I have extended Symbol to easily create Greek letters and think about
suggesting a change of the default (algebra) genererators
in finite fields from %A, %B to α, β. Any counter arguments?
(64) -> newGreek()$Symbol
(64) α
Type: Symbol
(65) -> newGreek()$Symbol
(65) β
Type: Symbol
(66) -> newGreek()$Symbol
(66) γ
Type: Symbol
(67) -> new()$Symbol
(67) %A
Type: Symbol
(68) -> new()$Symbol
(68) %B
Type: Symbol
(69) -> new()$Symbol
(69) %C
Type: Symbol
(70) -> newGreek()$Symbol
(70) δ
Type: Symbol
(71) -> resetNew()$Symbol
Type: Void
(72) -> new()$Symbol
(72) %A
Type: Symbol
(73) -> newGreek()$Symbol
(73) ε
Type: Symbol
(74) -> resetNewGreek()$Symbol
Type: Void
(75) -> newGreek()$Symbol
(75) α
--
Mit freundlichen Grüßen
Johannes Grabmeier
Prof. Dr. Johannes Grabmeier
Köckstraße 1, D-94469 Deggendorf
Tel. +49-(0)-991-2979584, Tel. +49-(0)-151-681-70756
Tel. +49-(0)-991-3615-141 (d), Fax: +49-(0)-32224-192688
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)abbrev domain SYMBOL Symbol
++ Author: Stephen Watt
++ Date Created: 1986
++ Date Last Updated: 17.09.2018 J. Grabmeier
++ Description:
++ Basic and scripted symbols. Extended to easily created Greek letters as
symbols.
++ Keywords: symbol.
Symbol() : Exports == Implementation where
L ==> List OutputForm
Scripts ==> Record(sub : L, sup : L, presup : L, presub : L, args : L)
Exports ==> Join(OrderedSet, ConvertibleTo InputForm, OpenMath,
ConvertibleTo Symbol,
ConvertibleTo Pattern Integer, ConvertibleTo Pattern Float,
PatternMatchable Integer, PatternMatchable Float) with
new : () -> %
++ new() returns a new symbol whose name starts with %.
newGreek : () -> %
++ newGreek() returns the next greek character.
new : % -> %
++ new(s) returns a new symbol whose name starts with %s.
resetNew : () -> Void
++ resetNew() resets the internals counters that new() and
++ new(s) use to return distinct symbols every time.
resetNewGreek : () -> Void
++ resetNewGreek() resets the internals counters that newGreek()
++ use to return distinct symbols every time.
coerce : String -> %
++ coerce(s) converts the string s to a symbol.
name : % -> %
++ name(s) returns s without its scripts.
scripted? : % -> Boolean
++ scripted?(s) is true if s has been given any scripts.
scripts : % -> Scripts
++ scripts(s) returns all the scripts of s.
script : (%, List L) -> %
++ script(s, [a, b, c, d, e]) returns s with subscripts a,
++ superscripts b, pre-superscripts c, pre-subscripts d,
++ and argument-scripts e. Omitted components are taken to be empty.
++ For example, \spad{script(s, [a, b, c])} is equivalent to
++ \spad{script(s, [a, b, c, [], []])}.
script : (%, Scripts) -> %
++ script(s, [a, b, c, d, e]) returns s with subscripts a,
++ superscripts b, pre-superscripts c, pre-subscripts d,
++ and argument-scripts e.
subscript : (%, L) -> %
++ subscript(s, [a1, ..., an]) returns s
++ subscripted by \spad{[a1, ..., an]}.
superscript : (%, L) -> %
++ superscript(s, [a1, ..., an]) returns s
++ superscripted by \spad{[a1, ..., an]}.
argscript : (%, L) -> %
++ argscript(s, [a1, ..., an]) returns s
++ arg-scripted by \spad{[a1, ..., an]}.
elt : (%, L) -> %
++ elt(s, [a1, ..., an]) or s([a1, ..., an]) returns s subscripted by
\spad{[a1, ..., an]}.
string : % -> String
++ string(s) converts the symbol s to a string.
++ Error: if the symbol is subscripted.
sample : constant -> %
++ sample() returns a sample of %
Implementation ==> add
import from Character
import from List(OutputForm)
import from List(%)
count : Reference(Integer) := ref 0
xcount : AssociationList(%, Integer) := empty()
greekCount : Reference(Integer) := ref 0
istrings : PrimitiveArray(String) :=
construct ["0","1","2","3","4","5","6","7","8","9"]
-- the following 3 strings shall be of empty intersection
nums:String := "0123456789"
ALPHAS:String := "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alphas:String := "abcdefghijklmnopqrstuvwxyz"
greekLetters : String := concat [index(i :: PositiveInteger)$Character ::
String for i in 946..970]
writeOMSym(dev : OpenMathDevice, x : %) : Void ==
scripted? x =>
error "Cannot convert a scripted symbol to OpenMath"
OMputVariable(dev, x pretend Symbol)
OMwrite(dev : OpenMathDevice, x : %, wholeObj : Boolean) : Void ==
if wholeObj then
OMputObject(dev)
writeOMSym(dev, x)
if wholeObj then
OMputEndObject(dev)
hd:String := "*"
lhd := #hd
ord0 := ord char("0")$Character
pcnt ==> 4
istring : Integer -> String
syprefix : Scripts -> String
syscripts : Scripts -> L
convert(s : %) : InputForm == convert(s pretend Symbol)$InputForm
convert(s : %) : Symbol == s pretend Symbol
coerce(s : String) : % == VALUES(INTERN(s)$Lisp)$Lisp
x = y == EQUAL(x, y)$Lisp
hashUpdate!(hs, s) == update!(hs, SXHASH(s)$Lisp)$HashState
x < y == GGREATERP(y, x)$Lisp
coerce(x : %) : OutputForm ==
not(scripted? x) => outputForm(x pretend Symbol)
ss : Scripts := scripts x
rsl : List(L) := [ss.presub, ss.presup, ss.sup, ss.sub]
sl : L := []
for si in rsl repeat
empty?(sl) and empty?(si) => "iterate"
se :=
#si = 1 => first(si)
commaSeparate(si)
sl := cons(se, sl)
x0 := scripts(outputForm(name(x) pretend Symbol), sl)
a := ss.args
empty?(a) => x0
prefix(x0, a)
subscript(sy, lx) == script(sy, [lx, [], [], [], []])
elt(sy, lx) == subscript(sy, lx)
superscript(sy, lx) == script(sy, [[], lx, [], [], []])
argscript(sy, lx) == script(sy, [[], [], [], [], lx])
patternMatch(x : %, p : Pattern Integer, l : PatternMatchResult(Integer,
%))==
(patternMatch(x pretend Symbol, p, l pretend
PatternMatchResult(Integer, Symbol))$PatternMatchSymbol(Integer))
pretend PatternMatchResult(Integer, %)
patternMatch(x : %, p : Pattern Float, l : PatternMatchResult(Float, %)) ==
(patternMatch(x pretend Symbol, p, l pretend
PatternMatchResult(Float, Symbol))$PatternMatchSymbol(Float))
pretend PatternMatchResult(Float, %)
convert(x : %) : Pattern(Float) ==
coerce(x pretend Symbol)$Pattern(Float)
convert(x : %) : Pattern(Integer) ==
coerce(x pretend Symbol)$Pattern(Integer)
syprefix sc ==
ns : List Integer := [#sc.sub, #sc.sup, #sc.presup, #sc.presub]
concat concat(concat(hd, istring(#sc.args)),
[istring n for n in ns])
syscripts sc ==
all := sc.presub
all := concat(sc.presup, all)
all := concat(sc.sup, all)
all := concat(sc.sub, all)
concat(all, sc.args)
script(sy : %, ls : List L) ==
sc : Scripts := [[], [], [], [], []]
if not(empty?(ls)) then (sc.sub := first(ls); ls := rest(ls))
if not(empty?(ls)) then (sc.sup := first(ls); ls := rest(ls))
if not(empty?(ls)) then (sc.presup := first(ls); ls := rest(ls))
if not(empty?(ls)) then (sc.presub := first(ls); ls := rest(ls))
if not(empty?(ls)) then (sc.args := first(ls); ls := rest(ls))
script(sy, sc)
script(sy : %, sc : Scripts) ==
scripted? sy => error "Cannot add scripts to a scripted symbol"
(concat(concat(syprefix sc, string name sy)::%::OutputForm,
syscripts sc)) pretend %
string e ==
not scripted? e => PNAME(e)$Lisp
error "Cannot form string from non-atomic symbols."
-- Scripts ==> Record(sub: L, sup: L, presup: L, presub: L, args: L)
latex e ==
s : String := (PNAME(name e)$Lisp) pretend String
if #s > 1 and s.1 ~= char "\" then
s := concat("\mbox{\it ", concat(s, "}")$String)$String
not scripted? e => s
ss : Scripts := scripts e
lo : List OutputForm := ss.sub
sc : String
if not empty? lo then
sc := "__{"
while not empty? lo repeat
sc := concat(sc, latex first lo)$String
lo := rest lo
if not empty? lo then sc := concat(sc, ", ")$String
sc := concat(sc, "}")$String
s := concat(s, sc)$String
lo := ss.sup
if not empty? lo then
sc := "^{"
while not empty? lo repeat
sc := concat(sc, latex first lo)$String
lo := rest lo
if not empty? lo then sc := concat(sc, ", ")$String
sc := concat(sc, "}")$String
s := concat(s, sc)$String
lo := ss.presup
if not empty? lo then
sc := "{}^{"
while not empty? lo repeat
sc := concat(sc, latex first lo)$String
lo := rest lo
if not empty? lo then sc := concat(sc, ", ")$String
sc := concat(sc, "}")$String
s := concat(sc, s)$String
lo := ss.presub
if not empty? lo then
sc := "{}__{"
while not empty? lo repeat
sc := concat(sc, latex first lo)$String
lo := rest lo
if not empty? lo then sc := concat(sc, ", ")$String
sc := concat(sc, "}")$String
s := concat(sc, s)$String
lo := ss.args
if not empty? lo then
sc := "\left( {"
while not empty? lo repeat
sc := concat(sc, latex first lo)$String
lo := rest lo
if not empty? lo then sc := concat(sc, ", ")$String
sc := concat(sc, "} \right)")$String
s := concat(s, sc)$String
s
anyRadix(n : Integer, s : String) : String ==
ns:String := ""
repeat
qr := divide(n, #s)
n := qr.quotient
ns := concat(s.(qr.remainder+minIndex s), ns)
if zero?(n) then return ns
new() ==
sym := anyRadix(count()::Integer, ALPHAS)
count() := count() + 1
concat("%",sym)::%
newGreek() ==
sym := anyRadix(greekCount()::Integer, greekLetters)
greekCount() := greekCount() + 1
sym :: %
new x ==
n : Integer :=
(u := search(x, xcount)) case "failed" => 0
inc(u::Integer)
xcount(x) := n
xx :=
not scripted? x => string x
string name x
xx := concat("%",xx)
xx :=
(position(xx.maxIndex(xx), nums)>=minIndex(nums)) =>
concat(xx, anyRadix(n, alphas))
concat(xx, anyRadix(n, nums))
not scripted? x => xx::%
script(xx::%, scripts x)
resetNew() ==
count() := 0
for k in keys xcount repeat remove!(k, xcount)
void
resetNewGreek() ==
greekCount() := 0
void
scripted? sy ==
not ATOM(sy)$Lisp
of_list(x : %) : L == x pretend L
name sy ==
not scripted? sy => sy
str := string(first(of_list(sy)) pretend %)
si := lhd + pcnt + 2
str(si..#str)::%
scripts sy ==
not scripted? sy => [[], [], [], [], []]
nscripts : List NonNegativeInteger := [0, 0, 0, 0, 0]
lscripts : List L := [[], [], [], [], []]
str := string(first(of_list(sy)) pretend %)
nstr := #str
m := minIndex nscripts
for i in m.. for j in (lhd + 1)..(lhd + pcnt + 1) repeat
nscripts.i := (ord(str.j) - ord0)::NonNegativeInteger
-- Put the number of function scripts at the end.
nscripts := concat(rest nscripts, first nscripts)
allscripts := rest(of_list(sy))
m := minIndex lscripts
for i in m.. for n in nscripts repeat
#allscripts < n => error "Improper script count in symbol"
lscripts.i := first(allscripts, n)
allscripts := rest(allscripts, n)
[lscripts.m, lscripts.(m+1), lscripts.(m+2),
lscripts.(m+3), lscripts.(m+4)]
istring n ==
n > 9 => error "Can have at most 9 scripts of each kind"
istrings.(n + minIndex istrings)
sample() == "aSymbol"::%
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
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