diff options
Diffstat (limited to 'src/algebra/numsolve.spad.pamphlet')
| -rw-r--r-- | src/algebra/numsolve.spad.pamphlet | 30 |
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)] |