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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

[1] signature: (INT,POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[2] signature: (INT,POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[3] signature: (NNI,POLY(INT)) -> POLY(INT)
implemented: slot $(NonNegativeInteger)$ from POLY(INT)
[4] signature: (PI,POLY(INT)) -> POLY(INT)
implemented: slot $(PositiveInteger)$ from POLY(INT)
[5] 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)

[1] signature: (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT))
implemented: slot $$$ from FRAC(POLY(INT))
[2] 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)

[1] 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))

[1] signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$ from DMP([x],EXPR(INT))

**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

[1] signature: (INT,POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[2] signature: (INT,POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[3] signature: (NNI,POLY(INT)) -> POLY(INT)
implemented: slot $(NonNegativeInteger)$ from POLY(INT)
[4] signature: (PI,POLY(INT)) -> POLY(INT)
implemented: slot $(PositiveInteger)$ from POLY(INT)
[5] 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)

[1] signature: (FRAC(POLY(INT)),FRAC(POLY(INT))) -> FRAC(POLY(INT))
implemented: slot $$$ from FRAC(POLY(INT))
[2] 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)))

[1] 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
[1] ((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))

[2] ((D4 -> D5),Fraction(D4)) -> Fraction(D5)
from FractionFunctions2(D4,D5)
if D4 has INTDOM and D5 has INTDOM

[1] 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)

[1] 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)

[1] signature: (DMP([x],EXPR(INT)),EXPR(INT)) -> DMP([x],EXPR(INT))
implemented: slot $$(Expression (Integer)) from DMP([x],EXPR(INT))
[2] signature: (EXPR(INT),EXPR(INT)) -> EXPR(INT)
implemented: slot $$$ 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))

[1] 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))

[1] signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$ from DMP([x],EXPR(INT))

**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

[1] 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
[1] (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD
[2] (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
[3] (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM
[4] (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
[5] (D,D1) -> D from D
if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD
[6] (D,D) -> D from D if D has GROUP
[7] (SparseMultivariatePolynomial(D2,Kernel(D)),
SparseMultivariatePolynomial(D2,Kernel(D))) -> D
from D if D2 has INTDOM and D2 has COMPAR and D has FS(D2)

[8] (Float,Integer) -> Float from Float
[9] (D,D) -> D from D if D has FIELD
[10] (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
[11] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
[12] (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

[1] 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
[1] ((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))

[2] ((D4 -> D5),Fraction(D4)) -> Fraction(D5)
from FractionFunctions2(D4,D5)
if D4 has INTDOM and D5 has INTDOM

[1] 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)))

[1] 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

[1] 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)))

[1] 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))

[1] signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$ from DMP([x],EXPR(INT))

**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))

[1] 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
[1] (D,D1) -> D from D if D has VSPACE(D1) and D1 has FIELD
[2] (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
[3] (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM
[4] (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
[5] (D,D1) -> D from D
if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD
[6] (D,D) -> D from D if D has GROUP
[7] (SparseMultivariatePolynomial(D2,Kernel(D)),
SparseMultivariatePolynomial(D2,Kernel(D))) -> D
from D if D2 has INTDOM and D2 has COMPAR and D has FS(D2)

[8] (Float,Integer) -> Float from Float
[9] (D,D) -> D from D if D has FIELD
[10] (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
[11] (DoubleFloat,Integer) -> DoubleFloat from DoubleFloat
[12] (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

[1] 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)

[1] 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
[1] Fraction(Polynomial(D3)) -> List(Symbol) from RationalFunction(
D3)
if D3 has INTDOM
[2] 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)
[3] D -> List(D4) from D
if D has PSCAT(D2,D3,D4) and D2 has RING and D3 has OAMON
and D4 has ORDSET
[4] D -> List(Symbol) from D if D has FS(D2) and D2 has COMPAR

[1] signature: FRAC(POLY(INT)) -> LIST(SYMBOL)
implemented: slot (List (Symbol))(Fraction (Polynomial (Integer))) from RF(INT)
[2] 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
[1] ((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))

[2] ((D4 -> D5),Fraction(D4)) -> Fraction(D5)
from FractionFunctions2(D4,D5)
if D4 has INTDOM and D5 has INTDOM

[1] 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))

**Type: **List(Symbol)

- )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
```

/'.

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

My Explanations (and errors) of the quiz results--Bill Page, Sun, 26 Feb 2006 15:03:48 -0600 reply