in PositiveInteger -> no appropriate * found in Variable(x) -> no appropriate * found in Integer -> no appropriate * found in Symbol -> no appropriate * found in Polynomial(Integer) -> no appropriate * found in PositiveInteger -> no appropriate * found in Variable(x) -> no appropriate * found in Integer -> no appropriate * found in Symbol  signature: (INT,POLY(INT)) -> POLY(INT) implemented: slot$(Integer)$from POLY(INT)  signature: (INT,POLY(INT)) -> POLY(INT) implemented: slot$(Integer)$from POLY(INT)  signature: (NNI,POLY(INT)) -> POLY(INT) implemented: slot$(NonNegativeInteger)$from POLY(INT)  signature: (PI,POLY(INT)) -> POLY(INT) implemented: slot$(PositiveInteger)$from POLY(INT)  signature: (POLY(INT),POLY(INT)) -> POLY(INT) implemented: slot $$from POLY(INT) Function Selection for / Arguments: (PI,VARIABLE(x)) Default target type: Fraction(Polynomial(Integer)) -> no appropriate / found in PositiveInteger -> no appropriate / found in Variable(x) -> no appropriate / found in Integer -> no appropriate / found in Symbol -> no appropriate / found in Fraction(Polynomial(Integer)) -> no appropriate / found in Polynomial(Integer) -> no appropriate / found in PositiveInteger -> no appropriate / found in Variable(x) -> no appropriate / found in Integer -> no appropriate / found in Symbol -> no appropriate / found in Polynomial(Integer)  signature: (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT)) implemented: slot$$$ from FRAC(POLY(INT))
  signature:   (POLY(INT),POLY(INT)) -> FRAC(POLY(INT))
implemented: slot $(Polynomial (Integer))(Polynomial (Integer)) from FRAC(POLY(INT)) Function Selection for + Arguments: (POLY(INT),FRAC(POLY(INT))) -> no appropriate + found in Polynomial(Integer) -> no appropriate + found in Fraction(Polynomial(Integer)) -> no appropriate + found in Polynomial(Integer)  signature: (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT)) implemented: slot $$from FRAC(POLY(INT)) Function Selection for variables Arguments: FRAC(POLY(INT)) Target type: LIST(OVAR([x])) From: DMP([x],EXPR(INT))  signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x])) implemented: slot (List (OrderedVariableList (x))) from DMP([x],EXPR(INT)) (1) Type: List(OrderedVariableList([x])) fricas )set mess bot on variables (2*y+1/y)DMP([y], INT) Function Selection for * Arguments: (PI,VARIABLE(y)) -> no appropriate * found in PositiveInteger -> no appropriate * found in Variable(y) -> no appropriate * found in Integer -> no appropriate * found in Symbol -> no appropriate * found in Polynomial(Integer) -> no appropriate * found in PositiveInteger -> no appropriate * found in Variable(y) -> no appropriate * found in Integer -> no appropriate * found in Symbol  signature: (INT,POLY(INT)) -> POLY(INT) implemented: slot (Integer) from POLY(INT)  signature: (INT,POLY(INT)) -> POLY(INT) implemented: slot (Integer) from POLY(INT)  signature: (NNI,POLY(INT)) -> POLY(INT) implemented: slot (NonNegativeInteger) from POLY(INT)  signature: (PI,POLY(INT)) -> POLY(INT) implemented: slot (PositiveInteger) from POLY(INT)  signature: (POLY(INT),POLY(INT)) -> POLY(INT) implemented: slot$$$ from POLY(INT)
Function Selection for /
Arguments: (PI,VARIABLE(y))
Default target type: Fraction(Polynomial(Integer))
-> no appropriate / found in PositiveInteger
-> no appropriate / found in Variable(y)
-> no appropriate / found in Integer
-> no appropriate / found in Symbol
-> no appropriate / found in Fraction(Polynomial(Integer))
-> no appropriate / found in Polynomial(Integer)
-> no appropriate / found in PositiveInteger
-> no appropriate / found in Variable(y)
-> no appropriate / found in Integer
-> no appropriate / found in Symbol
-> no appropriate / found in Polynomial(Integer)
  signature:   (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT))
implemented: slot $$from FRAC(POLY(INT))  signature: (POLY(INT),POLY(INT)) -> FRAC(POLY(INT)) implemented: slot (Polynomial (Integer))(Polynomial (Integer)) from FRAC(POLY(INT)) Function Selection for + Arguments: (POLY(INT),FRAC(POLY(INT)))  signature: (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT)) implemented: slot$$$from FRAC(POLY(INT)) Function Selection for variables Arguments: FRAC(POLY(INT)) Target type: LIST(OVAR([y])) From: DMP([y],INT) -> no appropriate variables found in DistributedMultivariatePolynomial([y],Integer) function not found in (DistributedMultivariatePolynomial ( [ y ] , Integer )) -> no function variables found for arguments FRAC(POLY(INT)) Function Selection for map by coercion facility (map) Arguments: ((POLY(INT) -> INT),FRAC(POLY(INT))) Target type: FRAC(INT) -> no appropriate map found in Fraction(Polynomial(Integer)) -> no appropriate map found in Fraction(Integer) -> no appropriate map found in Integer -> no appropriate map found in Polynomial(Integer) -> no appropriate map found in Integer Modemaps from Associated Packages  ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal( D11,D1,D2,D3) from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3) if D7 has EUCDOM and D8 has QFCAT(D7) and D9 has UPOLYC(D8) and D10 has Join(FramedAlgebra(D8,D9),RetractableTo(D8)) and D11 has EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC( D1) and D3 has Join(FramedAlgebra(D1,D2),RetractableTo(D1))  ((D4 -> D5),Fraction(D4)) -> Fraction(D5) from FractionFunctions2(D4,D5) if D4 has INTDOM and D5 has INTDOM  signature: ((POLY(INT) -> INT),FRAC(POLY(INT))) -> FRAC(INT) implemented: slot (Fraction (Integer))(Mapping (Integer) (Polynomial (Integer)))(Fraction (Polynomial (Integer))) from FRAC2(POLY(INT),INT) There are 4 exposed and 6 unexposed library operations named variables having 1 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op variables to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named variables with argument type(s) Fraction(Polynomial(Integer)) Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

fricas
)set mess bot on
a:=(2*x+1/x)$DMP([x], EXPR INT); variables a Function Selection for * Arguments: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) Target type: DMP([x],EXPR(INT)) -> no appropriate * found in Expression(Integer)  signature: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) -> DMP([x],EXPR(INT)) implemented: slot $$from DMP([x],EXPR(INT)) Function Selection for / Arguments: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) Target type: DMP([x],EXPR(INT)) -> no appropriate / found in DistributedMultivariatePolynomial([x],Expression(Integer)) -> no appropriate / found in Expression(Integer)  signature: (DMP([x],EXPR(INT)),EXPR(INT)) -> DMP([x],EXPR(INT)) implemented: slot$$(Expression (Integer)) from DMP([x],EXPR(INT))  signature: (EXPR(INT),EXPR(INT)) -> EXPR(INT) implemented: slot $$from EXPR(INT) Function Selection for + Arguments: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) Target type: DMP([x],EXPR(INT)) From: DMP([x],EXPR(INT))  signature: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) -> DMP([x],EXPR(INT)) implemented: slot$$$ from DMP([x],EXPR(INT))
Function Selection for variables
Arguments: DMP([x],EXPR(INT))
  signature:   DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$from DMP([x],EXPR(INT)) (2) Type: List(OrderedVariableList([x])) fricas )set mess bot on b:=(2*y+1/y)$DMP([y], INT); variables b
Function Selection for *
Arguments: (DMP([y],INT),DMP([y],INT))
Target type: DMP([y],INT)
-> no appropriate * found in Integer
  signature:   (DMP([y],INT),DMP([y],INT)) -> DMP([y],INT)
implemented: slot $$from DMP([y],INT) Function Selection for / Arguments: (DMP([y],INT),DMP([y],INT)) Target type: DMP([y],INT) -> no appropriate / found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate / found in Integer -> no appropriate / found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate / found in Integer Modemaps from Associated Packages no modemaps Remaining General Modemaps  (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD  (D,D1) -> D from D if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has Join(SemiRng, AbelianMonoid) and D4 has DIRPCAT(D3,D1) and D5 has DIRPCAT (D2,D1) and D1 has FIELD  (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM  (D,D1) -> D from D if D has MATCAT(D1,D2,D3) and D1 has Join(SemiRng, AbelianMonoid) and D2 has FLAGG(D1) and D3 has FLAGG(D1) and D1 has FIELD  (D,D1) -> D from D if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD  (D,D) -> D from D if D has GROUP  (SparseMultivariatePolynomial(D2,Kernel(D)), SparseMultivariatePolynomial(D2,Kernel(D))) -> D from D if D2 has INTDOM and D2 has COMPAR and D has FS(D2)  (Float,Integer) -> Float from Float  (D,D) -> D from D if D has FIELD  (D,D) -> D from D if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ(D1 ) and D1 has GROUP and D1 has TYPE  (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat  (D,D1) -> D from D if D has AMR(D1,D2) and D1 has Join(SemiRng,AbelianMonoid) and D2 has OAMON and D1 has FIELD  signature: (FRAC(DMP([y],INT)),FRAC(DMP([y],INT))) -> FRAC(DMP([y],INT)) implemented: slot$$$from FRAC(DMP([y],INT)) Function Selection for + Arguments: (DMP([y],INT),FRAC(DMP([y],INT))) Target type: DMP([y],INT) From: DMP([y],INT) -> no appropriate + found in DistributedMultivariatePolynomial([y],Integer) function not found in (DistributedMultivariatePolynomial ( [ y ] , Integer )) -> no function + found for arguments (DMP([y],INT),FRAC(DMP([y],INT))) Function Selection for map by coercion facility (map) Arguments: ((DMP([y],INT) -> INT),FRAC(DMP([y],INT))) Target type: FRAC(INT) -> no appropriate map found in Fraction(DistributedMultivariatePolynomial([y],Integer)) -> no appropriate map found in Fraction(Integer) -> no appropriate map found in Integer -> no appropriate map found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate map found in Integer Modemaps from Associated Packages  ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal( D11,D1,D2,D3) from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3) if D7 has EUCDOM and D8 has QFCAT(D7) and D9 has UPOLYC(D8) and D10 has Join(FramedAlgebra(D8,D9),RetractableTo(D8)) and D11 has EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC( D1) and D3 has Join(FramedAlgebra(D1,D2),RetractableTo(D1))  ((D4 -> D5),Fraction(D4)) -> Fraction(D5) from FractionFunctions2(D4,D5) if D4 has INTDOM and D5 has INTDOM  signature: ((DMP([y],INT) -> INT),FRAC(DMP([y],INT))) -> FRAC(INT) implemented: slot (Fraction (Integer))(Mapping (Integer) (DistributedMultivariatePolynomial (y) (Integer)))(Fraction (DistributedMultivariatePolynomial (y) (Integer))) from FRAC2(DMP([y],INT),INT) There are 11 exposed and 8 unexposed library operations named + having 2 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op + to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation. Cannot find a definition or applicable library operation named + with argument type(s) DistributedMultivariatePolynomial([y],Integer) Fraction(DistributedMultivariatePolynomial([y],Integer)) Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

fricas
)set mess bot on
x:DMP([x], EXPR INT):=x; variables (2*x+1/x)
Function Selection for *
Arguments: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT)))
  signature:   (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) -> DMP([x],EXPR(INT))
implemented: slot $$from DMP([x],EXPR(INT)) Function Selection for / Arguments: (PI,DMP([x],EXPR(INT))) -> no appropriate / found in PositiveInteger -> no appropriate / found in DistributedMultivariatePolynomial([x],Expression(Integer)) -> no appropriate / found in Integer -> no appropriate / found in PositiveInteger -> no appropriate / found in Integer  signature: (DMP([x],EXPR(INT)),EXPR(INT)) -> DMP([x],EXPR(INT)) implemented: slot$$(Expression (Integer)) from DMP([x],EXPR(INT))
Function Selection for +
Arguments: (DMP([x],EXPR(INT)),DMP([x],EXPR(INT)))
  signature:   (DMP([x],EXPR(INT)),DMP([x],EXPR(INT))) -> DMP([x],EXPR(INT))
implemented: slot $$from DMP([x],EXPR(INT)) Function Selection for variables Arguments: DMP([x],EXPR(INT))  signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x])) implemented: slot (List (OrderedVariableList (x))) from DMP([x],EXPR(INT)) (3) Type: List(OrderedVariableList([x])) fricas )set mess bot on y:DMP([y], INT):=y; variables (2*y+1/y) Function Selection for * Arguments: (DMP([y],INT),DMP([y],INT))  signature: (DMP([y],INT),DMP([y],INT)) -> DMP([y],INT) implemented: slot$$$from DMP([y],INT) Function Selection for / Arguments: (PI,DMP([y],INT)) -> no appropriate / found in PositiveInteger -> no appropriate / found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate / found in Integer -> no appropriate / found in PositiveInteger -> no appropriate / found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate / found in Integer Modemaps from Associated Packages no modemaps Remaining General Modemaps  (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD  (D,D1) -> D from D if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has Join(SemiRng, AbelianMonoid) and D4 has DIRPCAT(D3,D1) and D5 has DIRPCAT (D2,D1) and D1 has FIELD  (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM  (D,D1) -> D from D if D has MATCAT(D1,D2,D3) and D1 has Join(SemiRng, AbelianMonoid) and D2 has FLAGG(D1) and D3 has FLAGG(D1) and D1 has FIELD  (D,D1) -> D from D if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD  (D,D) -> D from D if D has GROUP  (SparseMultivariatePolynomial(D2,Kernel(D)), SparseMultivariatePolynomial(D2,Kernel(D))) -> D from D if D2 has INTDOM and D2 has COMPAR and D has FS(D2)  (Float,Integer) -> Float from Float  (D,D) -> D from D if D has FIELD  (D,D) -> D from D if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ(D1 ) and D1 has GROUP and D1 has TYPE  (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat  (D,D1) -> D from D if D has AMR(D1,D2) and D1 has Join(SemiRng,AbelianMonoid) and D2 has OAMON and D1 has FIELD  signature: (FRAC(DMP([y],INT)),FRAC(DMP([y],INT))) -> FRAC(DMP([y],INT)) implemented: slot $$from FRAC(DMP([y],INT)) Function Selection for + Arguments: (DMP([y],INT),FRAC(DMP([y],INT))) -> no appropriate + found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate + found in Fraction(DistributedMultivariatePolynomial([y],Integer)) -> no appropriate + found in DistributedMultivariatePolynomial([y],Integer)  signature: (FRAC(DMP([y],INT)),FRAC(DMP([y],INT))) -> FRAC(DMP([y],INT)) implemented: slot$$$ from FRAC(DMP([y],INT))
Function Selection for variables
Arguments: FRAC(DMP([y],INT))
-> no appropriate variables found in Fraction(DistributedMultivariatePolynomial([y],Integer))
-> no appropriate variables found in Fraction(DistributedMultivariatePolynomial([y],Integer))
Modemaps from Associated Packages
no modemaps
Remaining General Modemaps
 Fraction(Polynomial(D3)) -> List(Symbol) from RationalFunction(
D3)
if D3 has INTDOM
 D -> List(D4) from D
if D has PSETCAT(D2,D3,D4,D5) and D2 has RING and D3 has
OAMONS and D4 has ORDSET and D5 has RPOLCAT(D2,D3,D4)
 D -> List(D4) from D
if D has PSCAT(D2,D3,D4) and D2 has RING and D3 has OAMON
and D4 has ORDSET
 D -> List(Symbol) from D if D has FS(D2) and D2 has COMPAR
  signature:   FRAC(POLY(INT)) -> LIST(SYMBOL)
implemented: slot (List (Symbol))(Fraction (Polynomial (Integer))) from RF(INT)
  signature:   EXPR(DMP([y],INT)) -> LIST(SYMBOL)
implemented: slot (List (Symbol))$from EXPR(DMP([y],INT)) Function Selection for map by coercion facility (map) Arguments: ((DMP([y],INT) -> POLY(INT)),FRAC(DMP([y],INT))) Target type: FRAC(POLY(INT)) -> no appropriate map found in Fraction(DistributedMultivariatePolynomial([y],Integer)) -> no appropriate map found in Fraction(Polynomial(Integer)) -> no appropriate map found in Polynomial(Integer) -> no appropriate map found in DistributedMultivariatePolynomial([y],Integer) -> no appropriate map found in Polynomial(Integer) Modemaps from Associated Packages  ((D7 -> D11),FractionalIdeal(D7,D8,D9,D10)) -> FractionalIdeal( D11,D1,D2,D3) from FractionalIdealFunctions2(D7,D8,D9,D10,D11,D1,D2,D3) if D7 has EUCDOM and D8 has QFCAT(D7) and D9 has UPOLYC(D8) and D10 has Join(FramedAlgebra(D8,D9),RetractableTo(D8)) and D11 has EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC( D1) and D3 has Join(FramedAlgebra(D1,D2),RetractableTo(D1))  ((D4 -> D5),Fraction(D4)) -> Fraction(D5) from FractionFunctions2(D4,D5) if D4 has INTDOM and D5 has INTDOM  signature: ((DMP([y],INT) -> POLY(INT)),FRAC(DMP([y],INT))) -> FRAC(POLY(INT)) implemented: slot (Fraction (Polynomial (Integer)))(Mapping (Polynomial (Integer)) (DistributedMultivariatePolynomial (y) (Integer)))(Fraction (DistributedMultivariatePolynomial (y) (Integer))) from FRAC2(DMP([y],INT),POLY(INT)) (4) Type: List(Symbol) My Explanations (and errors) of the quiz results --Bill Page, Sun, 26 Feb 2006 15:03:48 -0600 reply )set mess bot off no cheating (1) variables (2*x+1/x)$DMP([x]?, EXPR INT)

(Got you, right? It got me too.

Yes. It took me a minute to realize that the interpreter parses this as:

(variables$DMP([x]?, EXPR INT))(2*x+1/x) To understand this, repeat with )set mess bot on. You must understand what the Interpreter was doing before starting quiz (2)) Ok, that was pretty easy. :) )set mess bot off (2) variables (2*y+1/y)$DMP([y]?, INT)

(Got me again! Repeat with )set mess bot on, read carefully, and compare with that from (1)).

This one is obvious. The only operation '/ in this domain is ?/? : (%,Integer) -> %' and y is not an Integer.

)set mess bot off (3) a:=(2*x + 1/x)$DMP([x]?, EXPR INT); variables a Obvious result: [x]? What is hard about that? )set mess bot off (4) b:=(2*y+1/y)$DMP([y]?, INT); variables b

Same error as in (2). But b is interpreted as a Variable which can be coerced to EXPR INT so result is [b]?

)set mess bot off (5) x:DMP([x]?, EXPR INT); variables (2*x+1/x)

Obvious. Result: [x]?. Essentially the same as (3)

)set mess bot off (6) y:DMP([y]?, INT); variables (2*y+1/y)

I wrote: "Error same as in (2)". So I have to admit I got this one wrong but I should not have. The explanation is simple. This is not a package call as it was in (2), so the interpreter is free to apply the usual coercion to 'FRAC DMP([y]?, INT) in order to obtain a selection for /'.

typo in quizzes --wyscc, Tue, 28 Feb 2006 04:06:46 -0600 reply
My apologies for putting up the wrong questions in Quizzes (5) and(6). The correct problems were given correctly on the Wiki pages but not in the email. In (5) x should have been assigned the value x (not just declared to be in DMP. Same for (6), where y should have been assigned the value y. In the version with the omissions, the first lines have no effect on the second lines.

William

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