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SandBox Spad

Edit detail for SandBox Spad revision 2 of 2

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Editor: test1 Time: 2013/07/31 18:13:42 GMT+0
Note:

changed:
-       degreeX:$ -> INT
       degreeX: % -> INT

changed:
-          a := [denom i for i in f::Rep]@List P  --  denom : FRAC UP -> UP(x,F)
-          b := map( (i) +-> degree i , a ) -- degree : UP -> NonNegativeInteger
          a := [denom i for i in f::Rep]@List(P)  --  denom : FRAC UP -> UP(x,F)
          b := map(di +-> degree(di), a)$ListFunctions2(P, INT) -- degree : UP -> NonNegativeInteger

removed:
-          12
-
-
-

added:

We need to package call 'map', otherwise compilation would fail.

From kratt6 Tue Apr 4 03:26:02 -0500 2006
From: kratt6
Date: Tue, 04 Apr 2006 03:26:02 -0500
Subject: 
Message-ID: <20060404032602-0500@wiki.axiom-developer.org>

The compiler is unable to find out the mode for '+->', since it doesn't know what map he is supposed to use. It is tedious, but the cure is to package call 'map'. Furthermore, it is usually easier to debug packages.

In fact, even with fully types '+->', the compilation fails, because the compiler can not find
appropriate 'map'.

changed:
-       degreeX:$ -> INT
       degreeX: LFRP -> INT

removed:
-          12
-
-

removed:
-
-From unknown Sat Apr 1 13:47:59 -0600 2006
-From: unknown
-Date: Sat, 01 Apr 2006 13:47:59 -0600
-Subject: 
-Message-ID: <20060401134759-0600@wiki.axiom-developer.org>
-
-I believe it's map (degree #1, a) we must type in *.spad files. 
-Last days I make the same error. I find this tips by grep *.spad file.
-
-FMy
-
-\begin{spad}
-)abbrev domain MINI MinimalInitialNotIntegrated
-MinimalInitialNotIntegrated(x,F): Exports == Implementation where
-    x: Symbol
-    F: Field
-
-    INT ==> Integer
-    P ==> UnivariatePolynomial(x,F)
-    FRP ==> Fraction P
-    LFRP ==> List FRP
-
-    Exports == with
-      
-       degreeX:$ -> INT
-
-    Implementation == add
-
-       Rep := LFRP
-
-       degreeX f ==
-          a := [denom i for i in f::Rep] --  denom : FRAC UP -> UP(x,F)
-          b := map( degree #1, a ) -- degree : UP -> NonNegativeInteger
-       -- b := [degree i for i in a ]
-          reduce( max, b ,0) :: INT
-          12
-
-\end{spad}
-
-I guess not yet
-
-From kratt6 Tue Apr 4 03:26:02 -0500 2006
-From: kratt6
-Date: Tue, 04 Apr 2006 03:26:02 -0500
-Subject: 
-Message-ID: <20060404032602-0500@wiki.axiom-developer.org>
-
-The compiler is unable to find out the mode for '#1', since it doesn't know what map he is supposed to use. It is tedious, but the cure is to package call 'map'. Furthermore, it is usually easier to debug packages.
-
-\begin{spad}
-)abbrev package MINI MinimalInitialNotIntegrated
-MinimalInitialNotIntegrated(x,F): Exports == Implementation where
-    x: Symbol
-    F: Field
-    INT ==> Integer
-    P ==> UnivariatePolynomial(x,F)
-    FRP ==> Fraction P
-    LFRP ==> List FRP
-    Exports == with
-       degreeX: LFRP -> INT
-    Implementation == add
-       degreeX f ==
-          a: List P := [denom i for i in f]
-          b := map(degree #1, a)$ListFunctions2(P, NonNegativeInteger)
-          reduce( max, b ,0) :: INT
-\end{spad}

A minimal exemple of my trouble.

fricas

(1) -> <spad>

fricas

)abbrev domain MINI MinimalInitialNotIntegrated
MinimalInitialNotIntegrated(x,F): Exports == Implementation where
    x: Symbol
    F: Field

    INT ==> Integer
    P ==> UnivariatePolynomial(x,F)
    FRP ==> Fraction P
    LFRP ==> List FRP

    Exports == with

       degreeX: % -> INT

    Implementation == add

       Rep := LFRP

       degreeX f ==
          a := [denom i for i in f::Rep]@List(P)  --  denom : FRAC UP -> UP(x,F)
          b := map(di +-> degree(di), a)$ListFunctions2(P, INT) -- degree : UP -> NonNegativeInteger
          --b := [degree i for i in a ]
          reduce( max, b ,0) :: INT</spad>

fricas

Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1973871146429693580-25px001.spad
      using old system compiler.
   MINI abbreviates domain MinimalInitialNotIntegrated 
------------------------------------------------------------------------
   initializing NRLIB MINI for MinimalInitialNotIntegrated 
   compiling into NRLIB MINI 
   compiling exported degreeX : % -> Integer
Time: 0.05 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MinimalInitialNotIntegrated| REDEFINED

;;;     ***       |MinimalInitialNotIntegrated| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MinimalInitialNotIntegrated
      Time: 0.05 seconds

   finalizing NRLIB MINI 
   Processing MinimalInitialNotIntegrated for Browser database:
--->-->MinimalInitialNotIntegrated(constructor): Not documented!!!!
--->-->MinimalInitialNotIntegrated((degreeX ((Integer) %))): Not documented!!!!
--->-->MinimalInitialNotIntegrated(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MINI.NRLIB/MINI.lsp" (written 01 NOV 2024 03:07:33 AM):

; wrote /var/aw/var/LatexWiki/MINI.NRLIB/MINI.fasl
; compilation finished in 0:00:00.008
------------------------------------------------------------------------
   MinimalInitialNotIntegrated is now explicitly exposed in frame 
      initial 
   MinimalInitialNotIntegrated will be automatically loaded when needed
      from /var/aw/var/LatexWiki/MINI.NRLIB/MINI

We need to package call map, otherwise compilation would fail.

... --kratt6, Tue, 04 Apr 2006 03:26:02 -0500 reply

The compiler is unable to find out the mode for +->, since it doesn't know what map he is supposed to use. It is tedious, but the cure is to package call map. Furthermore, it is usually easier to debug packages.

In fact, even with fully types +->, the compilation fails, because the compiler can not find appropriate map.

spad

)abbrev domain MINI MinimalInitialNotIntegrated
MinimalInitialNotIntegrated(x,F): Exports == Implementation where
    x: Symbol
    F: Field

    INT ==> Integer
    P ==> UnivariatePolynomial(x,F)
    FRP ==> Fraction P
    LFRP ==> List FRP

    Exports == with

       degreeX: LFRP -> INT

    Implementation == add

       Rep := LFRP

       degreeX f ==
          a := [denom i for i in f::Rep] --  denom : FRAC UP -> UP(x,F)
        --b := map( degree , a ) -- degree : UP -> NonNegativeInteger
          b := [degree i for i in a ]
          reduce( max, b ,0) :: INT

spad

   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/914813484557723871-25px002.spad
      using old system compiler.
   MINI abbreviates domain MinimalInitialNotIntegrated 
------------------------------------------------------------------------
   initializing NRLIB MINI for MinimalInitialNotIntegrated 
   compiling into NRLIB MINI 
   compiling exported degreeX : List Fraction UnivariatePolynomial(x,F) -> Integer
Time: 0.02 SEC.

(time taken in buildFunctor:  0)

;;;     ***       |MinimalInitialNotIntegrated| REDEFINED

;;;     ***       |MinimalInitialNotIntegrated| REDEFINED
Time: 0 SEC.

   Cumulative Statistics for Constructor MinimalInitialNotIntegrated
      Time: 0.02 seconds

   finalizing NRLIB MINI 
   Processing MinimalInitialNotIntegrated for Browser database:
--->/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1973871146429693580-25px001.spad-->MinimalInitialNotIntegrated(constructor): Not documented!!!!
--->/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1973871146429693580-25px001.spad-->MinimalInitialNotIntegrated((degreeX ((Integer) (List (Fraction (UnivariatePolynomial x F)))))): Not documented!!!!
--->/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1973871146429693580-25px001.spad-->MinimalInitialNotIntegrated(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MINI.NRLIB/MINI.lsp" (written 01 NOV 2024 03:07:33 AM):

; wrote /var/aw/var/LatexWiki/MINI.NRLIB/MINI.fasl
; compilation finished in 0:00:00.012
------------------------------------------------------------------------
   MinimalInitialNotIntegrated is already explicitly exposed in frame 
      initial 
   MinimalInitialNotIntegrated will be automatically loaded when needed
      from /var/aw/var/LatexWiki/MINI.NRLIB/MINI

fricas

list:List FRAC UP(x,FRAC INT):= [x^2+1/x::FRAC UP(x,FRAC INT), x+1/x^2]

$\label{eq1}\left[{\frac{{{x}^{3}}+ 1}{x}}, \:{\frac{{{x}^{3}}+ 1}{{x}^{2}}}\right]$

(1)

Type: List(Fraction(UnivariatePolynomial(x,Fraction(Integer))))

fricas

degreeX(list)$MINI(x, FRAC INT)

$\label{eq2}2$

(2)

Type: Integer