diff options
Diffstat (limited to 'src/algebra/xpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/xpoly.spad.pamphlet | 22 |
1 files changed, 11 insertions, 11 deletions
diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index 6ff416b1..160ee646 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -107,7 +107,7 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where x: List REC := listOfMonoms(w)$Rep null x => "failed" fx: REC := first x - fx.gen ^= l => "failed" + fx.gen ~= l => "failed" fx.exp = 1 => makeMulti rest(x) makeMulti [[fx.gen, (fx.exp - 1)::NNI ]$REC, :rest x] @@ -288,7 +288,7 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where monomials x == [ monom (t.k, t.c) for t in x] retractIfCan x == - numberOfMonomials(x) ^= 1 => "failed" + numberOfMonomials(x) ~= 1 => "failed" x.first.c = 1 => x.first.k "failed" @@ -578,7 +578,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where constant? p == (p = 0) or (maxdeg(p) = 1$E) constant p == coef(p,1$E) - quasiRegular? p == (p=0) or (last p).k ^= 1$E + quasiRegular? p == (p=0) or (last p).k ~= 1$E quasiRegular p == quasiRegular?(p) => p [t for t in p | not(t.k = 1$E)] @@ -746,10 +746,10 @@ XDistributedPolynomial(vl:OrderedSet,R:Ring): XDPcat == XDPdef where x * shw(rest w1,w2) + y * shw(w1,rest w2) lquo(p:%,q:%):% == - +/ [r * t.c for t in q | (r := lquo(p,t.k)) ^= 0] + +/ [r * t.c for t in q | (r := lquo(p,t.k)) ~= 0] rquo(p:%,q:%):% == - +/ [r * t.c for t in q | (r := rquo(p,t.k)) ^= 0] + +/ [r * t.c for t in q | (r := rquo(p,t.k)) ~= 0] coef(p:%,q:%):R == p = 0 => 0$R @@ -839,14 +839,14 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where p2 case R => p1 * p2::R p1 case R => p1 * p2.c0 x:REGPOLY := construct [[t.k, a]$TERM for t in ListOfTerms(p1.reg) _ - | (a:= rquo(t.c,p2)) ^= 0$% ]$LTERMS + | (a:= rquo(t.c,p2)) ~= 0$% ]$LTERMS simplifie [coef(p1,p2) , x]$VPOLY trunc(p,n) == n = 0 or (p case R) => (constant p)::% n1: NNI := (n-1)::NNI lt: LTERMS := [[t.k, r]$TERM for t in ListOfTerms p.reg _ - | (r := trunc(t.c, n1)) ^= 0]$LTERMS + | (r := trunc(t.c, n1)) ~= 0]$LTERMS x: REGPOLY := construct lt simplifie [constant p, x]$VPOLY @@ -854,7 +854,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where constant? p => (constant p)::% vl: List VarSet := sort(#1 > #2, varList p) x : REGPOLY := _ - construct [[v, unexpand r]$TERM for v in vl| (r:=lquo(p,v)) ^= 0] + construct [[v, unexpand r]$TERM for v in vl| (r:=lquo(p,v)) ~= 0] [constant p, x]$VPOLY if R has CommutativeRing then @@ -999,7 +999,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where rquo(p:%, v:VarSet):% == p case R => 0 x:REGPOLY := construct [[t.k, a]$TERM for t in ListOfTerms(p.reg) - | (a:= rquo(t.c,v)) ^= 0 ] + | (a:= rquo(t.c,v)) ~= 0 ] simplifie [constant(coefficient(p.reg,v)) , x]$VPOLY rquo(p:%, w:WORD):% == @@ -1026,7 +1026,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where p case R => p = 0 => error "XRPOLY.mindeg: polynome nul !!" 1$WORD - p.c0 ^= 0 => 1$WORD + p.c0 ~= 0 => 1$WORD "min"/[(t.k) *$WORD mindeg(t.c) for t in ListOfTerms p.reg] maxdeg p == @@ -1042,7 +1042,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where map(fn,p) == p case R => fn(p::R) x:REGPOLY := construct [[t.k,a]$TERM for t in ListOfTerms p.reg - |(a := map(fn,t.c)) ^= 0$R] + |(a := map(fn,t.c)) ~= 0$R] simplifie [fn(p.c0),x]$VPOLY varList p == |