diff options
Diffstat (limited to 'src/algebra/poly.spad.pamphlet')
| -rw-r--r-- | src/algebra/poly.spad.pamphlet | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index ad0206cd..fe9eb615 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -54,7 +54,7 @@ FreeModule(R:Ring,S:OrderedSet): -- one? r => x (r = 1) => x --map(r*#1,x) - [[u.k,a] for u in x | (a:=r*u.c) ^= 0$R] + [[u.k,a] for u in x | (a:=r*u.c) ~= 0$R] if R has EntireRing then x * r == zero? r => 0 @@ -68,7 +68,7 @@ FreeModule(R:Ring,S:OrderedSet): -- one? r => x (r = 1) => x --map(r*#1,x) - [[u.k,a] for u in x | (a:=u.c*r) ^= 0$R] + [[u.k,a] for u in x | (a:=u.c*r) ~= 0$R] coerce(x) : OutputForm == null x => (0$R) :: OutputForm @@ -288,7 +288,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C -- null p2 => 0 -- zero?(p1.first.k) => p1.first.c * p2 -- one? p2 => p1 --- +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ^= 0] +-- +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ~= 0] -- for t1 in reverse(p1)] -- -- This 'reverse' is an efficiency improvement: -- -- reduces both time and space [Abbott/Bradford/Davenport] @@ -348,7 +348,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp if R has approximate then @@ -501,7 +501,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp @@ -600,7 +600,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp pseudoRemainder(p1,p2) == @@ -651,7 +651,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with monicDivide(p1:%,p2:%) == null p2 => error "monicDivide: division by 0" - leadingCoefficient p2 ^= 1 => error "Divisor Not Monic" + leadingCoefficient p2 ~= 1 => error "Divisor Not Monic" p2 = 1 => [p1,0] null p1 => [0,0] degree p1 < (n:=degree p2) => [0,p1] @@ -679,7 +679,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with -- p:=pseudoRemainder(p1,p2) -- co:=1$R; -- e:= (p1.first.k - p2.first.k):NonNegativeInteger --- while not null p and p.first.k ^= 0 repeat +-- while not null p and p.first.k ~= 0 repeat -- p1:=p2; p2:=p; p:=pseudoRemainder(p1,p2) -- null p or p.first.k = 0 => "enuf" -- co:=(p1.first.c ** e exquo co ** max(0, (e-1))::NonNegativeInteger)::R @@ -727,7 +727,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with n:=p2.first.k p2:=p2.rest rout:=empty()$List(Term) - while p1 ^= 0 repeat + while p1 ~= 0 repeat (u:=subtractIfCan(p1.first.k, n)) case "failed" => leave rout:=[[u, ct * p1.first.c], :rout] p1:=fmecg(p1.rest, rout.first.k, rout.first.c, p2) @@ -938,7 +938,7 @@ 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 degree(ci)~=0 repeat ci:=(ci exquo pi)::P di:=(di exquo pi)::P - differentiate(ci) pi:=gcd(ci,di) @@ -960,7 +960,7 @@ 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 degree(di)~=0 repeat diprev := di di := gcd(ci,di) ci:=(ci exquo di)::P @@ -1081,7 +1081,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where cont1:=cont1*((unit listfin1)**uexp) pfaclist:=append(flistfin1,pfaclist) cont:=cont*cont1 - cont ^= 1 => + cont ~= 1 => sqp := squareFree cont pfaclist:= append (factorList sqp,pfaclist) makeFR(unit(sqp)*coefficient(unit squf,0),pfaclist) @@ -1090,7 +1090,7 @@ 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) + characteristic$RC ~=0 => finSqFr(p,variables p) up:=univariate(p,mv) cont := content up up := (up exquo cont)::SUP @@ -1098,7 +1098,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where pfaclist:List FF := [[u.flg,multivariate(u.fctr,mv),u.xpnt] for u in factorList squp] - cont ^= 1 => + cont ~= 1 => sqp := squareFree cont makeFR(unit(sqp)*coefficient(unit squp,0), append(factorList sqp, pfaclist)) |