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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 2 of 3

	1 2 3
Editor: test1 Time: 2014/04/15 17:41:06 GMT+0
Note:

added:
Actually, problem is because Axiom/FriCAS chooses different type for expression
which it can not coerce to Q

\begin{axiom}
quatern(1+%i*3,2-%i+t,3,4)
quatern(1+%i*3,2-%i+t,3,4)::Q
\end{axiom}

Probably we shoud enhance coercions to handle this case... 


added:

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:

fricas

Q:=Quaternion Complex Expression Integer

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

(1)

Type: Type

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q:Q

Type: Void

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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)))

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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)))

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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.

Actually, problem is because Axiom/FriCAS? chooses different type for expression which it can not coerce to Q

fricas

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

$\label{eq4}1 +{3 \ i}+{{\left(t + 2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(4)

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

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

   Cannot convert from type Quaternion(Polynomial(Complex(Integer))) to
      Quaternion(Complex(Expression(Integer))) for value
   1 + 3%i + (t + 2 - %i)i + 3j + 4k

Probably we shoud enhance coercions to handle this case...

Such a coercion exists in the follow similar case:

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QP:=Quaternion Complex Fraction Polynomial Integer

$\label{eq5}\hbox{\axiomType{Quaternion}\ } (\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Fraction}\ } (\hbox{\axiomType{Polynomial}\ } (\hbox{\axiomType{Integer}\ }))))$

(5)

Type: Type

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qp:QP

Type: Void

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

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

(6)

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

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

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

(7)

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

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

$\label{eq8}1 +{3 \ i}+{{\left(t + 2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(8)

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:

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C:=Complex Expression Integer

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

(9)

Type: Type

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t:C

Type: Void

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QC:=Quaternion C

$\label{eq10}\hbox{\axiomType{Quaternion}\ } (\hbox{\axiomType{Complex}\ } (\hbox{\axiomType{Expression}\ } (\hbox{\axiomType{Integer}\ })))$

(10)

Type: Type

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qc:QC

Type: Void

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

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

(11)

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

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

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

(12)

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

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

$\label{eq13}1 +{3 \ i}+{{\left(t + 2 - i \right)}\ i}+{3 \ j}+{4 \ k}$

(13)

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?