MathAction SandBox Trace EXPR and FRAC

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    - SandBox Trace EXPR and FRAC <-- You are here.

Trace may affect correct output of 1::EXPR INT . This page should be read in conjunction with IssueTracker #283. To suppress the infinite loop being displayed till overflow, add )math to the package traced (does not always work). I think the coercion 2/3::FRAC INT is where the main bug lies, but since it is affected by )trace, it may not be easy to find.

We first establish that without )trace , the following works as intended.

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2/3::FRAC INT

$\label{eq1}2 \over 3$

(1)

Type: Fraction(Integer)

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1::EXPR INT

$\label{eq2}1$

(2)

Type: Expression(Integer)

What led me to suspect that FRAC is involved in the )trace bug is the following trace obtained in a Windows session (but unfortunately, I no longer know the exact set up to reproduce this):

  (7) -> 1::EXPR INT
  1<enter SparseMultivariatePolynomial.zero?,17 :
   arg1= 1
  1>exit  SparseMultivariatePolynomial.zero?,17 :
   false
  1<enter Fraction.*,60 : 1\((0 . 1) 0 . 1)
   1<enter SparseMultivariatePolynomial.coerce,77 :
    arg1= 1
   1>exit  SparseMultivariatePolynomial.coerce,77 :
    1
   1<enter SparseMultivariatePolynomial.=,97 :
    arg1= 1
    arg2= 1
   1>exit  SparseMultivariatePolynomial.=,97 :
    true
   1<enter SparseMultivariatePolynomial.*,65 :
    arg1= 1
    arg2= 1
    1<enter SparseMultivariatePolynomial.*,90 :
     arg1= 1
     arg2= 1
    1>exit  SparseMultivariatePolynomial.*,90 :
     1
   1>exit  SparseMultivariatePolynomial.*,65 :
    1
   1<enter SparseMultivariatePolynomial.zero?,17 :
    arg1= 1
   1>exit  SparseMultivariatePolynomial.zero?,17 :
    false
   1<enter SparseMultivariatePolynomial.=,97 :
    arg1= 1
    arg2= 1
   1>exit  SparseMultivariatePolynomial.=,97 :
    true
  1>exit  Fraction.*,60 : ((0 . 1) 0 . 1)
  1<enter Fraction.denom,73 : ((0 . 1) 0 . 1)
   2<enter Fraction.denom,73 : ((0 . 1) 0 . 1)
    3<enter Fraction.denom,73 : ((0 . 1) 0 . 1)
     ...

The following, surprisingly also works (trying to recreate the above trace, but failed).

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)trace FRAC

   Parameterized constructors traced:
      FRAC

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)trace SMP )math

   Parameterized constructors traced:
      FRAC, SMP
1::EXPR INT

$\label{eq3}1$

(3)

Type: Expression(Integer)

Here are trace examples that produced Bind Stack Overflow.

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)trace INT

   Parameterized constructors traced:
      FRAC, SMP, INT

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)trace FRAC 

   Parameterized constructors traced:
      SMP, INT, FRAC

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)trace EXPR INT )math

   Packages traced: 
      Integer, Expression(Integer)
   Parameterized constructors traced:
      SMP, INT, FRAC

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)trace KERNEL EXPR INT

   Packages traced: 
      Integer, Expression(Integer), Kernel(Expression(Integer))
   Parameterized constructors traced:
      SMP, INT, FRAC

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)trace SMP(INT, KERNEL EXPR INT)

   Packages traced: 
      Integer, Expression(Integer), Kernel(Expression(Integer)), 
            SparseMultivariatePolynomial(Integer,Kernel(
            Expression(Integer)))
   Parameterized constructors traced:
      SMP, INT, FRAC

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)trace OutputForm

   Packages traced: 
      Integer, Expression(Integer), Kernel(Expression(Integer)), 
            SparseMultivariatePolynomial(Integer,Kernel(
            Expression(Integer)))
   Parameterized constructors traced:
      SMP, INT, FRAC, OUTFORM
1::EXPR INT

 1<enter Expression.coerce,61 : 
 arg1 = 1
 1>exit  Expression.coerce,61 : 
 1

 1<enter Expression.denom,101 : 
 arg1 = 1
 1>exit  Expression.denom,101 : 
 1
 1<enter Expression.numer,99 : 
 arg1 = 1
 1>exit  Expression.numer,99 : 
 1

$\label{eq4}1$

(4)

Type: Expression(Integer)

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2/3::FRAC INT

 1<enter Fraction./,126 : (2 . 1)\(3 . 1)
  1<enter Fraction.zero?,13 : (3 . 1)
   1<enter Integer.zero?,18 : 3
   1>exit  Integer.zero?,18 : NIL
  1>exit  Fraction.zero?,13 : NIL
  1<enter Fraction.recip,54 : (3 . 1)
   1<enter Integer.zero?,18 : 3
   1>exit  Integer.zero?,18 : NIL
   1<enter Integer.zero?,18 : 1
   1>exit  Integer.zero?,18 : NIL
   1<enter Integer.=,59 : 3\1
   1>exit  Integer.=,59 : NIL
   1<enter Integer.unitNormal,91 : 3
   1>exit  Integer.unitNormal,91 : #(1 3 1)
   1<enter Integer.zero?,18 : 3
   1>exit  Integer.zero?,18 : NIL
   1<enter Integer.*,68 : 1\1
    1<enter Integer.*,67 : 1\1
    1>exit  Integer.*,67 : 1
   1>exit  Integer.*,68 : 1
  1>exit  Fraction.recip,54 : (0 1 . 3)
  1<enter Fraction.*,60 : (2 . 1)\(1 . 3)
   1<enter Fraction.zero?,13 : (2 . 1)
    1<enter Integer.zero?,18 : 2
    1>exit  Integer.zero?,18 : NIL
   1>exit  Fraction.zero?,13 : NIL
   1<enter Fraction.zero?,13 : (1 . 3)
    1<enter Integer.zero?,18 : 1
    1>exit  Integer.zero?,18 : NIL
   1>exit  Fraction.zero?,13 : NIL
   1<enter Fraction.=,21 : (2 . 1)\(1 . 1)
    1<enter Integer.=,59 : 2\1
    1>exit  Integer.=,59 : NIL
   1>exit  Fraction.=,21 : NIL
   1<enter Fraction.=,21 : (1 . 3)\(1 . 1)
    1<enter Integer.=,59 : 1\1
    1>exit  Integer.=,59 : T
    1<enter Integer.=,59 : 3\1
    1>exit  Integer.=,59 : NIL
   1>exit  Fraction.=,21 : NIL
   1<enter Integer.=,59 : 3\1
   1>exit  Integer.=,59 : NIL
   1<enter Integer.gcd,89 : 2\3
   1>exit  Integer.gcd,89 : 1
   1<enter Integer.exquo,87 : 2\1
   1>exit  Integer.exquo,87 : (0 . 2)
   1<enter Integer.exquo,87 : 3\1
   1>exit  Integer.exquo,87 : (0 . 3)
   1<enter Integer.=,59 : 1\1
   1>exit  Integer.=,59 : T
   1<enter Integer.*,68 : 2\1
    1<enter Integer.*,67 : 2\1
    1>exit  Integer.*,67 : 2
   1>exit  Integer.*,68 : 2
   1<enter Integer.*,68 : 3\1
    1<enter Integer.*,67 : 3\1
    1>exit  Integer.*,67 : 3
   1>exit  Integer.*,68 : 3
   1<enter Integer.zero?,18 : 2
   1>exit  Integer.zero?,18 : NIL
   1<enter Integer.=,59 : 3\1
   1>exit  Integer.=,59 : NIL
   1<enter Integer.unitNormal,91 : 3
   1>exit  Integer.unitNormal,91 : #(1 3 1)
   1<enter Integer.zero?,18 : 3
   1>exit  Integer.zero?,18 : NIL
   1<enter Integer.*,68 : 2\1
    1<enter Integer.*,67 : 2\1
    1>exit  Integer.*,67 : 2
   1>exit  Integer.*,68 : 2
  1>exit  Fraction.*,60 : (2 . 3)
 1>exit  Fraction./,126 : (2 . 3)

$\label{eq5}2 \over 3$

(5)

Type: Fraction(Integer)

For a preliminary analysis, see SandBox Trace Analysed.

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