* src/algebra/: Systematically use not zero? when comparing for

	 equality with 0.

31 files changed, 59 insertions, 59 deletions

diff --git a/src/algebra/allfact.spad.pamphlet b/src/algebra/allfact.spad.pamphlet
index c45d662c..7d412271 100644
--- a/src/algebra/allfact.spad.pamphlet
+++ b/src/algebra/allfact.spad.pamphlet
@@ -171,7 +171,7 @@ MPolyCatRationalFunctionFactorizer(E,OV,R,PRF) : C == T
        ground? g => g
        rf:PRF:=0$PRF
        ug:=univariate(g,x)
-       while ug~=0 repeat
+       while not zero? ug repeat
          rf:=rf+pushdterm(ug,x)
          ug := reductum ug
        rf
diff --git a/src/algebra/clifford.spad.pamphlet b/src/algebra/clifford.spad.pamphlet
index 262afa86..8e85a25d 100644
--- a/src/algebra/clifford.spad.pamphlet
+++ b/src/algebra/clifford.spad.pamphlet
@@ -389,7 +389,7 @@ CliffordAlgebra(n, K, Q): T == Impl where
             c = 1 => be
             c::Ex * be
         coerce(x): Ex ==
-            tl := [coerceMonom(x.i,i) for i in 0..dim-1 | x.i~=0]
+            tl := [coerceMonom(x.i,i) for i in 0..dim-1 | not zero? x.i]
             null tl => "0"::Ex
             reduce("+", tl)
 
diff --git a/src/algebra/eigen.spad.pamphlet b/src/algebra/eigen.spad.pamphlet
index 9cab7430..db92f178 100644
--- a/src/algebra/eigen.spad.pamphlet
+++ b/src/algebra/eigen.spad.pamphlet
@@ -137,7 +137,7 @@ EigenPackage(R) : C == T
      tff(p:SUF,x:SE) : F ==
        degree p=0 => leadingCoefficient p
        r:F:=0$F
-       while p~=0 repeat
+       while not zero? p repeat
          r:=r+fft(p,x)
          p := reductum p
        r
diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet
index 007f1efd..95b5c316 100644
--- a/src/algebra/ffnb.spad.pamphlet
+++ b/src/algebra/ffnb.spad.pamphlet
@@ -236,7 +236,7 @@ InnerNormalBasisFieldFunctions(GF): Exports == Implementation where
                     else erg:VGF:=plist.(first(l))
       i:SI:=k
       for j in rest(l) repeat
-        if j~=0 then erg:=erg *$$ qPot(plist.j,i)$$
+        if not zero? j then erg:=erg *$$ qPot(plist.j,i)$$
         i:=i+k
       erg
 
diff --git a/src/algebra/fspace.spad.pamphlet b/src/algebra/fspace.spad.pamphlet
index 30c6fccd..684448f0 100644
--- a/src/algebra/fspace.spad.pamphlet
+++ b/src/algebra/fspace.spad.pamphlet
@@ -691,14 +691,14 @@ FunctionSpace(R: SetCategory): Category == Definition where
         u   := third l
         arg := argument k
         ans:% := 0
-        if (not member?(u,done)) and (ans := differentiate(u,x))~=0 then
+        if (not member?(u,done)) and not zero?(ans := differentiate(u,x)) then
           ans := ans * kernel(opdiff,
                [subst(expr, [kd], [kernel(opdiff, [first l, gg, gg])]),
                              gg, u])
         done := concat(gg, done)
         is?(k, opdiff) => ans + diffdiff0(arg, x, expr, k, done)
         for i in minIndex arg .. maxIndex arg for b in arg repeat
-          if (not member?(b,done)) and (bp:=differentiate(b,x))~=0 then
+          if (not member?(b,done)) and not zero?(bp:=differentiate(b,x)) then
             g   := symsub(gendiff, i)::%
             ans := ans + bp * kernel(opdiff, [subst(expr, [kd],
              [kernel(opdiff, [substArg(op, arg, i, g), gg, u])]), g, b])
diff --git a/src/algebra/gaussfac.spad.pamphlet b/src/algebra/gaussfac.spad.pamphlet
index bb4cb963..79d32551 100644
--- a/src/algebra/gaussfac.spad.pamphlet
+++ b/src/algebra/gaussfac.spad.pamphlet
@@ -180,7 +180,7 @@ GaussianFactorizationPackage() : C == T
         prime?(n)$IntegerPrimesPackage(Z)  => true
         re : Z := real a
         im : Z := imag a
-        re~=0 and im~=0 => false
+        not zero? re and not zero? im => false
         p : Z := abs(re+im)     -- a is of the form p, -p, %i*p or -%i*p
         p rem 4 ~= 3 => false
         -- return-value true, if p is a rational prime,
diff --git a/src/algebra/gaussian.spad.pamphlet b/src/algebra/gaussian.spad.pamphlet
index d8ac1583..44e9b918 100644
--- a/src/algebra/gaussian.spad.pamphlet
+++ b/src/algebra/gaussian.spad.pamphlet
@@ -327,12 +327,12 @@ ComplexCategory(R:CommutativeRing): Category ==
             xx := x * y1
             x1 := real(xx) rem r
             a  := x1
-            if x1~=0 and sizeLess?(r, 2 * x1) then
+            if not zero? x1 and sizeLess?(r, 2 * x1) then
               a := x1 - r
               if sizeLess?(x1, a) then a := x1 + r
             x2 := imag(xx) rem r
             b  := x2
-            if x2~=0 and sizeLess?(r, 2 * x2) then
+            if not zero? x2 and sizeLess?(r, 2 * x2) then
               b := x2 - r
               if sizeLess?(x2, b) then b := x2 + r
             y1 := (complex(a, b) exquo y1)::%
diff --git a/src/algebra/gdpoly.spad.pamphlet b/src/algebra/gdpoly.spad.pamphlet
index 2a212926..e477aa04 100644
--- a/src/algebra/gdpoly.spad.pamphlet
+++ b/src/algebra/gdpoly.spad.pamphlet
@@ -148,7 +148,7 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where
             p := reductum p
             for i in 1..n repeat
               maxdeg.i := max(maxdeg.i, tdeg.i)
-         [index(i:PositiveInteger) for i in 1..n | maxdeg.i~=0]
+         [index(i:PositiveInteger) for i in 1..n | not zero? maxdeg.i]
 
       reorder(p: %,perm: List Integer):% ==
          #perm ~= n => error "must be a complete permutation of all vars"
diff --git a/src/algebra/geneez.spad.pamphlet b/src/algebra/geneez.spad.pamphlet
index 3c449fe1..c3647b6c 100644
--- a/src/algebra/geneez.spad.pamphlet
+++ b/src/algebra/geneez.spad.pamphlet
@@ -96,7 +96,7 @@ GenExEuclid(R,BP) : C == T
     exactquo(u:BP,v:BP,p:R):Union(BP,"failed") ==
         invlcv:=modInverse(leadingCoefficient v,p)
         r:=monicDivide(u,reduction(invlcv*v,p))
-        reduction(r.remainder,p) ~=0 => "failed"
+        not zero? reduction(r.remainder,p) => "failed"
         reduction(invlcv*r.quotient,p)
 
     FP:=EuclideanModularRing(R,BP,R,reduction,merge,exactquo)
@@ -120,7 +120,7 @@ GenExEuclid(R,BP) : C == T
       ftab:Vector L FP :=
         map(reduceList(#1,lmod),table)$VectorFunctions2(List BP,List FP)
       sln:L FP:=[0$FP for xx in ftab.1 ]
-      for i in 0 .. d |(cc:=coefficient(err,i)) ~=0 repeat
+      for i in 0 .. d |not zero?(cc:=coefficient(err,i)) repeat
         sln:=[slp+reduce(cc::BP,lmod)*pp
               for pp in ftab.(i+1) for slp in sln]
       nsol:=[f-lmodk*reduction(g::BP,lmod) for f in oldsol for g in sln]
@@ -165,7 +165,7 @@ GenExEuclid(R,BP) : C == T
             -- Actually, there's no possibility of failure
         d:=degree m
         sln:L BP:=[0$BP for xx in table.1]
-        for i in 0 .. d | coefficient(m,i)~=0 repeat
+        for i in 0 .. d | not zero? coefficient(m,i) repeat
           sln:=[slp+coefficient(m,i)*pp
                 for pp in table.(i+1) for slp in sln]
         sln
@@ -192,7 +192,7 @@ GenExEuclid(R,BP) : C == T
           map(reduceList(#1,pmod),table)$VectorFunctions2(List BP,List FP)
         lpolys:L BP:=table.(#table)
         sln:L FP:=[0$FP for xx in ftab.1]
-        for i in 0 .. d | coefficient(m,i)~=0 repeat
+        for i in 0 .. d | not zero? coefficient(m,i) repeat
           sln:=[slp+reduce(coefficient(m,i)::BP,pmod)*pp
                 for pp in ftab.(i+1) for slp in sln]
         soln:=[slp::BP for slp in sln]
diff --git a/src/algebra/ghensel.spad.pamphlet b/src/algebra/ghensel.spad.pamphlet
index baf7e85c..64ff2a89 100644
--- a/src/algebra/ghensel.spad.pamphlet
+++ b/src/algebra/ghensel.spad.pamphlet
@@ -63,7 +63,7 @@ GeneralHenselPackage(RP,TP):C == T where
      exactquo(u:TP,v:TP,p:RP):Union(TP,"failed") ==
         invlcv:=modInverse(leadingCoefficient v,p)
         r:=monicDivide(u,reduction(invlcv*v,p))
-        reduction(r.remainder,p) ~=0 => "failed"
+        not zero? reduction(r.remainder,p) => "failed"
         reduction(invlcv*r.quotient,p)
 
      FP:=EuclideanModularRing(RP,TP,RP,reduction,merge,exactquo)
@@ -112,7 +112,7 @@ GeneralHenselPackage(RP,TP):C == T where
            fln = nfln and zero?(err:=poly-*/fln) => leave "finished"
            fln := nfln
            Modulus := prime*Modulus
-        if constp~=0 then fln:=cons(constp,fln)
+        if not zero? constp then fln:=cons(constp,fln)
         [fln,Modulus]
 
      completeHensel(m:TP,tl1:List TP,prime:RP,bound:PI) ==
diff --git a/src/algebra/groebsol.spad.pamphlet b/src/algebra/groebsol.spad.pamphlet
index 2fb8161e..95af1daf 100644
--- a/src/algebra/groebsol.spad.pamphlet
+++ b/src/algebra/groebsol.spad.pamphlet
@@ -97,7 +97,7 @@ GroebnerSolve(lv,F,R) : C == T
            then return "failed"
            newlpol :=concat(redPol(g::DPoly,newlpol),newlpol)
            rlvar:=rest rlvar
-         else if redPol(f,newlpol)~=0 then return"failed"
+         else if not zero? redPol(f,newlpol) then return"failed"
        newlpol
 
 
diff --git a/src/algebra/ideal.spad.pamphlet b/src/algebra/ideal.spad.pamphlet
index 311be81b..936b9d0c 100644
--- a/src/algebra/ideal.spad.pamphlet
+++ b/src/algebra/ideal.spad.pamphlet
@@ -174,7 +174,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T
        q=0$newPoly => 0$DPoly
        dq:newExpon:=degree q
        n:NNI:=selectfirst (dq)
-       n~=0 => "failed"
+       not zero? n => "failed"
        ((g:=oldpoly reductum q) case "failed") => "failed"
        monomial(leadingCoefficient q,selectsecond dq)$DPoly + (g::DPoly)
 
@@ -379,7 +379,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T
 	   vec2.i:=1
 	   g:nPoly:=0$nPoly
 	   pol:=0$P
-	   while f~=0 repeat
+	   while not zero? f repeat
 	     df:=degree(f-reductum f,lvint)
 	     lcf:=leadingCoefficient f
 	     pol:=pol+monompol(df,lcf,lvint)
@@ -400,7 +400,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T
 	 solsn:List P:=[]
 	 for q in lf repeat
 	   g:Polynomial F :=0
-	   while q~=0 repeat
+	   while not zero? q repeat
 	     dq:=degree q
 	     lcq:=leadingCoefficient q
 	     q:=reductum q
@@ -417,7 +417,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T
        empty? Idl => [0$DPoly] :: OutputForm
        Idl :: OutputForm
 
-     ideal(Id:List DPoly) :Ideal  ==  [[f for f in Id|f~=0],false]
+     ideal(Id:List DPoly) :Ideal  ==  [[f for f in Id|not zero? f],false]
 
      groebnerIdeal(Id:List DPoly) : Ideal == [Id,true]
 
diff --git a/src/algebra/idecomp.spad.pamphlet b/src/algebra/idecomp.spad.pamphlet
index 8dd14b10..d5c5d4e4 100644
--- a/src/algebra/idecomp.spad.pamphlet
+++ b/src/algebra/idecomp.spad.pamphlet
@@ -153,7 +153,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't
          lf:=Id.first
        ris:= generators(zeroRadComp(groebnerIdeal(Id.rest),truelist.rest))
        ris:=cons(lf,ris)
-       if pv~=0 then
+       if not zero? pv then
 	 ris:=[(univariate(h,x)).pw for h in ris]
        groebnerIdeal(groebner ris)
 
@@ -246,7 +246,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't
      pushdown(g:DPoly,x:OV) : DPoly ==
        rf:DPoly:=0$DPoly
        i:=position(x,lvint)
-       while g~=0 repeat
+       while not zero? g repeat
 	 g1:=reductum g
          rf:=rf+pushdterm(g-g1,x,i)
          g := g1
@@ -266,11 +266,11 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't
        rf:DPoly:=0$DPoly
        g := f
        xp := convert(x)@SE
-       while g~=0 repeat
+       while not zero? g repeat
          h:=lcm(trueden(denom leadingCoefficient g,xp),h)
          g:=reductum g
        f:=(h::F)*f
-       while f~=0 repeat
+       while not zero? f repeat
 	 g:=reductum f
          rf:=rf+pushuterm(f-g,xp,x)
          f:=g
diff --git a/src/algebra/leadcdet.spad.pamphlet b/src/algebra/leadcdet.spad.pamphlet
index 0c312914..7b7fb5a5 100644
--- a/src/algebra/leadcdet.spad.pamphlet
+++ b/src/algebra/leadcdet.spad.pamphlet
@@ -109,7 +109,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T
         for k in 1..(# lpol) repeat
           lexp.k=0 => "next factor"
           h:= checkpow(vl.k,c)
-          if h ~=0 then
+          if not zero? h then
            if h>lexp.k then return "failed"
            lexp.k:=lexp.k-h
            aux.i := aux.i*(lpol.k ** h)
diff --git a/src/algebra/lingrob.spad.pamphlet b/src/algebra/lingrob.spad.pamphlet
index 41956dea..95284786 100644
--- a/src/algebra/lingrob.spad.pamphlet
+++ b/src/algebra/lingrob.spad.pamphlet
@@ -215,7 +215,7 @@ LinGroebnerPackage(lv,F) : C == T
       part:List HDPoly :=[]
       for f in lr repeat
         g:=x::HDPoly * f
-        if redPo(g,mB).poly~=0 then part:=concat(g,part)
+        if not zero?(redPo(g,mB).poly) then part:=concat(g,part)
       concat(part,intcompBasis(x,part,mB))
 
 ----- coordinate of f with respect to the basis B -----
@@ -223,7 +223,7 @@ LinGroebnerPackage(lv,F) : C == T
     coord(f:HDPoly,B:List HDPoly) : VF ==
       ndim := #B
       vv:VF:=new(ndim,0$F)$VF
-      while f~=0 repeat
+      while not zero? f repeat
         rf := reductum f
         lf := f-rf
         lcf := leadingCoefficient f
diff --git a/src/algebra/listgcd.spad.pamphlet b/src/algebra/listgcd.spad.pamphlet
index fac17b6d..856e006b 100644
--- a/src/algebra/listgcd.spad.pamphlet
+++ b/src/algebra/listgcd.spad.pamphlet
@@ -78,7 +78,7 @@ HeuGcd (BP):C == T
     --compute the height of a polynomial
     height(f:BP):PI ==
       k:PI:=1
-      while f~=0 repeat
+      while not zero? f repeat
            k:=max(k,abs(leadingCoefficient(f)@Z)::PI)
            f:=reductum f
       k
@@ -88,7 +88,7 @@ HeuGcd (BP):C == T
     genpoly(dval:Z,value:PI):BP ==
       d:=0$BP
       val:=dval
-      for i in 0..  while (val~=0) repeat
+      for i in 0..  while not zero? val repeat
         val1:=negShiftz(val rem value,value)
         d:= d+monomial(val1,i)
         val:=(val-val1) quo value
diff --git a/src/algebra/mfinfact.spad.pamphlet b/src/algebra/mfinfact.spad.pamphlet
index 73483b86..bca79804 100644
--- a/src/algebra/mfinfact.spad.pamphlet
+++ b/src/algebra/mfinfact.spad.pamphlet
@@ -301,7 +301,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T
     pushup(f:P,x:OV) :PG ==
        ground? f => pushupconst((retract f)@R,x)
        rr:PG:=0
-       while f~=0 repeat
+       while not zero? f repeat
          lf:=leadingMonomial f
          cf:=pushupconst(leadingCoefficient f,x)
          lvf:=variables lf
@@ -314,7 +314,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T
        ground? g => ((retract g)@F)::R::P
        rf:P:=0$P
        ug:=univariate(g,x)
-       while ug~=0 repeat
+       while not zero? ug repeat
          cf:=monomial(1,degree ug)$R
          rf:=rf+cf*pushdcoef(leadingCoefficient ug)
          ug := reductum ug
@@ -324,7 +324,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T
     pushupconst(r:R,x:OV):PG ==
        ground? r => (retract r)@F ::PG
        rr:PG:=0
-       while r~=0 repeat
+       while not zero? r repeat
          rr:=rr+monomial((leadingCoefficient r)::PG,x,degree r)$PG
          r:=reductum r
        rr
@@ -385,14 +385,14 @@ MultFiniteFactorize(OV,E,F,PG) : C == T
        leadcomp1:=[retract eval(pol,lvar,lval) for pol in plist]
        testp and or/[unit? epl for epl in leadcomp1] => range:=range+1
        newm:SUP R:=completeEval(um,lvar,lval)
-       degum ~= degree newm or minimumDegree newm ~=0 => range:=range+1
+       degum ~= degree newm or not zero? minimumDegree newm => range:=range+1
        lffc1:=content newm
        newm:=(newm exquo lffc1)::SUP R
        testp and leadtest and not polCase(lffc1*clc,#plist,leadcomp1)
                            => range:=range+1
        Dnewm := differentiate newm
        D2newm := map(differentiate, newm)
-       degree(gcd [newm,Dnewm,D2newm])~=0 => range:=range+1
+       not zero? degree(gcd [newm,Dnewm,D2newm]) => range:=range+1
       -- if R has Integer then luniv:=henselFact(newm,false)$
       -- else
        lcnm:F:=1
diff --git a/src/algebra/moddfact.spad.pamphlet b/src/algebra/moddfact.spad.pamphlet
index 5cb2893d..9cf3d902 100644
--- a/src/algebra/moddfact.spad.pamphlet
+++ b/src/algebra/moddfact.spad.pamphlet
@@ -79,7 +79,7 @@ ModularDistinctDegreeFactorizer(U):C == T where
     exactquo(u:U,v:U,p:I):Union(U,"failed") ==
         invlcv:=modInverse(leadingCoefficient v,p)
         r:=monicDivide(u,reduction(invlcv*v,p))
-        reduction(r.remainder,p) ~=0 => "failed"
+        not zero? reduction(r.remainder,p) => "failed"
         reduction(invlcv*r.quotient,p)
     EMR := EuclideanModularRing(Integer,U,Integer,
                                 reduction,merge,exactquo)
diff --git a/src/algebra/modgcd.spad.pamphlet b/src/algebra/modgcd.spad.pamphlet
index b094a863..afe60ab5 100644
--- a/src/algebra/modgcd.spad.pamphlet
+++ b/src/algebra/modgcd.spad.pamphlet
@@ -205,7 +205,7 @@ InnerModularGcd(R,BP,pMod,nextMod):C == T
     exactquo(u:BP,v:BP,p:R):Union(BP,"failed") ==
         invlcv:=modInverse(leadingCoefficient v,p)
         r:=monicDivide(u,reduction(invlcv*v,p))
-        reduction(r.remainder,p) ~=0 => "failed"
+        not zero? reduction(r.remainder,p) => "failed"
         reduction(invlcv*r.quotient,p)
 
 
diff --git a/src/algebra/modmon.spad.pamphlet b/src/algebra/modmon.spad.pamphlet
index cb60793e..94872e38 100644
--- a/src/algebra/modmon.spad.pamphlet
+++ b/src/algebra/modmon.spad.pamphlet
@@ -139,7 +139,7 @@ ModMonic(R,Rep): C == T
 
           frobenius(a:%):% ==
             aq:% := 0
-            while a~=0 repeat
+            while not zero? a repeat
               aq:= aq + leadingCoefficient(a)*frobeniusPower(degree a)
               a := reductum a
             aq
diff --git a/src/algebra/multfact.spad.pamphlet b/src/algebra/multfact.spad.pamphlet
index de704ea2..86293e50 100644
--- a/src/algebra/multfact.spad.pamphlet
+++ b/src/algebra/multfact.spad.pamphlet
@@ -182,7 +182,7 @@ InnerMultFact(OV,E,R,P) : C == T
         "max"/[numberOfMonomials ff for ff in lum]
 
       "max"/[+/[euclideanSize cc for i in 0..degree ff|
-                (cc:= coefficient(ff,i))~=0] for ff in lum]
+                not zero? (cc:= coefficient(ff,i))] for ff in lum]
 
           ---  Choose the integer to reduce to univariate case  ---
     intChoose(um:USP,lvar:L OV,clc:R,plist:L P,ltry:L L R,
@@ -220,12 +220,12 @@ InnerMultFact(OV,E,R,P) : C == T
        leadcomp1:=[retract eval(pol,lvar,lval) for pol in plist]
        testp and or/[unit? epl for epl in leadcomp1] => range:=2*range
        newm:BP:=completeEval(um,lvar,lval)
-       degum ~= degree newm or minimumDegree newm ~=0 => range:=2*range
+       degum ~= degree newm or not zero? minimumDegree newm => range:=2*range
        lffc1:=content newm
        newm:=(newm exquo lffc1)::BP
        testp and leadtest and not polCase(lffc1*clc,#plist,leadcomp1)
                              => range:=2*range
-       degree(gcd [newm,differentiate(newm)])~=0 => range:=2*range
+       not zero? degree(gcd [newm,differentiate(newm)]) => range:=2*range
        luniv:=ufactor(newm)
        lunivf:= factors luniv
        lffc1:R:=retract(unit luniv)@R * lffc1
diff --git a/src/algebra/multsqfr.spad.pamphlet b/src/algebra/multsqfr.spad.pamphlet
index 6c54e72c..f1cd64f4 100644
--- a/src/algebra/multsqfr.spad.pamphlet
+++ b/src/algebra/multsqfr.spad.pamphlet
@@ -206,7 +206,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where
        makeFR(unit result,append(result1,factorList result))
  
      ldeg:=degree(f,lvar)          ---  general case ---
-     m:="min"/[j for j in ldeg|j~=0]
+     m:="min"/[j for j in ldeg| not zero? j]
      i:Z:=1
      for j in ldeg while j>m repeat i:=i+1
      x:=lvar.i
diff --git a/src/algebra/npcoef.spad.pamphlet b/src/algebra/npcoef.spad.pamphlet
index 47710d88..a1ada373 100644
--- a/src/algebra/npcoef.spad.pamphlet
+++ b/src/algebra/npcoef.spad.pamphlet
@@ -104,7 +104,7 @@ NPCoef(BP,E,OV,R,P) : C == T where
     #termlist=1 =>
       vterm:=termlist.first
       for elterm in vterm while doit<2 repeat
-        (cu1:=elterm.pcoef)~=0 => cfu:=cu1*cfu
+        not zero?(cu1:=elterm.pcoef) => cfu:=cu1*cfu
         doit:=doit+1
         poselt:=position(elterm,vterm):NNI
       doit=2  or (pp:=tterm.coefu exquo cfu) case "failed" => "failed"
@@ -148,7 +148,7 @@ NPCoef(BP,E,OV,R,P) : C == T where
       for celt in ctdet repeat
         if celt.cfpos.expt=cfexp then
           celt.cfpos.pcoef:=cfcoef
-          if (and/[cc.pcoef ~=0 for cc in celt]) then
+          if (and/[not zero? cc.pcoef for cc in celt]) then
             k:=position(celt,ctdet):NNI
             lterase:=cons(k,lterase)
             cterm.coefu:=(cterm.coefu - */[cc.pcoef for cc in celt])
diff --git a/src/algebra/numsolve.spad.pamphlet b/src/algebra/numsolve.spad.pamphlet
index 04935b6b..1c7a516c 100644
--- a/src/algebra/numsolve.spad.pamphlet
+++ b/src/algebra/numsolve.spad.pamphlet
@@ -169,7 +169,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where
            if lq~=[] then
              gb:=GroebnerInternalPackage(K,DirectProduct(#lv,NNI),OV,dmp)
              partRes:=[pr for pr in partRes|
-                       and/[(redPol(fq,pr pretend List(dmp))$gb) ~=0
+                       and/[not zero?(redPol(fq,pr pretend List(dmp))$gb)
                          for fq in lq]]
 
            -- select the components in "generic" form
diff --git a/src/algebra/pgcd.spad.pamphlet b/src/algebra/pgcd.spad.pamphlet
index 2caf53de..eb38b2c1 100644
--- a/src/algebra/pgcd.spad.pamphlet
+++ b/src/algebra/pgcd.spad.pamphlet
@@ -183,7 +183,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where
         (gd1,gd2):=(l,l)
         ul:=completeEval(l,lvar1,lval)
         dl:=degree ul
-        if degree gcd(ul,differentiate ul) ~=0 then
+        if not zero? degree gcd(ul,differentiate ul) then
           newchoice:=good(l,lvar1,ltry)
           ul:=newchoice.upol
           ltry:=newchoice.inval
@@ -195,7 +195,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where
           d:SUP:=gcd(cons(ul,ulist))
           if degree d =0 then return gd1
           lquo:=(ul exquo d)::SUP
-          if degree lquo ~=0 then
+          if not zero? degree lquo then
             lgcd:=gcd(cons(leadingCoefficient l,lcpol))
             (gdl:=lift(l,d,lquo,lgcd,lvar1,ldeg,lval)) case "failed" =>
                return notCoprime(g,p2,ldeg,lvar1,ltry)
diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet
index 71a7d8df..b86755a0 100644
--- a/src/algebra/poly.spad.pamphlet
+++ b/src/algebra/poly.spad.pamphlet
@@ -902,7 +902,7 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T
              makeFR(u,[["sqfr",c,1]])
            i:NonNegativeInteger:=0; lffe:List FF:=[]
            lcp := leadingCoefficient p
-           while degree(ci)~=0 repeat
+           while not zero? degree(ci) repeat
               ci:=(ci exquo pi)::P
               di:=(di exquo pi)::P - differentiate(ci)
               pi:=gcd(ci,di)
@@ -924,7 +924,7 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T
            di := (p exquo ci)::P
            i:NonNegativeInteger:=0; lffe:List FF:=[]
            dunit : P := 1
-           while degree(di)~=0 repeat
+           while not zero? degree(di) repeat
               diprev := di
               di := gcd(ci,di)
               ci:=(ci exquo di)::P
@@ -1054,7 +1054,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where
     squareFree(p:P) ==
        mv:=mainVariable p
        mv case "failed" => makeFR(p,[])$Factored(P)
-       characteristic$RC ~=0 => finSqFr(p,variables p)
+       not zero?(characteristic$RC) => finSqFr(p,variables p)
        up:=univariate(p,mv)
        cont := content up
        up := (up exquo cont)::SUP
diff --git a/src/algebra/qalgset.spad.pamphlet b/src/algebra/qalgset.spad.pamphlet
index f93f1ef0..4679a5c5 100644
--- a/src/algebra/qalgset.spad.pamphlet
+++ b/src/algebra/qalgset.spad.pamphlet
@@ -151,7 +151,7 @@ QuasiAlgebraicSet(R, Var,Expon,Dpoly) : C == T
        q=0$newPoly => 0$Dpoly
        dq:newExpon:=degree q
        n:NNI:=selectfirst (dq)
-       n~=0 => "failed"
+       not zero? n => "failed"
        ((g:=oldpoly reductum q) case "failed") => "failed"
        monomial(leadingCoefficient q,selectsecond dq)$Dpoly + (g::Dpoly)
  
diff --git a/src/algebra/smith.spad.pamphlet b/src/algebra/smith.spad.pamphlet
index 97fc3b76..34b8f55b 100644
--- a/src/algebra/smith.spad.pamphlet
+++ b/src/algebra/smith.spad.pamphlet
@@ -157,7 +157,7 @@ SmithNormalForm(R,Row,Col,M) : Exports == Implementation where
     lastStep(sf : SmithForm) : SmithForm ==
       m:=sf.Smith
       m1:=min(nrows m,ncols m)
-      for i in 1..m1 while (mii:=m(i,i)) ~=0 repeat
+      for i in 1..m1 while not zero?(mii:=m(i,i)) repeat
         for j in i+1..m1 repeat
           if (m(j,j) exquo mii) case "failed" then return
              lastStep(ijDivide(sf,i,j))
diff --git a/src/algebra/syssolp.spad.pamphlet b/src/algebra/syssolp.spad.pamphlet
index 8fd97610..3fb9ba0a 100644
--- a/src/algebra/syssolp.spad.pamphlet
+++ b/src/algebra/syssolp.spad.pamphlet
@@ -153,7 +153,7 @@ SystemSolvePackage(R): Cat == Cap where
            if lq~=[] then
              gb:=GroebnerInternalPackage(P R,DirectProduct(#lv,NNI),OV,dmp)
              parRes:=[pr for pr in parRes|
-                       and/[(redPol(fq,pr pretend List(dmp))$gb) ~=0
+                       and/[not zero?(redPol(fq,pr pretend List(dmp))$gb)
                          for fq in lq]]
            [[retract pushdown(pf,lvv)$push for pf in pr] for pr in parRes]
 
diff --git a/src/algebra/twofact.spad.pamphlet b/src/algebra/twofact.spad.pamphlet
index fb560b20..fd51789d 100644
--- a/src/algebra/twofact.spad.pamphlet
+++ b/src/algebra/twofact.spad.pamphlet
@@ -43,7 +43,7 @@ NormRetractPackage(F, ExtF, SUEx, ExtP, n):C  == T where
 
       Frobenius(ff:ExtP):ExtP ==
          fft:ExtP:=0
-         while ff~=0 repeat
+         while not zero? ff repeat
            fft:=fft + monomial(map(Frobenius, leadingCoefficient ff),
                                degree ff)
            ff:=reductum ff
@@ -230,7 +230,7 @@ TwoFactorize(F) : C == T
           i:=i+1
           zero? elt(lcm, vval) => "next value"
           umv := map(elt(#1,vval), m)$UPCF2(R, P, F, R)
-          degree(gcd(umv,differentiate umv))~=0 => "next val"
+          not zero? degree(gcd(umv,differentiate umv)) => "next val"
           n := 1
           look := false
        extField:=FiniteFieldExtension(F,n)
@@ -238,7 +238,7 @@ TwoFactorize(F) : C == T
        TP:=SparseUnivariatePolynomial SUEx
        mm:TP:=0
        m1:=m
-       while m1~=0 repeat
+       while not zero? m1 repeat
          mm:=mm+monomial(map(coerce,leadingCoefficient m1)$UPCF2(F,R,
                 extField,SUEx),degree m1)
          m1:=reductum m1
@@ -253,7 +253,7 @@ TwoFactorize(F) : C == T
          i:=i+1
          elt(lcmm,val)=0 => "next value"
          umex := map(elt(#1,val), mm)$UPCF2(SUEx, TP, extField, SUEx)
-         degree(gcd(umex,differentiate umex))~=0 => "next val"
+         not zero? degree(gcd(umex,differentiate umex)) => "next val"
          look:=false
        prime:SUEx:=monomial(1,1)-monomial(val,0)
        fumex:=factor(umex)$DistinctDegreeFactorize(extField,SUEx)
diff --git a/src/algebra/unifact.spad.pamphlet b/src/algebra/unifact.spad.pamphlet
index f3437a81..119ee5d4 100644
--- a/src/algebra/unifact.spad.pamphlet
+++ b/src/algebra/unifact.spad.pamphlet
@@ -173,7 +173,7 @@ UnivariateFactorize(ZP) : public == private where
          q:=nextPrime(q)$IntegerPrimesPackage(Z) pretend PI
          (rr:=lcm rem q) = 0$Z => "next prime"
          disc:=gcd(m,differentiate m,q)
-         (degree disc)~=0 => "next prime"
+         not zero?(degree disc) => "next prime"
          k := k+1
          newdd := ddFact(m,q)
          ((n := numFactors(newdd)) < 9) =>
@@ -215,7 +215,7 @@ UnivariateFactorize(ZP) : public == private where
        d,d2: Z
        d := coefficient(m,1)**2-4*coefficient(m,0)*coefficient(m,2)
        d2 := sqroot(d)
-       (d-d2**2)~=0 => [m]
+       not zero?(d-d2**2) => [m]
        alpha: Z := coefficient(m,1)+d2
        beta: Z := 2*coefficient(m,2)
        d := gcd(alpha,beta)