login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

PositiveInteger and NonNegativeInteger are subdomains of Integer.

Domain is a domain whose values are all domains. Categories are values of the domain SubDomain Domain. For example:

fricas
Integer

\label{eq1}\hbox{\axiomType{Integer}\ }(1)
Type: Type
fricas
Ring

\label{eq2}\hbox{\axiomType{Ring}\ }(2)
Type: Category

Unfortunately the original Axiom library did not include definitions of these domains.

fricas
[Integer,PrimeField(3)]
LISP output: (UNPRINTABLE UNPRINTABLE)
Type: List(Type)

fricas
[Ring,Field]
LISP output: (UNPRINTABLE UNPRINTABLE)
Type: List(Category)

OpenAxiom has implemented Domain and replaced SubDomain Domain with Category. Here we try to provide something similar for FriCAS.

spad
)abbrev domain DOMAIN Domain
Domain():SetCategory
  == add
    coerce(x:%):OutputForm ==
      n:SExpression:=devaluate(x)$Lisp
      #n=1 => car(n) pretend OutputForm
      n pretend OutputForm
    x = y ==
      devaluate(x)$Lisp = devaluate(y)$Lisp
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1491057242942260927-25px004.spad
      using old system compiler.
   DOMAIN abbreviates domain Domain 
------------------------------------------------------------------------
   initializing NRLIB DOMAIN for Domain 
   compiling into NRLIB DOMAIN 
   compiling exported coerce : $ -> OutputForm
Time: 0 SEC.
compiling exported = : ($,$) -> Boolean Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Domain| REDEFINED
;;; *** |Domain| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor Domain Time: 0 seconds
finalizing NRLIB DOMAIN Processing Domain for Browser database: --->-->Domain(): Missing Description ; compiling file "/var/aw/var/LatexWiki/DOMAIN.NRLIB/DOMAIN.lsp" (written 14 JUL 2013 10:09:16 AM):
; /var/aw/var/LatexWiki/DOMAIN.NRLIB/DOMAIN.fasl written ; compilation finished in 0:00:00.016 ------------------------------------------------------------------------ Domain is now explicitly exposed in frame initial Domain will be automatically loaded when needed from /var/aw/var/LatexWiki/DOMAIN.NRLIB/DOMAIN

spad
)abbrev domain SUBDOM SubDomain
SubDomain(D:Domain):SetCategory
  == add
    coerce(x:%):OutputForm ==
      n:SExpression:=devaluate(x)$Lisp
      #n=1 => car(n) pretend OutputForm
      n pretend OutputForm
    x = y ==
      devaluate(x)$Lisp = devaluate(y)$Lisp
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1455332092143083773-25px005.spad
      using old system compiler.
   SUBDOM abbreviates domain SubDomain 
------------------------------------------------------------------------
   initializing NRLIB SUBDOM for SubDomain 
   compiling into NRLIB SUBDOM 
   compiling exported coerce : $ -> OutputForm
Time: 0.01 SEC.
compiling exported = : ($,$) -> Boolean Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |SubDomain| REDEFINED
;;; *** |SubDomain| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor SubDomain Time: 0.01 seconds
finalizing NRLIB SUBDOM Processing SubDomain for Browser database: --->-->SubDomain(): Missing Description ; compiling file "/var/aw/var/LatexWiki/SUBDOM.NRLIB/SUBDOM.lsp" (written 14 JUL 2013 10:09:16 AM):
; /var/aw/var/LatexWiki/SUBDOM.NRLIB/SUBDOM.fasl written ; compilation finished in 0:00:00.015 ------------------------------------------------------------------------ SubDomain is now explicitly exposed in frame initial SubDomain will be automatically loaded when needed from /var/aw/var/LatexWiki/SUBDOM.NRLIB/SUBDOM

fricas
[Integer,PrimeField(3)]
LISP output: (UNPRINTABLE UNPRINTABLE)
Type: List(Type)
fricas
%.1

\label{eq3}\hbox{\axiomType{Integer}\ }(3)
Type: Type

fricas
[Ring,Field,IntegerNumberSystem]
LISP output: (UNPRINTABLE UNPRINTABLE UNPRINTABLE)
Type: List(Category)

Also we would like to be able to coerce both Domain and SubDomain to InputForm

fricas
Integer::InputForm

\label{eq4}\left(\hbox{\axiomType{Integer}\ } \right)(4)
Type: InputForm

Coercions like these are a special case in the Axiom interpreter. Here we modify the treatment for InputForm in references to '(InputForm) below.

From: interp/i-coerce.boot

boot
coerceInteractive(triple,t2) ==
  -- bind flag for recording/reporting instantiations
  -- (see recordInstantiation)
  t1 := objMode triple
  val := objVal triple
  null(t2) or t2 = $EmptyMode => NIL
  t2 = t1 => triple
  t2 = '$NoValueMode => objNew(val,t2)
  if t2 is ['SubDomain,x,.] then t2:= x
  -- JHD added category Aug 1996 for BasicMath
  -- WSP modified for coercion to InputForm Sept 2008
  t1 in '((Category) (Mode) (Domain) (SubDomain (Domain))) =>
    t2 = $OutputForm => objNew(val,t2)
    t2 = '(InputForm) => objNewWrap(val,t2)
    NIL
  t1 = '$NoValueMode =>
    if $compilingMap then clearDependentMaps($mapName,nil)
    throwKeyedMsg("S2IC0009",[t2,$mapName])
  $insideCoerceInteractive: local := true
  expr2 := EQUAL(t2,$OutputForm)
  if expr2 then startTimingProcess 'print
  else startTimingProcess 'coercion
  -- next 2 lines handle cases like '"failed"
  result :=
    expr2 and (t1 = val) => objNew(val,$OutputForm)
    expr2 and t1 is ['Variable,var] => objNewWrap(var,$OutputForm)
    t2 = '(InputForm) => objNewWrap(val,t2)
    coerceInt0(triple,t2)
  if expr2 then stopTimingProcess 'print
  else stopTimingProcess 'coercion
  result
boot
 
   >> System error:
   invalid number of arguments: 1
; compiling file "/var/aw/var/LatexWiki/5299509375252708736-25px009.clisp" (written 05 APR 2011 12:19:05 PM):
; /var/aw/var/LatexWiki/5299509375252708736-25px009.fasl written ; compilation finished in 0:00:00.054 Value = T

Now we get

fricas
a:=Integer::InputForm
>> System error: The function BOOT::BOOT-EQUAL is undefined.

Here is a useful function for parsing input strings

fricas
parse(s:String):InputForm == ncParseFromString(s)$Lisp pretend InputForm
Function declaration parse : String -> InputForm has been added to workspace.
>> System error: The function BOOT::BOOT-EQUAL is undefined.

There are still problems problems with values of domains in types

fricas
)set output tex off
 
fricas
)set output algebra on

fricas
CliffordAlgebra(4,Fraction Integer, quadraticForm matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]])
>> System error: The function BOOT::BOOT-EQUAL is undefined.

We can easily implement similar functionality at the Spad (algebra library) level by extending the InputFormFunction1 package. But limitation of FriCAS that prevent us from passing domain-values as parameters of functions mean we must do it this way.

spad
)abbrev package INFORM1 InputFormFunctions1
--)boot $noSubsumption := false
++ Tools for manipulating input forms ++ Author: Manuel Bronstein ++ Date Created: ??? ++ Date Last Updated: 19 April 1991 ++ Description: Tools for manipulating input forms.
InputFormFunctions1(R:Type):with packageCall: Symbol -> InputForm ++ packageCall(f) returns the input form corresponding to f$R. interpret : InputForm -> R ++ interpret(f) passes f to the interpreter, and transforms ++ the result into an object of type R. domainToInputForm: () -> InputForm ++ convert a domain to InputForm == add domainToInputForm():InputForm == devaluate(R)$Lisp
packageCall name == convert([convert("$elt"::Symbol), domainToInputForm(), convert name]$List(InputForm))@InputForm
interpret form ==
retract(interpret(convert([convert("@"::Symbol), form, domainToInputForm()]$List(InputForm))@InputForm)$InputForm)$AnyFunctions1(R)
spad
   Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/8025279438643830910-25px014.spad
      using old system compiler.
   INFORM1 abbreviates package InputFormFunctions1 
------------------------------------------------------------------------
   initializing NRLIB INFORM1 for InputFormFunctions1 
   compiling into NRLIB INFORM1 
   compiling exported domainToInputForm : () -> InputForm
Time: 0 SEC.
compiling exported packageCall : Symbol -> InputForm Time: 0.01 SEC.
compiling exported interpret : InputForm -> R Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |InputFormFunctions1| REDEFINED
;;; *** |InputFormFunctions1| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor InputFormFunctions1 Time: 0.01 seconds
finalizing NRLIB INFORM1 Processing InputFormFunctions1 for Browser database: --------constructor--------- --------(packageCall ((InputForm) (Symbol)))--------- --------(interpret (R (InputForm)))--------- --------(domainToInputForm ((InputForm)))--------- --->/usr/local/lib/fricas/target/x86_64-unknown-linux/../../src/algebra/INFORM1.spad-->InputFormFunctions1((domainToInputForm ((InputForm)))): Improper first word in comments: convert "convert a domain to InputForm" ; compiling file "/var/aw/var/LatexWiki/INFORM1.NRLIB/INFORM1.lsp" (written 14 JUL 2013 10:09:16 AM):
; /var/aw/var/LatexWiki/INFORM1.NRLIB/INFORM1.fasl written ; compilation finished in 0:00:00.013 ------------------------------------------------------------------------ InputFormFunctions1 is now explicitly exposed in frame initial InputFormFunctions1 will be automatically loaded when needed from /var/aw/var/LatexWiki/INFORM1.NRLIB/INFORM1

fricas
domainToInputForm()$INFORM1(PrimeField 7)
>> System error: The function BOOT::BOOT-EQUAL is undefined.




  Subject:   Be Bold !!
  ( 13 subscribers )  
Please rate this page: