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(1) -> <spad>
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)abbrev category ACAT A_Categeroy
A_Categeroy() : Category == SetCategory with
degree : % -> Polynomial Integer

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)abbrev domain BDOM B
B(p) : Exports == Implementation where
p : Polynomial Integer
BOP ==> BasicOperator
ACAT ==> A_Categeroy
Exports == A_Categeroy with
coerce : Symbol -> %
Implementation == BOP add
Rep := BOP
coerce(s:Symbol):% == operator s
degree x == p

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)abbrev domain CDOM C
C(a,b) : Exports == Implementation where
ACAT ==> A_Categeroy
OF ==> OutputForm
a:ACAT
b:ACAT
PINT ==> Polynomial Integer
Exports == ACAT with
_* : (a,b) -> %
Rep := Record(left:a,right:b)
x * y == [x,y]@Rep
degree x == degree(x.left)$a + degree(x.right)$b
coerce(x:%):OutputForm == tensor(x.left::OF,x.right::OF)

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)abbrev domain DDOM D
D(a) : Exports == Implementation where
ACAT ==> A_Categeroy
OF ==> OutputForm
a:ACAT
PINT ==> Polynomial Integer
Exports == ACAT with
d : % -> B(r)
d : a -> %
Rep := Record(arg:a)
r:PINT
NullForm:B(r):="NULL"::Symbol::B(r)
d(x:%): B(r) == NullForm
d(x:a):% == [x]@Rep
degree x == 1 + degree(x.arg)$a coerce(x:%):OutputForm == hconcat(outputForm("d"::Symbol)$OF,bracket(x.arg::OF))</spad>
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Compiling FriCAS source code from file
using old system compiler.
ACAT abbreviates category A_Categeroy
------------------------------------------------------------------------
initializing NRLIB ACAT for A_Categeroy
compiling into NRLIB ACAT
;;;     ***       |A_Categeroy| REDEFINED
Time: 0 SEC.
finalizing NRLIB ACAT
Processing A_Categeroy for Browser database:
--->-->A_Categeroy(constructor): Not documented!!!!
--->-->A_Categeroy((degree ((Polynomial (Integer)) %))): Not documented!!!!
--->-->A_Categeroy(): Missing Description
; compiling file "/var/aw/var/LatexWiki/ACAT.NRLIB/ACAT.lsp" (written 01 SEP 2022 02:53:46 PM):
; /var/aw/var/LatexWiki/ACAT.NRLIB/ACAT.fasl written
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
A_Categeroy is now explicitly exposed in frame initial
A_Categeroy will be automatically loaded when needed from
/var/aw/var/LatexWiki/ACAT.NRLIB/ACAT
BDOM abbreviates domain B
------------------------------------------------------------------------
initializing NRLIB BDOM for B
compiling into NRLIB BDOM
compiling exported coerce : Symbol -> $Time: 0.01 SEC. compiling exported degree :$ -> Polynomial Integer
Time: 0.03 SEC.
(time taken in buildFunctor:  0)
;;;     ***       B REDEFINED
;;;     ***       B REDEFINED
Time: 0 SEC.
Cumulative Statistics for Constructor B
Time: 0.04 seconds
--------------non extending category----------------------
.. B(#1) of cat
(|Join| (|A_Categeroy|) (CATEGORY |domain| (SIGNATURE |coerce| ($(|Symbol|))))) has no (|OrderedSet|) finalizing NRLIB BDOM Processing B for Browser database: --->-->B(constructor): Not documented!!!! --->-->B((coerce (% (Symbol)))): Not documented!!!! --->-->B(): Missing Description ; compiling file "/var/aw/var/LatexWiki/BDOM.NRLIB/BDOM.lsp" (written 01 SEP 2022 02:53:46 PM): ; /var/aw/var/LatexWiki/BDOM.NRLIB/BDOM.fasl written ; compilation finished in 0:00:00.028 ------------------------------------------------------------------------ B is now explicitly exposed in frame initial B will be automatically loaded when needed from /var/aw/var/LatexWiki/BDOM.NRLIB/BDOM CDOM abbreviates domain C ------------------------------------------------------------------------ initializing NRLIB CDOM for C compiling into NRLIB CDOM Local variable Rep type redefined: (Join (SetCategory) (CATEGORY domain (SIGNATURE construct ((Record (: left a) (: right b)) a b)) (SIGNATURE ~= ((Boolean) (Record (: left a) (: right b)) (Record (: left a) (: right b)))) (SIGNATURE coerce ((OutputForm) (Record (: left a) (: right b)))) (SIGNATURE elt (a (Record (: left a) (: right b)) left)) (SIGNATURE elt (b (Record (: left a) (: right b)) right)) (SIGNATURE setelt! (a (Record (: left a) (: right b)) left a)) (SIGNATURE setelt! (b (Record (: left a) (: right b)) right b)) (SIGNATURE copy ((Record (: left a) (: right b)) (Record (: left a) (: right b)))))) to (Join (OrderedSet) (CATEGORY domain (SIGNATURE name ((Symbol)$)) (SIGNATURE properties ((AssociationList (Symbol) (None)) $)) (SIGNATURE copy ($ $)) (SIGNATURE operator ($ (Symbol))) (SIGNATURE operator ($(Symbol) (NonNegativeInteger))) (SIGNATURE arity ((Union (NonNegativeInteger) failed)$)) (SIGNATURE nullary? ((Boolean) $)) (SIGNATURE unary? ((Boolean)$)) (SIGNATURE nary? ((Boolean) $)) (SIGNATURE weight ((NonNegativeInteger)$)) (SIGNATURE weight ( (NonNegativeInteger))) (SIGNATURE equality ( (Mapping (Boolean) ))) (SIGNATURE comparison ( (Mapping (Boolean) ))) (SIGNATURE display ((Union (Mapping (OutputForm) (List (OutputForm))) failed) $)) (SIGNATURE display ($ $(Mapping (OutputForm) (List (OutputForm))))) (SIGNATURE display ($ $(Mapping (OutputForm) (OutputForm)))) (SIGNATURE input ($ $(Mapping (InputForm) (List (InputForm))))) (SIGNATURE input ((Union (Mapping (InputForm) (List (InputForm))) failed)$)) (SIGNATURE is? ((Boolean) $(Symbol))) (SIGNATURE has? ((Boolean)$ (Symbol))) (SIGNATURE assert ( (Symbol))) (SIGNATURE deleteProperty! ( (Symbol))) (SIGNATURE property ((Union (None) failed) $(Symbol))) (SIGNATURE setProperty ($ $(Symbol) (None))) (SIGNATURE setProperties ($ $(AssociationList (Symbol) (None)))))) compiling exported * : (a,b) ->$
CDOM;*;ab$;1 is replaced by CONS Time: 0 SEC. compiling exported degree :$ -> Polynomial Integer
Time: 0 SEC.
compiling exported coerce : $-> OutputForm Time: 0 SEC. (time taken in buildFunctor: 0) ;;; *** C REDEFINED ;;; *** C REDEFINED Time: 0 SEC. Warnings:  degree: left has no value  degree: right has no value Cumulative Statistics for Constructor C Time: 0 seconds finalizing NRLIB CDOM Processing C for Browser database: --->-->C(constructor): Not documented!!!! --->-->C((* (% a b))): Not documented!!!! --->-->C(): Missing Description ; compiling file "/var/aw/var/LatexWiki/CDOM.NRLIB/CDOM.lsp" (written 01 SEP 2022 02:53:46 PM): ; /var/aw/var/LatexWiki/CDOM.NRLIB/CDOM.fasl written ; compilation finished in 0:00:00.015 ------------------------------------------------------------------------ C is now explicitly exposed in frame initial C will be automatically loaded when needed from /var/aw/var/LatexWiki/CDOM.NRLIB/CDOM DDOM abbreviates domain D ------------------------------------------------------------------------ initializing NRLIB DDOM for D compiling into NRLIB DDOM Local variable Rep type redefined: (Join (SetCategory) (CATEGORY domain (SIGNATURE construct ((Record (: arg a)) a)) (SIGNATURE ~= ((Boolean) (Record (: arg a)) (Record (: arg a)))) (SIGNATURE coerce ((OutputForm) (Record (: arg a)))) (SIGNATURE elt (a (Record (: arg a)) arg)) (SIGNATURE setelt! (a (Record (: arg a)) arg a)) (SIGNATURE copy ((Record (: arg a)) (Record (: arg a)))))) to (Join (SetCategory) (CATEGORY domain (SIGNATURE construct ((Record (: left a) (: right b)) a b)) (SIGNATURE ~= ((Boolean) (Record (: left a) (: right b)) (Record (: left a) (: right b)))) (SIGNATURE coerce ((OutputForm) (Record (: left a) (: right b)))) (SIGNATURE elt (a (Record (: left a) (: right b)) left)) (SIGNATURE elt (b (Record (: left a) (: right b)) right)) (SIGNATURE setelt! (a (Record (: left a) (: right b)) left a)) (SIGNATURE setelt! (b (Record (: left a) (: right b)) right b)) (SIGNATURE copy ((Record (: left a) (: right b)) (Record (: left a) (: right b)))))) compiling exported d :$ -> B r
Time: 0 SEC.
compiling exported d : a -> $DDOM;d;a$;2 is replaced by LIST
Time: 0 SEC.
compiling exported degree : $-> Polynomial Integer Time: 0.04 SEC. compiling exported coerce :$ -> OutputForm
Time: 0 SEC.
(time taken in buildFunctor:  0)
;;;     ***       D REDEFINED
;;;     ***       D REDEFINED
Time: 0 SEC.
Warnings:
  r has no value
 degree:  arg has no value
 coerce:  arg has no value
Cumulative Statistics for Constructor D
Time: 0.04 seconds
finalizing NRLIB DDOM
Processing D for Browser database:
--->-->D(constructor): Not documented!!!!
--->-->D((d ((B r) %))): Not documented!!!!
--->-->D((d (% a))): Not documented!!!!
--->-->D(): Missing Description
; compiling file "/var/aw/var/LatexWiki/DDOM.NRLIB/DDOM.lsp" (written 01 SEP 2022 02:53:46 PM):
; /var/aw/var/LatexWiki/DDOM.NRLIB/DDOM.fasl written
; compilation finished in 0:00:00.016
------------------------------------------------------------------------
D is now explicitly exposed in frame initial
D will be automatically loaded when needed from
/var/aw/var/LatexWiki/DDOM.NRLIB/DDOM

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a:=a::B(p) (1)
Type: B(p)
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b:=b::B(q) (2)
Type: B(q)
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c:=c::B(99) (3)
Type: B(99)
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o:=o::B(0) (4)
Type: B(0)
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test(degree a = p) (5)
Type: Boolean
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test(degree o = 0) (6)
Type: Boolean
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r := a*b (7)
Type: C(B(p),B(q))
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s := c*o (8)
Type: C(B(99),B(0))
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degree r (9)
Type: Polynomial(Integer)
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degree s (10)
Type: Polynomial(Integer)
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degree (r*s) (11)
Type: Polynomial(Integer)
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d r (12)
Type: D(C(B(p),B(q)))
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d (r*c) (13)
Type: D(C(C(B(p),B(q)),B(99)))
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a* d (b*a*b) (14)
Type: C(B(p),D(C(C(B(q),B(p)),B(q))))
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degree % (15)
Type: Polynomial(Integer)
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d r*d a (16)
Type: C(D(C(B(p),B(q))),D(B(p)))
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d % (17)
Type: D(C(D(C(B(p),B(q))),D(B(p))))
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degree % (18)
Type: Polynomial(Integer)
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-- r=0 -> :(
d d r (19)
Type: B(r)

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