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Edit detail for SandBoxSymbolic revision 7 of 35

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Editor: Bill Page
Time: 2008/05/22 14:37:38 GMT-7
Note: Indeterminant domain

changed:
-eval(lambda(ab,['a,'b]))
a:=1
b:=-3
eval ab

Symbolic Integers

axiom
a:Union(Symbol,Integer)
Type: Void
axiom
b:Union(Symbol,Integer)
Type: Void
axiom
c:=a*3-b*2
LatexWiki Image(1)
Type: Polynomial Integer
axiom
p:UP(x,Integer):=x*2-7
LatexWiki Image(2)
Type: UnivariatePolynomial?(x,Integer)
axiom
pc := p c
LatexWiki Image(3)
Type: Fraction Polynomial Integer
axiom
f(x)==x^3-x^2+1
Type: Void
axiom
fb := f b
axiom
Compiling function f with type Symbol -> Polynomial Integer
LatexWiki Image(4)
Type: Polynomial Integer
axiom
a:=1
LatexWiki Image(5)
Type: Union(Integer,...)
axiom
b:=-3
LatexWiki Image(6)
Type: Union(Integer,...)
axiom
eval(pc,['a=a,'b=b])
LatexWiki Image(7)
Type: Fraction Polynomial Integer
axiom
eval(c,['a=a,'b=b])
LatexWiki Image(8)
Type: Polynomial Integer
axiom
eval(fb,['a=a,'b=b])
LatexWiki Image(9)
Type: Polynomial Integer
axiom
a:=3.14 Cannot convert right-hand side of assignment 3.14 to an object of the type Union(Symbol,Integer) of the left-hand side.

spad
)abbrev domain INDET Indeterminant ++ Description: ++ Based on InputForm Indeterminant(): Join(SExpressionCategory(String,Symbol,Integer,DoubleFloat,OutputForm), ConvertibleTo SExpression) with eval: % -> Any ++ eval(f) passes f to the interpreter. convert : SExpression -> % ++ convert(s) makes s into an input form. binary : (%, List %) -> % ++ \spad{binary(op, [a1,...,an])} returns the input form ++ corresponding to \spad{a1 op a2 op ... op an}. function : (%, List Symbol, Symbol) -> % ++ \spad{function(code, [x1,...,xn], f)} returns the input form ++ corresponding to \spad{f(x1,...,xn) == code}. lambda : (%, List Symbol) -> % ++ \spad{lambda(code, [x1,...,xn])} returns the input form ++ corresponding to \spad{(x1,...,xn) +-> code} if \spad{n > 1}, ++ or to \spad{x1 +-> code} if \spad{n = 1}. "+" : (%, %) -> % ++ \spad{a + b} returns the input form corresponding to \spad{a + b}. "-" : (%, %) -> % ++ \spad{a - b} returns the input form corresponding to \spad{a - b}. "-" : % -> % ++ \spad{-a} returns the input form corresponding to \spad{-a}. "*" : (%, %) -> % ++ \spad{a * b} returns the input form corresponding to \spad{a * b}. "/" : (%, %) -> % ++ \spad{a / b} returns the input form corresponding to \spad{a / b}. "**" : (%, NonNegativeInteger) -> % ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}. "**" : (%, Integer) -> % ++ \spad{a ** b} returns the input form corresponding to \spad{a ** b}. 0 : constant -> % ++ \spad{0} returns the input form corresponding to 0. 1 : constant -> % ++ \spad{1} returns the input form corresponding to 1. flatten : % -> % ++ flatten(s) returns an input form corresponding to s with ++ all the nested operations flattened to triples using new ++ local variables. ++ If s is a piece of code, this speeds up ++ the compilation tremendously later on. unparse : % -> String ++ unparse(f) returns a string s such that the parser ++ would transform s to f. ++ Error: if f is not the parsed form of a string. declare : List % -> Symbol ++ declare(t) returns a name f such that f has been ++ declared to the interpreter to be of type t, but has ++ not been assigned a value yet. ++ Note: t should be created as \spad{devaluate(T)$Lisp} where T is the ++ actual type of f (this hack is required for the case where ++ T is a mapping type). compile : (Symbol, List %) -> Symbol ++ \spad{compile(f, [t1,...,tn])} forces the interpreter to compile ++ the function f with signature \spad{(t1,...,tn) -> ?}. ++ returns the symbol f if successful. ++ Error: if f was not defined beforehand in the interpreter, ++ or if the ti's are not valid types, or if the compiler fails. coerce : Integer -> % == SExpression add Rep := SExpression mkProperOp: Symbol -> % strsym : % -> String tuplify : List Symbol -> % flatten0 : (%, Symbol, NonNegativeInteger) -> Record(lst: List %, symb:%) 0 == convert(0::Integer) 1 == convert(1::Integer) coerce(x:Integer):% == convert(x) coerce(x:%):OutputForm == expr x convert(x:%):SExpression == x pretend SExpression convert(x:SExpression):% == x conv(ll : List %): % == convert(ll pretend List SExpression)$SExpression pretend % lambda(f,l) == conv([convert(+->),tuplify l,f]$List(%)) eval x == v := interpret(x)$Lisp mkObj(unwrap(objVal(v)$Lisp)$Lisp, objMode(v)$Lisp)$Lisp convert(x:DoubleFloat):% == zero? x => 0 (x = 1) => 1 convert(x)$Rep flatten s == -- will not compile if I use 'or' atom? s => s every?(atom?,destruct s)$List(%) => s sy := new()$Symbol n:NonNegativeInteger := 0 l2 := [flatten0(x, sy, n := n + 1) for x in rest(l := destruct s)] conv(concat(convert(SEQ)@%, concat(concat [u.lst for u in l2], conv( [convert(exit)@%, 1$%, conv(concat(first l, [u.symb for u in l2]))@%]$List(%))@%)))@% flatten0(s, sy, n) == atom? s => [nil(), s] a := convert(concat(string sy, convert(n)@String)::Symbol)@% l2 := [flatten0(x, sy, n := n+1) for x in rest(l := destruct s)] [concat(concat [u.lst for u in l2], conv([convert( LET)@%, a, conv(concat(first l, [u.symb for u in l2]))@%]$List(%))@%), a] strsym s == string? s => string s symbol? s => string symbol s error "strsym: form is neither a string or symbol" unparse x == atom?(s:% := form2String(x)$Lisp) => strsym s concat [strsym a for a in destruct s] declare signature == declare(name := new()$Symbol, signature)$Lisp name compile(name, types) == symbol car cdr car selectLocalMms(mkProperOp name, convert(name)@%, types, nil$List(%))$Lisp mkProperOp name == op := mkAtree(nme := convert(name)@%)$Lisp transferPropsToNode(nme, op)$Lisp convert op binary(op, args) == (n := #args) < 2 => error "Need at least 2 arguments" n = 2 => convert([op, first args, last args]$List(%)) convert([op, first args, binary(op, rest args)]$List(%)) tuplify l == empty? rest l => convert first l conv concat(convert(Tuple), [convert x for x in l]$List(%)) function(f, l, name) == nn := convert(new(1 + #l, convert(nil()$List(%)))$List(%))@% conv([convert(DEF), conv(cons(convert(name)@%, [convert(x)@% for x in l])), nn, nn, f]$List(%)) s1 + s2 == conv [convert(+), s1, s2]$List(%) s1 - s2 == conv [convert(-), s1, s2]$List(%) _-(s1) == conv [convert(-), s1]$List(%) s1 * s2 == conv [convert(*), s1, s2]$List(%) s1:% ** n:Integer == s1 = 0 and n > 0 => 0 s1 = 1 or zero? n => 1 (n = 1) => s1 conv [convert(**), s1, convert n]$List(%) s1:% ** n:NonNegativeInteger == s1 ** (n::Integer) s1 / s2 == s2 = 1 => s1 conv [convert(/), s1, s2]$List(%)
spad
   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/7037715791149105850-25px002.spad using 
      old system compiler.
   INDET abbreviates domain Indeterminant 
------------------------------------------------------------------------
   initializing NRLIB INDET for Indeterminant 
   compiling into NRLIB INDET 
   compiling exported Zero : () -> $
Time: 0.12 SEC.
   compiling exported One : () -> $
Time: 0.01 SEC.
   compiling exported coerce : Integer -> $
Time: 0 SEC.
   compiling exported coerce : $ -> OutputForm
Time: 0 SEC.
   compiling exported convert : $ -> SExpression
      INDET;convert;$Se;5 is replaced by x 
Time: 0 SEC.
   compiling exported convert : SExpression -> $
      INDET;convert;Se$;6 is replaced by x 
Time: 0 SEC.
   compiling local conv : List $ -> $
Time: 0.06 SEC.
   compiling exported lambda : ($,List Symbol) -> $
Time: 0.08 SEC.
   compiling exported eval : $ -> Any
Time: 0 SEC.
   compiling exported convert : DoubleFloat -> $
Time: 0 SEC.
   compiling exported flatten : $ -> $
Time: 0.11 SEC.
   compiling local flatten0 : ($,Symbol,NonNegativeInteger) -> Record(lst: List $,symb: $)
Time: 0.14 SEC.
   compiling local strsym : $ -> String
Time: 0.01 SEC.
   compiling exported unparse : $ -> String
Time: 0.02 SEC.
   compiling exported declare : List $ -> Symbol
Time: 0 SEC.
   compiling exported compile : (Symbol,List $) -> Symbol
Time: 0.07 SEC.
   compiling local mkProperOp : Symbol -> $
Time: 0 SEC.
   compiling exported binary : ($,List $) -> $
Time: 0.02 SEC.
   compiling local tuplify : List Symbol -> $
Time: 0.01 SEC.
   compiling exported function : ($,List Symbol,Symbol) -> $
Time: 0.04 SEC.
   compiling exported + : ($,$) -> $
Time: 0 SEC.
   compiling exported - : ($,$) -> $
Time: 0 SEC.
   compiling exported - : $ -> $
Time: 0.01 SEC.
   compiling exported * : ($,$) -> $
Time: 0.01 SEC.
   compiling exported ** : ($,Integer) -> $
Time: 0.08 SEC.
   compiling exported ** : ($,NonNegativeInteger) -> $
Time: 0 SEC.
   compiling exported / : ($,$) -> $
Time: 0.01 SEC.
(time taken in buildFunctor:  1)
;;;     ***       |Indeterminant| REDEFINED
;;;     ***       |Indeterminant| REDEFINED
Time: 0.01 SEC.
   Warnings: 
      [1] conv: pretend$ -- should replace by @
   Cumulative Statistics for Constructor Indeterminant
      Time: 0.81 seconds
   finalizing NRLIB INDET 
   Processing Indeterminant for Browser database:
--------(eval ((Any) %))---------
--------(convert (% (SExpression)))---------
--------(binary (% % (List %)))---------
--------(function (% % (List (Symbol)) (Symbol)))---------
--------(lambda (% % (List (Symbol))))---------
--------(+ (% % %))---------
--------(- (% % %))---------
--------(- (% %))---------
--------(* (% % %))---------
--------(/ (% % %))---------
--------(** (% % (NonNegativeInteger)))---------
--------(** (% % (Integer)))---------
--------((Zero) (%) constant)---------
--------((One) (%) constant)---------
--------(flatten (% %))---------
--------(unparse ((String) %))---------
--------(declare ((Symbol) (List %)))---------
--------(compile ((Symbol) (Symbol) (List %)))---------
--->-->Indeterminant((coerce (% (Integer)))): Not documented!!!!
--------constructor---------
------------------------------------------------------------------------
   Indeterminant is now explicitly exposed in frame initial 
   Indeterminant will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/INDET.NRLIB/code

Symbolic Matrices

axiom
)clear all All user variables and function definitions have been cleared.

axiom
m:Union(Indeterminant,Matrix Integer)
Type: Void
axiom
n:Union(Indeterminant,Matrix Integer)
Type: Void
axiom
a:Union(Indeterminant,Integer)
Type: Void
axiom
b:Union(Indeterminant,Integer)
Type: Void
axiom
ab:=(a+b)*(a-b)
LatexWiki Image(10)
Type: Indeterminant
axiom
a:=1
LatexWiki Image(11)
Type: Union(Indeterminant,...)
axiom
b:=-3
LatexWiki Image(12)
Type: Union(Integer,...)
axiom
eval ab
LatexWiki Image(13)
Type: Indeterminant
axiom
mn1:= m*n-n*m
LatexWiki Image(14)
Type: Indeterminant
axiom
mn2:=(m+n)*(m-n)
LatexWiki Image(15)
Type: Indeterminant
axiom
m:=matrix [[1,2],[3,4]]
LatexWiki Image(16)
Type: Union(Matrix Integer,...)
axiom
n:=matrix [[-1,-2],[-3,4]]
LatexWiki Image(17)
Type: Union(Matrix Integer,...)
axiom
eval mn1
LatexWiki Image(18)
Type: Matrix Integer
axiom
eval mn2
LatexWiki Image(19)
Type: Matrix Integer