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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) -> %
Implementation == add
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 -> %
Implementation == add
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>
fricas
Compiling FriCAS source code from file
/var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/46105402477848525-25px001.spad
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:
[1] degree: left has no value
[2] 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:
[1] r has no value
[2] degree: arg has no value
[3] 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/DDOMfricas
a:=a::B(p)
Type: B(p)
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b:=b::B(q)
Type: B(q)
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c:=c::B(99)
Type: B(99)
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o:=o::B(0)
Type: B(0)
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test(degree a = p)
Type: Boolean
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test(degree o = 0)
Type: Boolean
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r := a*b
Type: C(B(p),B(q))
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s := c*o
Type: C(B(99),B(0))
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degree r
Type: Polynomial(Integer)
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degree s
Type: Polynomial(Integer)
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degree (r*s)
Type: Polynomial(Integer)
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d r
Type: D(C(B(p),B(q)))
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d (r*c)
Type: D(C(C(B(p),B(q)),B(99)))
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a* d (b*a*b)
Type: C(B(p),D(C(C(B(q),B(p)),B(q))))
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degree %
Type: Polynomial(Integer)
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d r*d a
Type: C(D(C(B(p),B(q))),D(B(p)))
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d %
Type: D(C(D(C(B(p),B(q))),D(B(p))))
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degree %
Type: Polynomial(Integer)
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-- r=0 -> :(
d d r
Type: B(r)
![\label{eq12}d{\left[ a \otimes b \right]}](images/3281652875183584412-16.0px.png "\label{eq12}d{\left[ a \otimes b \right]}")
![\label{eq13}d{\left[{a \otimes b}\otimes c \right]}](images/7674733874168304739-16.0px.png "\label{eq13}d{\left[{a \otimes b}\otimes c \right]}")
![\label{eq14}a \otimes{d{\left[{b \otimes a}\otimes b \right]}}](images/5743897914045288104-16.0px.png "\label{eq14}a \otimes{d{\left[{b \otimes a}\otimes b \right]}}")
![\label{eq16}{d{\left[ a \otimes b \right]}}\otimes{d{\left[ a \right]}}](images/2619238367240642269-16.0px.png "\label{eq16}{d{\left[ a \otimes b \right]}}\otimes{d{\left[ a \right]}}")
![\label{eq17}d{\left[{d{\left[ a \otimes b \right]}}\otimes{d{\left[ a \right]}}\right]}](images/1107500171493477037-16.0px.png "\label{eq17}d{\left[{d{\left[ a \otimes b \right]}}\otimes{d{\left[ a \right]}}\right]}")
