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#363 A slow summation ←	↑	→ #365 random does not produce arbitrarily large numbers

#364 coerce is missing from domain Expression

Edit detail for #364 coerce is missing from domain Expression revision 1 of 3

	1 2 3
Editor: Time: 2007/11/17 22:33:32 GMT-8
Note:

changed:
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The domain 'Expression(R:OrderedSet)' should always be able to coerce something of type R to an Expression, but this fails in some cases. For example:
\begin{axiom}
Q:=Quaternion Complex Expression Integer
q:Q
q:=quatern(1+%i*3,2-%i,3,4)
q:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)
q:=quatern(1+%i*3,2-%i+t,3,4)
\end{axiom}

Such a coercion exists in the follow similar case:
\begin{axiom}
QP:=Quaternion Complex Fraction Polynomial Integer
qp:QP
qp:=quatern(1+%i*3,2-%i,3,4)
qp:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)
qp:=quatern(1+%i*3,2-%i+t,3,4)
\end{axiom}

The error can also be avoided if more type information is provided since this changes the chain of inferences made by the Axiom intepreter:
\begin{axiom}
C:=Complex Expression Integer
t:C
QC:=Quaternion C
qc:QC
qc:=quatern(1+%i*3,2-%i,3,4)
qc:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)
qc:=quatern(1+%i*3,2-%i+t,3,4)
\end{axiom}

The formatting of the error message::

  Function:  coerce : Quaternion Complex Integer -> % is missing from
  domain: Expression Quaternion Complex Integer
    Internal Error
    The function coerce with signature $(Quaternion (Complex (Integer))) is
       missing from domain Expression(Quaternion (Complex (Integer)))

also leaves a lot to be desired. Why is it said twice, the second time badly?

The domain Expression(R:OrderedSet) should always be able to coerce something of type R to an Expression, but this fails in some cases. For example:

axiom

Q:=Quaternion Complex Expression Integer

$\label{eq1}\hbox{\axiomType{Quaternion}\ } (\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ })))$

(1)

Type: Type

axiom

q:Q

Type: Void

axiom

q:=quatern(1+%i*3,2-%i,3,4)

$\label{eq2}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(2)

Type: Quaternion(Complex(Expression(Integer)))

axiom

q:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)

$\label{eq3}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{{\left(t + 3 \right)}\ j}+{{\left({t^2}+ t + 4 \right)}\ k}$

(3)

Type: Quaternion(Complex(Expression(Integer)))

axiom

q:=quatern(1+%i*3,2-%i+t,3,4)

   Cannot convert right-hand side of assignment
   1 + 3%i + (t + 2 - %i)i + 3j + 4k

      to an object of the type Quaternion(Complex(Expression(Integer)))
      of the left-hand side.

Such a coercion exists in the follow similar case:

axiom

QP:=Quaternion Complex Fraction Polynomial Integer

$\label{eq4}\hbox{\axiomType{Quaternion}\ } (\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Polynomial}\ } (\hbox{\axiomType{Integer}\ }))))$

(4)

Type: Type

axiom

qp:QP

Type: Void

axiom

qp:=quatern(1+%i*3,2-%i,3,4)

$\label{eq5}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(5)

Type: Quaternion(Complex(Fraction(Polynomial(Integer))))

axiom

qp:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)

$\label{eq6}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{{\left(t + 3 \right)}\ j}+{{\left({t^2}+ t + 4 \right)}\ k}$

(6)

Type: Quaternion(Complex(Fraction(Polynomial(Integer))))

axiom

qp:=quatern(1+%i*3,2-%i+t,3,4)

$\label{eq7}1 +{3 \ i}+{{\left(t + 2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(7)

Type: Quaternion(Complex(Fraction(Polynomial(Integer))))

The error can also be avoided if more type information is provided since this changes the chain of inferences made by the Axiom intepreter:

axiom

C:=Complex Expression Integer

$\label{eq8}\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ }))$

(8)

Type: Type

axiom

t:C

Type: Void

axiom

QC:=Quaternion C

$\label{eq9}\hbox{\axiomType{Quaternion}\ } (\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ })))$

(9)

Type: Type

axiom

qc:QC

Type: Void

axiom

qc:=quatern(1+%i*3,2-%i,3,4)

$\label{eq10}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(10)

Type: Quaternion(Complex(Expression(Integer)))

axiom

qc:=quatern(1+%i*3,2-%i,3+t,4+t+t^2)

$\label{eq11}1 +{3 \ i}+{{\left(2 - i \right)}\ i}+{{\left(t + 3 \right)}\ j}+{{\left({t^2}+ t + 4 \right)}\ k}$

(11)

Type: Quaternion(Complex(Expression(Integer)))

axiom

qc:=quatern(1+%i*3,2-%i+t,3,4)

$\label{eq12}1 +{3 \ i}+{{\left(t + 2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(12)

Type: Quaternion(Complex(Expression(Integer)))

The formatting of the error message:

  Function:  coerce : Quaternion Complex Integer -> % is missing from
  domain: Expression Quaternion Complex Integer
    Internal Error
    The function coerce with signature $(Quaternion (Complex (Integer))) is
       missing from domain Expression(Quaternion (Complex (Integer)))

also leaves a lot to be desired. Why is it said twice, the second time badly?