* 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.

1 files changed, 49 insertions, 49 deletions

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)