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-rw-r--r--src/ChangeLog36
-rw-r--r--src/algebra/Makefile.in1
-rw-r--r--src/algebra/carten.spad.pamphlet22
-rw-r--r--src/algebra/clifford.spad.pamphlet8
-rw-r--r--src/algebra/combinat.spad.pamphlet20
-rw-r--r--src/algebra/defintef.spad.pamphlet2
-rw-r--r--src/algebra/elfuts.spad.pamphlet2
-rw-r--r--src/algebra/ffnb.spad.pamphlet2
-rw-r--r--src/algebra/fnla.spad.pamphlet4
-rw-r--r--src/algebra/intaux.spad.pamphlet2
-rw-r--r--src/algebra/intfact.spad.pamphlet3
-rw-r--r--src/algebra/lodop.spad.pamphlet2
-rw-r--r--src/algebra/naalgc.spad.pamphlet4
-rw-r--r--src/algebra/numtheor.spad.pamphlet4
-rw-r--r--src/algebra/odealg.spad.pamphlet2
-rw-r--r--src/algebra/padic.spad.pamphlet10
-rw-r--r--src/algebra/patmatch1.spad.pamphlet4
-rw-r--r--src/algebra/perman.spad.pamphlet6
-rw-r--r--src/algebra/puiseux.spad.pamphlet4
-rw-r--r--src/algebra/radix.spad.pamphlet8
-rw-r--r--src/algebra/solvedio.spad.pamphlet2
-rw-r--r--src/algebra/special.spad.pamphlet12
-rw-r--r--src/algebra/sttf.spad.pamphlet98
23 files changed, 153 insertions, 105 deletions
diff --git a/src/ChangeLog b/src/ChangeLog
index 3037cb37..b026d971 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,5 +1,41 @@
2011-10-24 Gabriel Dos Reis <gdr@cs.tamu.edu>
+ * algebra/perman.spad.pamphlet (Permanent): Specify type of local
+ variable j.
+ * algebra/patmatch1.spad.pamphlet (PatternMatchTools): Tidy.
+ * algebra/padic.spad.pamphlet: Restrict type of literal constants.
+ * algebra/sttf.spad.pamphlet: Likewise.
+ * algebra/puiseux.spad.pamphlet: Likewise.
+ * algebra/odealg.spad.pamphlet (SystemODESolver) [applyLodo0]:
+ Specify type of local variable ans.
+ * algebra/numtheor.spad.pamphlet (IntegerNumberTheoryFunctions): Tidy.
+ * algebra/naalgc.spad.pamphlet (MonadWithUnit) [rightPower]:
+ Specify type of local variable res.
+ [leftPower]: Likewise.
+ * algebra/lodop.spad.pamphlet (NonCommutativeOperatorDivision)
+ [leftLcm]: Specify type of local variable v.
+ * algebra/intfact.spad.pamphlet (IntegerRoots) [approxSqrt]:
+ Specify type of local variables old and new.
+ * algebra/elfuts.spad.pamphlet
+ (EllipticFunctionsUnivariateTaylorSeries): Restrict types of
+ literal constants.
+ * algebra/ffnb.spad.pamphlet
+ (FiniteFieldNormalBasisExtensionByPolynomial): Likewise.
+ * algebra/fnla.spad.pamphlet (FreeNilpotentLie): Likewise.
+ * algebra/intaux.spad.pamphlet (IntegrationResult): Likewise.
+ * algebra/defintef.spad.pamphlet
+ (ElementaryFunctionDefiniteIntegration) [checkSMP]: Specify type
+ in the definition of local variable n.
+ * algebra/combinat.spad.pamphlet (IntegerCombinatoricFunctions):
+ Tidy definition of local variables.
+ * algebra/clifford.spad.pamphlet (CliffordAlgebra): Specify type in
+ the definition of local variables k, exchanges, bz.
+ * algebra/catdef.spad.pamphlet (CartesianTensor): Specify type in the
+ definition of local varibles rx and offz.
+ Remove useless variables zol, xol, oly, and zoly.
+
+2011-10-24 Gabriel Dos Reis <gdr@cs.tamu.edu>
+
* interp/compiler.boot (compArgumentsAndTryAgain): Fail only if
elaboration of all arguments fails.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index dcd03071..aad21917 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -1164,6 +1164,7 @@ axiom_algebra_layer_10_objects = \
$(addprefix $(OUT)/, \
$(addsuffix .$(FASLEXT),$(axiom_algebra_layer_10)))
$(OUT)/ARRAY2.$(FASLEXT): $(OUT)/IFARRAY.$(FASLEXT)
+$(OUT)/ORESUP.$(FASLEXT): $(OUT)/PR.$(FASLEXT)
axiom_algebra_layer_11 = \
APPLYORE ARRAY1 ARRAY12 ARRAY2 \
diff --git a/src/algebra/carten.spad.pamphlet b/src/algebra/carten.spad.pamphlet
index a1fd01f6..7cc2fbbb 100644
--- a/src/algebra/carten.spad.pamphlet
+++ b/src/algebra/carten.spad.pamphlet
@@ -272,7 +272,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
v = dim2 => 2
v = dim3 => 3
v = dim4 => 4
- rx := 0
+ rx: NNI := 0
while v ~= 0 repeat
qr := divide(v, dim)
v := qr.quotient
@@ -431,7 +431,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
z
coerce(m: SM(dim,R)): % ==
z := new(dim**2, 0)
- offz := 0
+ offz: NNI := 0
for i in 0..dim-1 repeat
for j in 0..dim-1 repeat
set!(z, offz + j, m(i+1,j+1))
@@ -500,7 +500,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
error "Improper index for contraction"
if i > j then (i,j) := (j,i)
- rl:= (rx- j) pretend NNI; nl:= dim**rl; zol:= 1; xol:= zol
+ rl:= (rx- j) pretend NNI; nl:= dim**rl
rm:= (j-i-1) pretend NNI; nm:= dim**rm; zom:= nl; xom:= zom*dim
rh:= (i - 1) pretend NNI; nh:= dim**rh; zoh:= nl*nm
xoh:= zoh*dim**2
@@ -511,7 +511,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
for m in 1..nm _
for xm in xh.. by xom for zm in zh.. by zom repeat
for l in 1..nl _
- for xl in xm.. by xol for zl in zm.. by zol repeat
+ for xl in xm.. for zl in zm.. repeat
set!(z, zl, 0)
for k in 1..dim for xk in xl.. by xok repeat
set!(z, zl, get(z,zl) + get(x,xk))
@@ -524,11 +524,11 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
i < 1 or i > rx or j < 1 or j > ry =>
error "Improper index for contraction"
- rly:= (ry-j) pretend NNI; nly:= dim**rly; oly:= 1; zoly:= 1
+ rly:= (ry-j) pretend NNI; nly:= dim**rly
rhy:= (j -1) pretend NNI; nhy:= dim**rhy
- ohy:= nly*dim; zohy:= zoly*nly
+ ohy:= nly*dim; zohy:= nly
rlx:= (rx-i) pretend NNI; nlx:= dim**rlx
- olx:= 1; zolx:= zohy*nhy
+ zolx:= zohy*nhy
rhx:= (i -1) pretend NNI; nhx:= dim**rhx
ohx:= nlx*dim; zohx:= zolx*nlx
@@ -537,11 +537,11 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
for dxh in 1..nhx _
for xh in 0.. by ohx for zhx in 0.. by zohx repeat
for dxl in 1..nlx _
- for xl in xh.. by olx for zlx in zhx.. by zolx repeat
+ for xl in xh.. for zlx in zhx.. by zolx repeat
for dyh in 1..nhy _
for yh in 0.. by ohy for zhy in zlx.. by zohy repeat
for dyl in 1..nly _
- for yl in yh.. by oly for zly in zhy.. by zoly repeat
+ for yl in yh.. for zly in zhy.. repeat
set!(z, zly, 0)
for k in 1..dim _
for xk in xl.. by nlx for yk in yl.. by nly repeat
@@ -556,13 +556,13 @@ CartesianTensor(minix, dim, R): Exports == Implementation where
error "Improper indicies for transposition"
if i > j then (i,j) := (j,i)
- rl:= (rx- j) pretend NNI; nl:= dim**rl; zol:= 1; zoi := zol*nl
+ rl:= (rx- j) pretend NNI; nl:= dim**rl; zoi := nl
rm:= (j-i-1) pretend NNI; nm:= dim**rm; zom:= nl*dim; zoj := zom*nm
rh:= (i - 1) pretend NNI; nh:= dim**rh; zoh:= nl*nm*dim**2
z := new(#x, 0)
for h in 1..nh for zh in 0.. by zoh repeat _
for m in 1..nm for zm in zh.. by zom repeat _
- for l in 1..nl for zl in zm.. by zol repeat _
+ for l in 1..nl for zl in zm.. repeat _
for p in 1..dim _
for zp in zl.. by zoi for xp in zl.. by zoj repeat
for q in 1..dim _
diff --git a/src/algebra/clifford.spad.pamphlet b/src/algebra/clifford.spad.pamphlet
index 2ae3cffb..ab4c481e 100644
--- a/src/algebra/clifford.spad.pamphlet
+++ b/src/algebra/clifford.spad.pamphlet
@@ -316,7 +316,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
bz := b2
for i in 0..n-1 | bit?(b1,i) repeat
-- Apply rule ei*ej = -ej*ei for i~=j
- k := 0
+ k: NNI := 0
for j in i+1..n-1 | bit?(b1, j) repeat k := k+1
for j in 0..i-1 | bit?(bz, j) repeat k := k+1
if odd? k then c := -c
@@ -344,7 +344,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
-- The Rep assumes n is small so bubble sort is ok.
-- Using bubble sort keeps the exchange info obvious.
wasordered := false
- exchanges := 0
+ exchanges: NNI := 0
while not wasordered repeat
wasordered := true
for i in 1..#lb-1 repeat
@@ -356,7 +356,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
-- 2. Prepare the basis element
-- Apply identity ei*ei = Q(ei).
- bz := 0
+ bz: NNI := 0
for b in lb repeat
bn := (b-1)::NNI
if bit?(bz, bn) then
@@ -364,7 +364,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
bz:= ( bz - 2**bn )::NNI
else
bz:= bz + 2**bn
- [c, bz::NNI]
+ [c, bz]
monomial(c, lb) ==
r := canonMonom(c, lb)
diff --git a/src/algebra/combinat.spad.pamphlet b/src/algebra/combinat.spad.pamphlet
index f597f98f..23b4a1eb 100644
--- a/src/algebra/combinat.spad.pamphlet
+++ b/src/algebra/combinat.spad.pamphlet
@@ -72,8 +72,8 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
n < m::I => P(convert(n)@Z)
concat!(P, new((convert(n+1)@Z - m)::N,0)$IndexedFlexibleArray(I,0))
for i in m..convert(n)@Z repeat
- s:I := 1
- t:I := 0
+ s: I := 1
+ t: I := 0
for k in 1.. repeat
l := (3*k*k-k) quo 2
l > i => leave
@@ -96,18 +96,23 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
F.Fv := f
binomial(n, m) ==
- s,b:I
negative? n or negative? m or m > n => 0
m = 0 => 1
n < 2*m => binomial(n, n-m)
- (s,b) := (0,1)
+ s: I := 0
+ b: I := 1
if B.Bn = n then
B.Bm = m+1 =>
b := (B.Bv * (m+1)) quo (n-m)
B.Bn := n
B.Bm := m
return(B.Bv := b)
- if m >= B.Bm then (s := B.Bm; b := B.Bv) else (s,b) := (0,1)
+ if m >= B.Bm then
+ s := B.Bm
+ b := B.Bv
+ else
+ s := 0
+ b := 1
for k in convert(s+1)@Z .. convert(m)@Z repeat
b := (b*(n-k::I+1)) quo k::I
B.Bn := n
@@ -122,12 +127,13 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with
factorial n quo s
permutation(n, m) ==
- t:I
negative? m or n < m => 0
m := n-m
p:I := 1
for k in convert(m+1)@Z .. convert(n)@Z by 2 repeat
- if k::I = n then t := n else t := (k*(k+1))::I
+ t: I :=
+ k::I = n => n
+ (k*(k+1))::I
p := p * t
p
diff --git a/src/algebra/defintef.spad.pamphlet b/src/algebra/defintef.spad.pamphlet
index 34eb5e03..fc604038 100644
--- a/src/algebra/defintef.spad.pamphlet
+++ b/src/algebra/defintef.spad.pamphlet
@@ -131,7 +131,7 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where
((w := checkSMP(t, x, k, a, b)) case "failed") or (w::B) => return w
false
(v := isPlus p) case List(P) =>
- n := 0 -- number of summand having a pole
+ n: Z := 0 -- number of summand having a pole
for t in v::List(P) repeat
(w := checkSMP(t, x, k, a, b)) case "failed" => return w
if w::B then n := n + 1
diff --git a/src/algebra/elfuts.spad.pamphlet b/src/algebra/elfuts.spad.pamphlet
index 89b64578..23b4f781 100644
--- a/src/algebra/elfuts.spad.pamphlet
+++ b/src/algebra/elfuts.spad.pamphlet
@@ -57,7 +57,7 @@ EllipticFunctionsUnivariateTaylorSeries(Coef,UTS):
integrate(1,sign*k**2*$UPS scd.1*$UPS scd.2*$UPS dx)]
sncndn(z,k) ==
- empty? z => [0 :: ST,1 :: ST,1::ST]
+ empty? z => [0@Coef :: ST,1@Coef :: ST,1@Coef::ST]
frst z = 0 => YS(sncndnre(k,#1,deriv z,-1),3)
error "ELFUTS:sncndn: constant coefficient should be 0"
sn(x,k) == series sncndn.(coefficients x,k).1
diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet
index 673fd906..b0b42e01 100644
--- a/src/algebra/ffnb.spad.pamphlet
+++ b/src/algebra/ffnb.spad.pamphlet
@@ -590,7 +590,7 @@ FiniteFieldNormalBasisExtensionByPolynomial(GF,uni): Exports == _
one? x.i => b
((x.i)::OUT) *$OUT b
l:=cons(mon,l)$(List OUT)
- null(l)$(List OUT) => (0::OUT)
+ null(l)$(List OUT) => (0@GF::OUT)
r:=reduce("+",l)$(List OUT)
r
diff --git a/src/algebra/fnla.spad.pamphlet b/src/algebra/fnla.spad.pamphlet
index 4feb3a97..b82a1288 100644
--- a/src/algebra/fnla.spad.pamphlet
+++ b/src/algebra/fnla.spad.pamphlet
@@ -283,12 +283,12 @@ FreeNilpotentLie(n:NNI,class:NNI,R: CommutativeRing): Export == Implement where
r::O * mkcomm(mkcomm(coms(k).1)$Com,mkcomm(coms(k).3)$Com)$Com::O
shallowExpand(f) ==
- f = 0 => 0::O
+ f = 0 => 0@R::O
reductum(f) = 0 => shallowE(lC f,lS f)
shallowE(lC f,lS f) + shallowExpand(reductum f)
deepExpand(f) ==
- f = 0 => 0::O
+ f = 0 => 0@R::O
reductum(f) = 0 =>
lC(f)=1 => Fac(value(lS f))::O
lC(f)::O * Fac(value(lS f))::O
diff --git a/src/algebra/intaux.spad.pamphlet b/src/algebra/intaux.spad.pamphlet
index d88eb62b..b5267540 100644
--- a/src/algebra/intaux.spad.pamphlet
+++ b/src/algebra/intaux.spad.pamphlet
@@ -171,7 +171,7 @@ IntegrationResult(F:Field): Exports == Implementation where
l := reverse! [LOG2O f for f in logpart u]$List(O)
if ratpart u ~= 0 then l := concat(ratpart(u)::O, l)
if not elem? u then l := concat([NE2O f for f in notelem u], l)
- null l => 0::O
+ null l => 0@F::O
reduce("+", l)
NE2O ne ==
diff --git a/src/algebra/intfact.spad.pamphlet b/src/algebra/intfact.spad.pamphlet
index f405476f..f24922c5 100644
--- a/src/algebra/intfact.spad.pamphlet
+++ b/src/algebra/intfact.spad.pamphlet
@@ -324,7 +324,8 @@ IntegerRoots(I:IntegerNumberSystem): Exports == Implementation where
s := shift(s, n)
return ((1 + s + a quo s) quo two)
-- initial approximation for the root is within a factor of 2
- (new, old) := (shift(1, n quo two), 1)
+ old: I := 1
+ new: I := shift(1, n quo two)
while new ~= old repeat
(new, old) := ((1 + new + a quo new) quo two, new)
new
diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet
index 53a38c6c..758dcf12 100644
--- a/src/algebra/lodop.spad.pamphlet
+++ b/src/algebra/lodop.spad.pamphlet
@@ -186,7 +186,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where
b = 0 =>a
b0 := b
u := monomial(1,0)$P
- v := 0
+ v: P := 0
while leadingCoefficient b ~= 0 repeat
qr := leftDivide(a,b)
(a, b) := (b, qr.remainder)
diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet
index c256691a..ce4b81ef 100644
--- a/src/algebra/naalgc.spad.pamphlet
+++ b/src/algebra/naalgc.spad.pamphlet
@@ -119,12 +119,12 @@ MonadWithUnit(): Category == Monad with
expt(x,n pretend PositiveInteger)
rightPower(a: %,n: NonNegativeInteger) ==
zero? n => 1
- res := 1
+ res: % := 1
for i in 1..n repeat res := res * a
res
leftPower(a: %,n: NonNegativeInteger) ==
zero? n => 1
- res := 1
+ res: % := 1
for i in 1..n repeat res := a * res
res
diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet
index f1251618..4a8101ea 100644
--- a/src/algebra/numtheor.spad.pamphlet
+++ b/src/algebra/numtheor.spad.pamphlet
@@ -335,8 +335,8 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where
fibonacci n ==
n = 0 => 0
negative? n => (odd? n => 1; -1) * fibonacci(-n)
- f1, f2 : I
- (f1,f2) := (0,1)
+ f1: I := 0
+ f2: I := 1
for k in length(n)-2 .. 0 by -1 repeat
t := f2**2
(f1,f2) := (t+f1**2,t+2*f1*f2)
diff --git a/src/algebra/odealg.spad.pamphlet b/src/algebra/odealg.spad.pamphlet
index 1a3d355d..b96ffa9d 100644
--- a/src/algebra/odealg.spad.pamphlet
+++ b/src/algebra/odealg.spad.pamphlet
@@ -205,7 +205,7 @@ SystemODESolver(F, LO): Exports == Implementation where
-- computes +/[m(r, i) mm(i, c) for i ranging over the last n columns of m]
applyLodo0(m, r, mm, c, n) ==
- ans := 0
+ ans: F := 0
rr := maxRowIndex mm
cc := maxColIndex m
for i in 1..n repeat
diff --git a/src/algebra/padic.spad.pamphlet b/src/algebra/padic.spad.pamphlet
index d7265998..260bb580 100644
--- a/src/algebra/padic.spad.pamphlet
+++ b/src/algebra/padic.spad.pamphlet
@@ -289,7 +289,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where
showAll?() == true
coerce(x:%):OUT ==
- empty?(st := stream x) => 0 :: OUT
+ empty?(st := stream x) => 0@I :: OUT
count : NNI := _$streamCount$Lisp
l : L OUT := empty()
n : NNI := 0
@@ -309,8 +309,8 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where
explicitlyEmpty? st => l
eq?(st,rst st) and frst st = 0 => l
concat(prefix("O" :: OUT,[PEXPR ** (n :: OUT)]),l)
- empty? l => 0 :: OUT
- reduce("+",reverse! l)
+ empty? l => 0@I :: OUT
+ reduce(_+,reverse! l)
@
\section{domain PADIC PAdicInteger}
@@ -515,7 +515,7 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where
m := getExpon x; zp := getZp x
uu := digits zp
l : L OUT := empty()
- empty? uu => 0 :: OUT
+ empty? uu => 0@I :: OUT
count : NNI := _$streamCount$Lisp
n : NNI := 0
while n <= count and not empty? uu repeat
@@ -535,7 +535,7 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where
explicitlyEmpty? uu => l
eq?(uu,rst uu) and frst uu = 0 => l
concat(prefix("O" :: OUT,[PEXPR ** ((n :: I) + m) :: OUT]),l)
- empty? l => 0 :: OUT
+ empty? l => 0@I :: OUT
reduce("+",reverse! l)
@
diff --git a/src/algebra/patmatch1.spad.pamphlet b/src/algebra/patmatch1.spad.pamphlet
index 2b7da476..e0812ea2 100644
--- a/src/algebra/patmatch1.spad.pamphlet
+++ b/src/algebra/patmatch1.spad.pamphlet
@@ -532,10 +532,10 @@ PatternMatchTools(S, R, P): Exports == Implementation where
l1:PRS := failed()
t : P
for x in setDifference(ls, bad)
- while (t := x; failed?(l1 := pmatch(x, p, l))) repeat 0
+ while (t := x; failed?(l1 := pmatch(x, p, l))) repeat nil
failed? l1 =>
for x in bad
- while (t := x; failed?(l1 := pmatch(x, p, l))) repeat 0
+ while (t := x; failed?(l1 := pmatch(x, p, l))) repeat nil
failed? l1 => [addMatchRestricted(p, ident, l, ident), ls]
[l1, remove(t, ls)]
[l1, remove(t, ls)]
diff --git a/src/algebra/perman.spad.pamphlet b/src/algebra/perman.spad.pamphlet
index b45620a4..73e20b31 100644
--- a/src/algebra/perman.spad.pamphlet
+++ b/src/algebra/perman.spad.pamphlet
@@ -164,7 +164,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
vv : V V I := firstSubsetGray(n)$GRAY
-- For the meaning of the elements of vv, see GRAY.
w : V R := new(n,0$R)
- j := 1 -- Will be the number of the element changed in subset
+ j: I := 1 -- Will be the number of the element changed in subset
while j ~= (n+1) repeat -- we sum over all subsets of (1,...,n)
sgn := -sgn
b := sgn
@@ -209,7 +209,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
for i in 1..n repeat
b := b * w.i
a := a+b
- j := 1 -- Will be the number of the element changed in subset
+ j: I := 1 -- Will be the number of the element changed in subset
while j ~= n repeat -- we sum over all subsets of (1,...,n-1)
sgn := -sgn
b := sgn
@@ -255,7 +255,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")):
for i in 1..n repeat
b := b *$R w.i
a := a +$R b
- j := 1 -- Will be the number of the element changed in subset
+ j: I := 1 -- Will be the number of the element changed in subset
while j ~= n repeat -- we sum over all subsets of (1,...,n-1)
sgn := -sgn
b := sgn
diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet
index b465790c..0abb2891 100644
--- a/src/algebra/puiseux.spad.pamphlet
+++ b/src/algebra/puiseux.spad.pamphlet
@@ -532,7 +532,7 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
termsToOutputForm:(RN,RN,ST,OUT) -> OUT
termsToOutputForm(m,rat,uu,xxx) ==
l : L OUT := empty()
- empty? uu => 0 :: OUT
+ empty? uu => 0@Coef :: OUT
count : NNI := _$streamCount$Lisp
n : NNI := 0
while n <= count and not empty? uu repeat
@@ -552,7 +552,7 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where
explicitlyEmpty? uu => l
eq?(uu,rst uu) and frst uu = 0 => l
concat(prefix("O" :: OUT,[xxx ** (((n::I) * rat + m) :: OUT)]),l)
- empty? l => 0 :: OUT
+ empty? l => 0@Coef :: OUT
reduce("+",reverse! l)
coerce(upxs:%):OUT ==
diff --git a/src/algebra/radix.spad.pamphlet b/src/algebra/radix.spad.pamphlet
index df8308ad..ae148819 100644
--- a/src/algebra/radix.spad.pamphlet
+++ b/src/algebra/radix.spad.pamphlet
@@ -113,7 +113,7 @@ RadixExpansion(bb): Exports == Implementation where
coerce(a):RN == (wholePart a) :: RN + fractionPart a
coerce(n):% == n :: RN :: %
coerce(q):% ==
- s := 1; if negative? q then (s := -1; q := -q)
+ s: I := 1; if negative? q then (s := -1; q := -q)
qr := divide(numer q,denom q)
whole := radixInt (qr.quotient,bb)
fractn := radixFrac(qr.remainder,denom q,bb)
@@ -130,11 +130,11 @@ RadixExpansion(bb): Exports == Implementation where
floor a == floor(a::RN)
wholePart a ==
- n0 := 0
+ n0: I := 0
for r in a.int repeat n0 := bb*n0 + r
a.sgn*n0
fractionPart(a: %): Fraction Integer ==
- n0 := 0
+ n0: I := 0
for r in a.pfx repeat n0 := bb*n0 + r
null a.cyc =>
a.sgn*n0/bb**((#a.pfx)::NNI)
@@ -188,7 +188,7 @@ RadixExpansion(bb): Exports == Implementation where
if not null a.pfx then le := concat(intgroup a.pfx,le)
if not null le then le := concat("." :: OUT,le)
if not null a.int then le := concat(intgroup a.int,le)
- else le := concat(0 :: OUT,le)
+ else le := concat(0@I :: OUT,le)
rex := exprgroup le
if negative? a.sgn then -rex else rex
diff --git a/src/algebra/solvedio.spad.pamphlet b/src/algebra/solvedio.spad.pamphlet
index f83c9cb6..7b68eb4b 100644
--- a/src/algebra/solvedio.spad.pamphlet
+++ b/src/algebra/solvedio.spad.pamphlet
@@ -156,7 +156,7 @@ DiophantineSolutionPackage(): Cat == Capsule where
verifyMinimality(sol, graph, flag) ==
-- test whether sol contains a minimal homogeneous solution
flag => -- sol is a homogeneous solution
- i := 1
+ i: I := 1
while sol.i = 0 repeat
i := i + 1
x := sol.i
diff --git a/src/algebra/special.spad.pamphlet b/src/algebra/special.spad.pamphlet
index 8a619f7b..b8c1c293 100644
--- a/src/algebra/special.spad.pamphlet
+++ b/src/algebra/special.spad.pamphlet
@@ -294,7 +294,8 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where
laguerreL(n, x) ==
n = 0 => 1
- (p1, p0) := (-x + 1, 1)
+ p0: R := 1
+ p1: R := -x + 1
for i in 1..n-1 repeat
(p1, p0) := ((2*i::R + 1 - x)*p1 - i**2*p0, p1)
p1
@@ -312,19 +313,22 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where
p1
chebyshevT(n, x) ==
n = 0 => 1
- (p1, p0) := (x, 1)
+ p0: R := 1
+ p1: R := x
for i in 1..n-1 repeat
(p1, p0) := (2*x*p1 - p0, p1)
p1
chebyshevU(n, x) ==
n = 0 => 1
- (p1, p0) := (2*x, 1)
+ p0: R := 1
+ p1: R := 2*x
for i in 1..n-1 repeat
(p1, p0) := (2*x*p1 - p0, p1)
p1
hermiteH(n, x) ==
n = 0 => 1
- (p1, p0) := (2*x, 1)
+ p0: R := 1
+ p1: R := 2*x
for i in 1..n-1 repeat
(p1, p0) := (2*x*p1 - 2*i*p0, p1)
p1
diff --git a/src/algebra/sttf.spad.pamphlet b/src/algebra/sttf.spad.pamphlet
index f65e7bbc..682d3fb7 100644
--- a/src/algebra/sttf.spad.pamphlet
+++ b/src/algebra/sttf.spad.pamphlet
@@ -134,7 +134,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
expre(r,e,dx) == lazyIntegrate(r,e*dx)
exp z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(coef := frst z) = 0 => YS expre(1,#1,deriv z)
TRANSFCN => YS expre(exp coef,#1,deriv z)
error concat("exp: ",TRCONST)
@@ -165,7 +165,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
-- [lazyIntegrate(rs,st1),lazyIntegrate(rc,st2)]
sincos z ==
- empty? z => [0 :: ST,1 :: ST]
+ empty? z => [0@Coef :: ST,1@Coef :: ST]
l :=
(coef := frst z) = 0 => YS(sincosre(0,1,#1,deriv z,-1),2)
TRANSFCN => YS(sincosre(sin coef,cos coef,#1,deriv z,-1),2)
@@ -176,7 +176,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
cos z == sincos(z).cos
tanre:(Coef,ST,ST,Coef) -> ST
- tanre(r,t,dx,sign) == lazyIntegrate(r,((1 :: ST) + sign*t*t)*dx)
+ tanre(r,t,dx,sign) == lazyIntegrate(r,((1@Coef :: ST) + sign*t*t)*dx)
-- When the compiler had difficulties with the above definition,
-- I did the following to help it:
@@ -191,13 +191,13 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
-- lazyIntegrate(r,st1)
tan z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(coef := frst z) = 0 => YS tanre(0,#1,deriv z,1)
TRANSFCN => YS tanre(tan coef,#1,deriv z,1)
error concat("tan: ",TRCONST)
cotre:(Coef,ST,ST) -> ST
- cotre(r,t,dx) == lazyIntegrate(r,-((1 :: ST) + t*t)*dx)
+ cotre(r,t,dx) == lazyIntegrate(r,-((1@Coef :: ST) + t*t)*dx)
-- When the compiler had difficulties with the above definition,
-- I did the following to help it:
@@ -218,7 +218,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
error concat("cot: ",TRCONST)
sec z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
frst z = 0 => recip(cos z) :: ST
TRANSFCN =>
cosz := cos z
@@ -245,12 +245,12 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
"failed"
asin z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(coef := frst z) = 0 =>
- integrate(0,powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+ integrate(0,powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
TRANSFCN =>
coef = 1 or coef = -1 =>
- x := (1 :: ST) - z*z
+ x := (1@Coef :: ST) - z*z
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("asin: ",MAYFPOW)
@@ -260,7 +260,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(quot := (deriv z) exquo squirt) case "failed" =>
error concat("asin: ",NOTINV)
integrate(asin coef,quot :: ST)
- integrate(asin coef,powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+ integrate(asin coef,powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
error concat("asin: ",TRCONST)
acos z ==
@@ -270,7 +270,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
TRANSFCN =>
coef := frst z
coef = 1 or coef = -1 =>
- x := (1 :: ST) - z*z
+ x := (1@Coef :: ST) - z*z
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("acos: ",MAYFPOW)
@@ -280,15 +280,15 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(quot := (-deriv z) exquo squirt) case "failed" =>
error concat("acos: ",NOTINV)
integrate(acos coef,quot :: ST)
- integrate(acos coef,-powern(-1/2,(1 :: ST) - z*z) * (deriv z))
+ integrate(acos coef,-powern(-1/2,(1@Coef :: ST) - z*z) * (deriv z))
error concat("acos: ",TRCONST)
atan z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(coef := frst z) = 0 =>
- integrate(0,(recip((1 :: ST) + z*z) :: ST) * (deriv z))
+ integrate(0,(recip((1@Coef :: ST) + z*z) :: ST) * (deriv z))
TRANSFCN =>
- (y := recip((1 :: ST) + z*z)) case "failed" =>
+ (y := recip((1@Coef :: ST) + z*z)) case "failed" =>
error concat("atan: ",LOGS)
integrate(atan coef,(y :: ST) * (deriv z))
error concat("atan: ",TRCONST)
@@ -298,7 +298,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
TRANSFCN => acot(0)$Coef :: ST
error concat("acot: ",TRCONST)
TRANSFCN =>
- (y := recip((1 :: ST) + z*z)) case "failed" =>
+ (y := recip((1@Coef :: ST) + z*z)) case "failed" =>
error concat("acot: ",LOGS)
integrate(acot frst z,-(y :: ST) * (deriv z))
error concat("acot: ",TRCONST)
@@ -309,7 +309,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(coef := frst z) = 0 =>
error "asec: constant coefficient should not be 0"
coef = 1 or coef = -1 =>
- x := z*z - (1 :: ST)
+ x := z*z - (1@Coef :: ST)
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("asec: ",MAYFPOW)
@@ -321,7 +321,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(quot2 := (quot :: ST) exquo z) case "failed" =>
error concat("asec: ",NOTINV)
integrate(asec coef,quot2 :: ST)
- integrate(asec coef,(powern(-1/2,z*z-(1::ST))*(deriv z)) / z)
+ integrate(asec coef,(powern(-1/2,z*z-(1@Coef::ST))*(deriv z)) / z)
error concat("asec: ",TRCONST)
acsc z ==
@@ -330,7 +330,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(coef := frst z) = 0 =>
error "acsc: constant coefficient should not be zero"
coef = 1 or coef = -1 =>
- x := z*z - (1 :: ST)
+ x := z*z - (1@Coef :: ST)
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("acsc: ",MAYFPOW)
@@ -342,13 +342,13 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
(quot2 := (quot :: ST) exquo z) case "failed" =>
error concat("acsc: ",NOTINV)
integrate(acsc coef,quot2 :: ST)
- integrate(acsc coef,-(powern(-1/2,z*z-(1::ST))*(deriv z)) / z)
+ integrate(acsc coef,-(powern(-1/2,z*z-(1@Coef::ST))*(deriv z)) / z)
error concat("acsc: ",TRCONST)
--% Hyperbolic Trigonometric Functions
sinhcosh z ==
- empty? z => [0 :: ST,1 :: ST]
+ empty? z => [0@Coef :: ST,1@Coef :: ST]
l :=
(coef := frst z) = 0 => YS(sincosre(0,1,#1,deriv z,1),2)
TRANSFCN => YS(sincosre(sinh coef,cosh coef,#1,deriv z,1),2)
@@ -359,7 +359,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
cosh z == sinhcosh(z).cosh
tanh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(coef := frst z) = 0 => YS tanre(0,#1,deriv z,-1)
TRANSFCN => YS tanre(tanh coef,#1,deriv z,-1)
error concat("tanh: ",TRCONST)
@@ -381,10 +381,10 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
recip(sinhz) :: ST
asinh z ==
- empty? z => 0 :: ST
- (coef := frst z) = 0 => log(z + powern(1/2,(1 :: ST) + z*z))
+ empty? z => 0@Coef :: ST
+ (coef := frst z) = 0 => log(z + powern(1/2,(1@Coef :: ST) + z*z))
TRANSFCN =>
- x := (1 :: ST) + z*z
+ x := (1@Coef :: ST) + z*z
-- compute order of 'x', in case coefficient(z,0) = +- %i
(ord := orderOrFailed x) case "failed" =>
error concat("asinh: ",MAYFPOW)
@@ -401,7 +401,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
TRANSFCN =>
coef := frst z
coef = 1 or coef = -1 =>
- x := z*z - (1 :: ST)
+ x := z*z - (1@Coef :: ST)
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("acosh: ",MAYFPOW)
@@ -409,16 +409,16 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
odd? order => error concat("acosh: ",FPOWERS)
-- the argument to 'log' must have a non-zero constant term
log(z + powern(1/2,x))
- log(z + powern(1/2,z*z - (1 :: ST)))
+ log(z + powern(1/2,z*z - (1@Coef :: ST)))
error concat("acosh: ",TRCONST)
atanh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(coef := frst z) = 0 =>
- (inv(2::RN)::Coef) * log(((1 :: ST) + z)/((1 :: ST) - z))
+ (inv(2::RN)::Coef) * log(((1@Coef :: ST) + z)/((1@Coef :: ST) - z))
TRANSFCN =>
coef = 1 or coef = -1 => error concat("atanh: ",LOGS)
- (inv(2::RN)::Coef) * log(((1 :: ST) + z)/((1 :: ST) - z))
+ (inv(2::RN)::Coef) * log(((1@Coef :: ST) + z)/((1@Coef :: ST) - z))
error concat("atanh: ",TRCONST)
acoth z ==
@@ -427,7 +427,7 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
error concat("acoth: ",TRCONST)
TRANSFCN =>
frst z = 1 or frst z = -1 => error concat("acoth: ",LOGS)
- (inv(2::RN)::Coef) * log((z + (1 :: ST))/(z - (1 :: ST)))
+ (inv(2::RN)::Coef) * log((z + (1@Coef :: ST))/(z - (1@Coef :: ST)))
error concat("acoth: ",TRCONST)
asech z ==
@@ -435,27 +435,27 @@ StreamTranscendentalFunctions(Coef): Exports == Implementation where
TRANSFCN =>
(coef := frst z) = 0 => error concat("asech: ",NPOWLOG)
coef = 1 or coef = -1 =>
- x := (1 :: ST) - z*z
+ x := (1@Coef :: ST) - z*z
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("asech: ",MAYFPOW)
(order := ord :: I) = -1 => return asech(coef) :: ST
odd? order => error concat("asech: ",FPOWERS)
- log(((1 :: ST) + powern(1/2,x))/z)
- log(((1 :: ST) + powern(1/2,(1 :: ST) - z*z))/z)
+ log(((1@Coef :: ST) + powern(1/2,x))/z)
+ log(((1@Coef :: ST) + powern(1/2,(1@Coef :: ST) - z*z))/z)
error concat("asech: ",TRCONST)
acsch z ==
empty? z => error "acsch: acsch(0) is undefined"
TRANSFCN =>
frst z = 0 => error concat("acsch: ",NPOWLOG)
- x := z*z + (1 :: ST)
+ x := z*z + (1@Coef :: ST)
-- compute order of 'x'
(ord := orderOrFailed x) case "failed" =>
error concat("acsc: ",MAYFPOW)
(order := ord :: I) = -1 => return acsch(frst z) :: ST
odd? order => error concat("acsch: ",FPOWERS)
- log(((1 :: ST) + powern(1/2,x))/z)
+ log(((1@Coef :: ST) + powern(1/2,x))/z)
error concat("acsch: ",TRCONST)
@
@@ -563,7 +563,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
--% Exponentials and Logarithms
exp z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(frst z) = 0 =>
expx := exp(monom(1,1))$STTF
compose(expx,z)
@@ -581,21 +581,21 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
--% Trigonometric Functions
sin z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
sinx := sin(monom(1,1))$STTF
compose(sinx,z)
error concat("sin: ",ZERO)
cos z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(frst z) = 0 =>
cosx := cos(monom(1,1))$STTF
compose(cosx,z)
error concat("cos: ",ZERO)
tan z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
tanx := tan(monom(1,1))$STTF
compose(tanx,z)
@@ -607,7 +607,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
error concat("cot: ",ZERO)
sec z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(frst z) = 0 =>
secx := sec(monom(1,1))$STTF
compose(secx,z)
@@ -619,14 +619,14 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
error concat("csc: ",ZERO)
asin z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
asinx := asin(monom(1,1))$STTF
compose(asinx,z)
error concat("asin: ",ZERO)
atan z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
atanx := atan(monom(1,1))$STTF
compose(atanx,z)
@@ -640,21 +640,21 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
--% Hyperbolic Trigonometric Functions
sinh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
sinhx := sinh(monom(1,1))$STTF
compose(sinhx,z)
error concat("sinh: ",ZERO)
cosh z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(frst z) = 0 =>
coshx := cosh(monom(1,1))$STTF
compose(coshx,z)
error concat("cosh: ",ZERO)
tanh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
tanhx := tanh(monom(1,1))$STTF
compose(tanhx,z)
@@ -666,7 +666,7 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
error concat("coth: ",ZERO)
sech z ==
- empty? z => 1 :: ST
+ empty? z => 1@Coef :: ST
(frst z) = 0 =>
sechx := sech(monom(1,1))$STTF
compose(sechx,z)
@@ -678,14 +678,14 @@ StreamTranscendentalFunctionsNonCommutative(Coef): _
error concat("csch: ",ZERO)
asinh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
asinhx := asinh(monom(1,1))$STTF
compose(asinhx,z)
error concat("asinh: ",ZERO)
atanh z ==
- empty? z => 0 :: ST
+ empty? z => 0@Coef :: ST
(frst z) = 0 =>
atanhx := atanh(monom(1,1))$STTF
compose(atanhx,z)
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-23 19:59:30 +0000