aboutsummaryrefslogtreecommitdiff
path: root/src/algebra/numsolve.spad.pamphlet
diff options
context:
space:
mode:
authordos-reis <gdr@axiomatics.org>2008-04-03 04:23:42 +0000
committerdos-reis <gdr@axiomatics.org>2008-04-03 04:23:42 +0000
commit001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532 (patch)
treeda9e2fe5d81ff4cd7709d12e44b8c3e348b8a8e3 /src/algebra/numsolve.spad.pamphlet
parenta7bab9a6c2070d05e2dbd256ce455079c8ced385 (diff)
downloadopen-axiom-001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532.tar.gz
Replace `^=' with `~='.
Diffstat (limited to 'src/algebra/numsolve.spad.pamphlet')
-rw-r--r--src/algebra/numsolve.spad.pamphlet30
1 files changed, 15 insertions, 15 deletions
diff --git a/src/algebra/numsolve.spad.pamphlet b/src/algebra/numsolve.spad.pamphlet
index b640b925..edb7898c 100644
--- a/src/algebra/numsolve.spad.pamphlet
+++ b/src/algebra/numsolve.spad.pamphlet
@@ -148,7 +148,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where
p0 := primitivePart multivariate(vec.0, mainvar)
p1 := primitivePart(multivariate(vec.1, mainvar),mainvar)
zero? p1 or
- gcd(p0, leadingCoefficient(univariate(p1,mainvar))) ^=1 =>
+ gcd(p0, leadingCoefficient(univariate(p1,mainvar))) ~=1 =>
innerSolve(cons(0,lp),empty(),lv,eps)
findGenZeros([p1, p0], reverse lv, eps)
@@ -161,15 +161,15 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where
DP:=DirectProduct(#lv,NonNegativeInteger)
dmp:=DistributedMultivariatePolynomial(lv,K)
lq:L dmp:=[]
- if ld^=[] then
+ if ld~=[] then
lq:= [(pToDmp(q1)$PolToPol(lv,K)) pretend dmp for q1 in ld]
partRes:=groebSolve(lnp,lvv)$GroebnerSolve(lv,K,K) pretend (L L dmp)
partRes=list [] => []
-- remove components where denominators vanish
- if lq^=[] then
+ if lq~=[] then
gb:=GroebnerInternalPackage(K,DirectProduct(#lv,NNI),OV,dmp)
partRes:=[pr for pr in partRes|
- and/[(redPol(fq,pr pretend List(dmp))$gb) ^=0
+ and/[(redPol(fq,pr pretend List(dmp))$gb) ~=0
for fq in lq]]
-- select the components in "generic" form
@@ -182,7 +182,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where
"and"/[("max"/degree(f,rrlvv))=1 for f in res1] =>
listGen:=concat(res pretend (L dmp),listGen)
result:L L F := []
- if listGen^=[] then
+ if listGen~=[] then
listG :L L P K:=
[[dmpToP(pf)$PolToPol(lv,K) for pf in pr] for pr in listGen]
result:=
@@ -286,14 +286,14 @@ FloatingRealPackage(Par): Cat == Cap where
-- real zeros of the system of polynomial lp --
realRoots(lp:L RFI,lv:L SE,eps: Par) : L L Par ==
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par)
solve(lp:L RFI,eps : Par) : L L EQ P Par ==
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
lv:="setUnion"/[variables np for np in lnum]
- if lden^=[] then
+ if lden~=[] then
lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden])
[makeEq(numres,lv) for numres
in innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par)]
@@ -301,9 +301,9 @@ FloatingRealPackage(Par): Cat == Cap where
solve(le:L EQ RFI,eps : Par) : L L EQ P Par ==
lp:=[lhs ep - rhs ep for ep in le]
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
lv:="setUnion"/[variables np for np in lnum]
- if lden^=[] then
+ if lden~=[] then
lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden])
[makeEq(numres,lv) for numres
in innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par)]
@@ -406,14 +406,14 @@ FloatingComplexPackage(Par): Cat == Cap where
-- find the complex zeros of an univariate polynomial --
complexRoots(lp:L FPK,lv:L SE,eps:Par) : L L C Par ==
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par)
complexSolve(lp:L FPK,eps : Par) : L L EQ P C Par ==
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
lv:="setUnion"/[variables np for np in lnum]
- if lden^=[] then
+ if lden~=[] then
lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden])
[[equation(x::(P C Par),r::(P C Par)) for x in lv for r in nres]
for nres in innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par)]
@@ -421,9 +421,9 @@ FloatingComplexPackage(Par): Cat == Cap where
complexSolve(le:L EQ FPK,eps : Par) : L L EQ P C Par ==
lp:=[lhs ep - rhs ep for ep in le]
lnum:=[numer p for p in lp]
- lden:=[dp for p in lp |(dp:=denom p)^=1]
+ lden:=[dp for p in lp |(dp:=denom p)~=1]
lv:="setUnion"/[variables np for np in lnum]
- if lden^=[] then
+ if lden~=[] then
lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden])
[[equation(x::(P C Par),r::(P C Par)) for x in lv for r in nres]
for nres in innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par)]