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SymbolicNonAssociativeExpressions

Edit detail for SymbolicNonAssociativeExpressions revision 1 of 2

	1 2
Editor: Bill Page Time: 2017/02/03 20:28:07 GMT+0
Note: only limited pattern matching

changed:
-
\begin{axiom}
)lib AXIOM SINF SYMCAT SYMB AND SEXPR
)lib ALTAX ALTAX- ALT
)lib ASSAX ASSAX- ASSAX+ ASSAXS ASS+ ASSS
)lib CANAX CANAX- CAN
)lib COMAX COMAX- COMAX+ COM+ COMAX1 COMS COMAX2 COMAX3
)lib DBLAX DBLAX- DBL
)lib DISAX DISAX- DIS
)lib DIVAX DIVAX- DIV
)lib IDAX IDAX- ID
)lib INVAX INVAX- INV
)lib SQAX SQAX- SQ
\end{axiom}

Just identities for addition and multiplication (required for pattern matching)
\begin{axiom}
MYSYM:=Symbolic(Integer,ID)
(x,y,z):MYSYM
\end{axiom}

\begin{axiom}
x:=1+2+3
simplify x
simplify(x+y)
\end{axiom}

\begin{axiom}
r1:=_rule(2,4)$RewriteRule(Integer,Integer,MYSYM)
z:=r1 x
simplify z
\end{axiom}

fricas

)lib AXIOM SINF SYMCAT SYMB AND SEXPR

   Axiom is now explicitly exposed in frame initial 
   Axiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/AXIOM.NRLIB/AXIOM
   SINFunctions is now explicitly exposed in frame initial 
   SINFunctions will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SINF.NRLIB/SINF
   SymbolicCategory is now explicitly exposed in frame initial 
   SymbolicCategory will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SYMCAT.NRLIB/SYMCAT
   Symbolic is now explicitly exposed in frame initial 
   Symbolic will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SYMB.NRLIB/SYMB
   /\ is now explicitly exposed in frame initial 
   /\ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/AND.NRLIB/AND
   SymbolicExpression is now explicitly exposed in frame initial 
   SymbolicExpression will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SEXPR.NRLIB/SEXPR

fricas

)lib ALTAX ALTAX- ALT

   AntiCommutativeAxiom is now explicitly exposed in frame initial 
   AntiCommutativeAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ALTAX.NRLIB/ALTAX
   AntiCommutativeAxiom& is now explicitly exposed in frame initial 
   AntiCommutativeAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ALTAX-.NRLIB/ALTAX-
   AntiCommutative is now explicitly exposed in frame initial 
   AntiCommutative will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ALT.NRLIB/ALT

fricas

)lib ASSAX ASSAX- ASSAX+ ASSAXS ASS+ ASSS

   AssociativeAxiom is now explicitly exposed in frame initial 
   AssociativeAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASSAX.NRLIB/ASSAX
   AssociativeAxiom& is now explicitly exposed in frame initial 
   AssociativeAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASSAX-.NRLIB/ASSAX-
   AssociativeAxiom+ is now explicitly exposed in frame initial 
   AssociativeAxiom+ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASSAX+.NRLIB/ASSAX+
   AssociativeAxiom* is now explicitly exposed in frame initial 
   AssociativeAxiom* will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASSAXS.NRLIB/ASSAXS
   Associative+ is now explicitly exposed in frame initial 
   Associative+ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASS+.NRLIB/ASS+
   Associative* is now explicitly exposed in frame initial 
   Associative* will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ASSS.NRLIB/ASSS

fricas

)lib CANAX CANAX- CAN

   CancelsAxiom is now explicitly exposed in frame initial 
   CancelsAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/CANAX.NRLIB/CANAX
   CancelsAxiom& is now explicitly exposed in frame initial 
   CancelsAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/CANAX-.NRLIB/CANAX-
   Cancels is now explicitly exposed in frame initial 
   Cancels will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/CAN.NRLIB/CAN

fricas

)lib COMAX COMAX- COMAX+ COM+ COMAX1 COMS COMAX2 COMAX3

   CommutativeAxiom is now explicitly exposed in frame initial 
   CommutativeAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX.NRLIB/COMAX
   CommutativeAxiom& is now explicitly exposed in frame initial 
   CommutativeAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX-.NRLIB/COMAX-
   CommutativeAxiom+ is now explicitly exposed in frame initial 
   CommutativeAxiom+ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX+.NRLIB/COMAX+
   Commutative+ is now explicitly exposed in frame initial 
   Commutative+ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COM+.NRLIB/COM+
   CommutativeAxiom* is now explicitly exposed in frame initial 
   CommutativeAxiom* will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX1.NRLIB/COMAX1
   Commutative* is now explicitly exposed in frame initial 
   Commutative* will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMS.NRLIB/COMS
   CommutativeAxiom** is now explicitly exposed in frame initial 
   CommutativeAxiom** will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX2.NRLIB/COMAX2
   CommutativeAxiom/\ is now explicitly exposed in frame initial 
   CommutativeAxiom/\ will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/COMAX3.NRLIB/COMAX3

fricas

)lib DBLAX DBLAX- DBL

   DoublesAxiom is now explicitly exposed in frame initial 
   DoublesAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DBLAX.NRLIB/DBLAX
   DoublesAxiom& is now explicitly exposed in frame initial 
   DoublesAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DBLAX-.NRLIB/DBLAX-
   Doubles is now explicitly exposed in frame initial 
   Doubles will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DBL.NRLIB/DBL

fricas

)lib DISAX DISAX- DIS

   DistributiveAxiom is now explicitly exposed in frame initial 
   DistributiveAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DISAX.NRLIB/DISAX
   DistributiveAxiom& is now explicitly exposed in frame initial 
   DistributiveAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DISAX-.NRLIB/DISAX-
   Distributive is now explicitly exposed in frame initial 
   Distributive will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DIS.NRLIB/DIS

fricas

)lib DIVAX DIVAX- DIV

   DividesAxiom is now explicitly exposed in frame initial 
   DividesAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DIVAX.NRLIB/DIVAX
   DividesAxiom& is now explicitly exposed in frame initial 
   DividesAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DIVAX-.NRLIB/DIVAX-
   Divides is now explicitly exposed in frame initial 
   Divides will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/DIV.NRLIB/DIV

fricas

)lib IDAX IDAX- ID

   IdentityAxiom is now explicitly exposed in frame initial 
   IdentityAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/IDAX.NRLIB/IDAX
   IdentityAxiom& is now explicitly exposed in frame initial 
   IdentityAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/IDAX-.NRLIB/IDAX-
   Identities is now explicitly exposed in frame initial 
   Identities will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/ID.NRLIB/ID

fricas

)lib INVAX INVAX- INV

   InverseAxiom is now explicitly exposed in frame initial 
   InverseAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/INVAX.NRLIB/INVAX
   InverseAxiom& is now explicitly exposed in frame initial 
   InverseAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/INVAX-.NRLIB/INVAX-
   Inverse is now explicitly exposed in frame initial 
   Inverse will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/INV.NRLIB/INV

fricas

)lib SQAX SQAX- SQ

   SquaresAxiom is now explicitly exposed in frame initial 
   SquaresAxiom will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SQAX.NRLIB/SQAX
   SquaresAxiom& is now explicitly exposed in frame initial 
   SquaresAxiom& will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SQAX-.NRLIB/SQAX-
   Squares is now explicitly exposed in frame initial 
   Squares will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/SQ.NRLIB/SQ

Just identities for addition and multiplication (required for pattern matching)

fricas

MYSYM:=Symbolic(Integer,ID)

$\label{eq1}\hbox{\axiomType{Symbolic}\ } (\hbox{\axiomType{Integer}\ } , \hbox{\axiomType{Identities}\ })$

(1)

Type: Type

fricas

(x,y,z):MYSYM

Type: Void

fricas

x:=1+2+3

$\label{eq2}{\left(1 + 2 \right)}+ 3$

(2)

Type: Symbolic(Integer,Identities)

fricas

simplify x

$\label{eq3}6$

(3)

Type: Symbolic(Integer,Identities)

fricas

simplify(x+y)

$\label{eq4}y + 6$

(4)

Type: Symbolic(Integer,Identities)

fricas

r1:=_rule(2,4)$RewriteRule(Integer,Integer,MYSYM)

$\label{eq5}2 \mbox{\rm = =}4$

(5)

Type: RewriteRule?(Integer,Integer,Symbolic(Integer,Identities))

fricas

z:=r1 x

$\label{eq6}{\left(1 + 4 \right)}+ 3$

(6)

Type: Symbolic(Integer,Identities)

fricas

simplify z

$\label{eq7}8$

(7)

Type: Symbolic(Integer,Identities)