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Edit detail for SubDomain revision 6 of 7

1 2 3 4 5 6 7
Editor: Bill Page
Time: 2008/09/19 10:33:41 GMT-7
Note: coercion of domain to InputForm in Spad

added:
We can easily implement similar functionality at the Spad
(algebra library) level by extending the 'InputFormFunction1'
package.
\begin{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)

\end{spad}

\begin{axiom}
domainToInputForm()$INFORM1(PrimeField 7)
parse(s:String):InputForm == ncParseFromString(s)$Lisp pretend InputForm
interpret(parse("x^2+1"))$INFORM1(Polynomial Float)
\end{axiom}


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:

axiom
Integer
LatexWiki Image(1)
Type: Domain
axiom
Ring
LatexWiki Image(2)
Type: SubDomain? Domain

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

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

axiom
[Ring,Field]
LISP output: (UNPRINTABLE UNPRINTABLE)
Type: List SubDomain? Domain

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/zope2/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: 0.01 SEC.
compiling exported = : ($,$) -> Boolean Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |Domain| REDEFINED
;;; *** |Domain| REDEFINED Time: 0.01 SEC.
Cumulative Statistics for Constructor Domain Time: 0.02 seconds
finalizing NRLIB DOMAIN Processing Domain for Browser database: --->-->Domain(): Missing Description ------------------------------------------------------------------------ Domain is now explicitly exposed in frame initial Domain will be automatically loaded when needed from /var/zope2/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/zope2/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 ------------------------------------------------------------------------ SubDomain is now explicitly exposed in frame initial SubDomain will be automatically loaded when needed from /var/zope2/var/LatexWiki/SUBDOM.NRLIB/SUBDOM

axiom
[Integer,PrimeField(3)]
LatexWiki Image(3)
Type: List Domain
axiom
%.1
LatexWiki Image(4)
Type: Domain

axiom
[Ring,Field,IntegerNumberSystem]
LatexWiki Image(5)
Type: List SubDomain? Domain

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

axiom
Integer::InputForm
Cannot convert from type Domain to InputForm for value Integer()

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
Value = T
; (DEFUN |coerceInteractive| ...) is being compiled.
;; The variable |$OutputForm| is undefined.
;; The compiler will assume this variable is a global.
Value = 2544

Now we get

axiom
a:=Integer::InputForm
LatexWiki Image(6)
Type: InputForm?
axiom
interpret(a)$InputForm
LatexWiki Image(7)
Type: Domain
axiom
unparse(a)$InputForm
LatexWiki Image(8)
Type: String
axiom
b:=PrimeField(11)::InputForm
LatexWiki Image(9)
Type: InputForm?
axiom
interpret(b)$InputForm
LatexWiki Image(10)
Type: Domain
axiom
unparse(b)$InputForm
LatexWiki Image(11)
Type: String
axiom
c:=DirectProduct(3,Fraction Integer)::InputForm
LatexWiki Image(12)
Type: InputForm?
axiom
interpret(c)$InputForm
LatexWiki Image(13)
Type: Domain
axiom
unparse(c)$InputForm
LatexWiki Image(14)
Type: String
axiom
d:=Ring::InputForm
LatexWiki Image(15)
Type: InputForm?
axiom
interpret(d)$InputForm
LatexWiki Image(16)
Type: SubDomain? Domain
axiom
unparse(d)$InputForm
LatexWiki Image(17)
Type: String
axiom
K := Fraction Integer
LatexWiki Image(18)
Type: Domain
axiom
g := matrix [[1,0,0,0], [0,-1,0,0], [0,0,-1,0], [0,0,0,-1]]
LatexWiki Image(19)
Type: Matrix Integer
axiom
D := CliffordAlgebra(4,K, quadraticForm g)
LatexWiki Image(20)
Type: Domain
axiom
D::InputForm
LatexWiki Image(21)
Type: InputForm?
axiom
unparse %
LatexWiki Image(22)
Type: String

We can easily implement similar functionality at the Spad (algebra library) level by extending the InputFormFunction1 package.

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/zope2/var/LatexWiki/8025279438643830910-25px011.spad using 
      old system compiler.
   INFORM1 abbreviates package InputFormFunctions1 
------------------------------------------------------------------------
   initializing NRLIB INFORM1 for InputFormFunctions1 
   compiling into NRLIB INFORM1 
   compiling exported domainToInputForm : () -> InputForm
Time: 0.01 SEC.
compiling exported packageCall : Symbol -> InputForm Time: 0.09 SEC.
compiling exported interpret : InputForm -> R Time: 0.08 SEC.
(time taken in buildFunctor: 0)
;;; *** |InputFormFunctions1| REDEFINED
;;; *** |InputFormFunctions1| REDEFINED Time: 0 SEC.
Cumulative Statistics for Constructor InputFormFunctions1 Time: 0.18 seconds
finalizing NRLIB INFORM1 Processing InputFormFunctions1 for Browser database: --------(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" --------constructor--------- ------------------------------------------------------------------------ InputFormFunctions1 is now explicitly exposed in frame initial InputFormFunctions1 will be automatically loaded when needed from /var/zope2/var/LatexWiki/INFORM1.NRLIB/INFORM1

axiom
domainToInputForm()$INFORM1(PrimeField 7)
LatexWiki Image(23)
Type: InputForm?
axiom
parse(s:String):InputForm == ncParseFromString(s)$Lisp pretend InputForm
Function declaration parse : String -> InputForm has been added to workspace.
Type: Void
axiom
interpret(parse("x^2+1"))$INFORM1(Polynomial Float)
axiom
Compiling function parse with type String -> InputForm
LatexWiki Image(24)
Type: Polynomial Float