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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 $$$ from FRAC(POLY(INT))
Function Selection for variables
Arguments: FRAC(POLY(INT))
Target type: LIST(OVAR([x]))
From: DMP([x],EXPR(INT))
[1] signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$ from DMP([x],EXPR(INT))
fricas
)set mess bot on
variables (2*y+1/y)$DMP([y], INT)
Function Selection for *
Arguments: (PI, VARIABLE(y))
-> no appropriate * found in PositiveInteger
-> no appropriate * found in Variable(y)
-> no appropriate * found in Integer
-> no appropriate * found in Symbol
-> no appropriate * found in Polynomial(Integer)
-> no appropriate * found in PositiveInteger
-> no appropriate * found in Variable(y)
-> no appropriate * found in Integer
-> no appropriate * found in Symbol
[1] signature: (INT, POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[2] signature: (INT, POLY(INT)) -> POLY(INT)
implemented: slot $(Integer)$ from POLY(INT)
[3] signature: (NNI, POLY(INT)) -> POLY(INT)
implemented: slot $(NonNegativeInteger)$ from POLY(INT)
[4] signature: (PI, POLY(INT)) -> POLY(INT)
implemented: slot $(PositiveInteger)$ from POLY(INT)
[5] signature: (POLY(INT), POLY(INT)) -> POLY(INT)
implemented: slot $$$ 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(FRAMALG(D8,D9),RETRACT(D8)) and D11 has
EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC(D1) and D3
has Join(FRAMALG(D1,D2),RETRACT(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 7 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))
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 $$$ from DMP([y],INT)
Function Selection for /
Arguments: (DMP([y],INT), DMP([y],INT))
Target type: DMP([y],INT)
-> no appropriate / found in DistributedMultivariatePolynomial([y],Integer)
-> no appropriate / found in Integer
-> no appropriate / found in DistributedMultivariatePolynomial([y],Integer)
-> no appropriate / found in Integer
Modemaps from Associated Packages
no modemaps
Remaining General Modemaps
[1] (D,D1) -> D from D if D has XF(D1) and D1 has FIELD
[2] (D,D1) -> D from D
if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has Join(SRNG,
ABELMON) and D4 has DIRPCAT(D3,D1) and D5 has DIRPCAT(D2,D1
) and D1 has FIELD
[3] (D1,D1) -> D from D if D has QFCAT(D1) and D1 has INTDOM
[4] (D,D1) -> D from D
if D has MATCAT(D1,D2,D3) and D1 has ABELMON and D2 has
FLAGG(D1) and D3 has FLAGG(D1) and D1 has FIELD
[5] (D,D1) -> D from D
if D has LIECAT(D1) and D1 has COMRING and D1 has FIELD
[6] (D,D) -> D from D if D has GROUP
[7] (SparseMultivariatePolynomial(D2,Kernel(D)),
SparseMultivariatePolynomial(D2,Kernel(D))) -> D
from D if D2 has INTDOM and D2 has COMPAR and D has FS(D2)
[8] (D,Integer) -> D from D if D has FPS
[9] (D,D) -> D from D if D has FIELD
[10] (D,D) -> D from D
if D = EQ(D1) and D1 has FIELD and D1 has TYPE or D = EQ(D1
) and D1 has GROUP and D1 has TYPE
[11] (D,D1) -> D from D
if D has AMR(D1,D2) and D1 has Join(SRNG,ABELMON) and D2
has OAMON and D1 has FIELD
[1] signature: (FRAC(DMP([y],INT)), FRAC(DMP([y],INT))) -> FRAC(DMP([y],INT))
implemented: slot $$$ 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(FRAMALG(D8,D9),RETRACT(D8)) and D11 has
EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC(D1) and D3
has Join(FRAMALG(D1,D2),RETRACT(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 13 exposed and 11 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 $$$ from DMP([x],EXPR(INT))
Function Selection for variables
Arguments: DMP([x],EXPR(INT))
[1] signature: DMP([x],EXPR(INT)) -> LIST(OVAR([x]))
implemented: slot (List (OrderedVariableList (x)))$ from DMP([x],EXPR(INT))
fricas
)set mess bot on
y:DMP([y], INT):=y; variables (2*y+1/y)
Function Selection for *
Arguments: (DMP([y],INT), DMP([y],INT))
[1] signature: (DMP([y],INT), DMP([y],INT)) -> DMP([y],INT)
implemented: slot $$$ 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 XF(D1) and D1 has FIELD
[2] (D,D1) -> D from D
if D has RMATCAT(D2,D3,D1,D4,D5) and D1 has Join(SRNG,
ABELMON) 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 ABELMON 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] (D,Integer) -> D from D if D has FPS
[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] (D,D1) -> D from D
if D has AMR(D1,D2) and D1 has Join(SRNG,ABELMON) 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(Symbol) from D if D has FS(D2) and D2 has COMPAR
[4] List(D) -> List(Symbol) from D if D has FS(D3) and D3 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(FRAMALG(D8,D9),RETRACT(D8)) and D11 has
EUCDOM and D1 has QFCAT(D11) and D2 has UPOLYC(D1) and D3
has Join(FRAMALG(D1,D2),RETRACT(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