diff options
Diffstat (limited to 'src/algebra/newpoly.spad.pamphlet')
| -rw-r--r-- | src/algebra/newpoly.spad.pamphlet | 66 |
1 files changed, 22 insertions, 44 deletions
diff --git a/src/algebra/newpoly.spad.pamphlet b/src/algebra/newpoly.spad.pamphlet index db2974e2..8fee6315 100644 --- a/src/algebra/newpoly.spad.pamphlet +++ b/src/algebra/newpoly.spad.pamphlet @@ -114,8 +114,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where ground? y => error "in monicModulo$NSUP: ground? #2" yy := rep y --- not one? (yy.first.c) => - not ((yy.first.c) = 1) => + not one? (yy.first.c) => error "in monicModulo$NSUP: not monic #2" xx := rep x; empty? xx => x e := yy.first.k; y := per(yy.rest) @@ -148,8 +147,7 @@ NewSparseUnivariatePolynomial(R): Exports == Implementation where error "in lazyPseudoRemainder$NSUP: ground? #2" ground? x => x yy := rep y; co := yy.first.c --- one? co => monicModulo(x,y) - (co = 1) => monicModulo(x,y) + one? co => monicModulo(x,y) (co = -1) => - monicModulo(-x,-y) xx:= rep x; e := yy.first.k; y := per(yy.rest) repeat @@ -633,20 +631,17 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca coerce(p:$):O == ground? (p) => (ground(p))::O --- if one?((ip := init(p))) - if (((ip := init(p))) = 1) + if one?((ip := init(p))) then if zero?((tp := tail(p))) then --- if one?((dp := mdeg(p))) - if (((dp := mdeg(p))) = 1) + if one?((dp := mdeg(p))) then return((mvar(p))::O) else return(((mvar(p))::O **$O (dp::O))) else --- if one?((dp := mdeg(p))) - if (((dp := mdeg(p))) = 1) + if one?((dp := mdeg(p))) then return((mvar(p))::O +$O (tp::O)) else @@ -654,15 +649,13 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca else if zero?((tp := tail(p))) then --- if one?((dp := mdeg(p))) - if (((dp := mdeg(p))) = 1) + if one?((dp := mdeg(p))) then return((ip::O) *$O (mvar(p))::O) else return((ip::O) *$O ((mvar(p))::O **$O (dp::O))) else --- if one?(mdeg(p)) - if ((mdeg(p)) = 1) + if one?(mdeg(p)) then return(((ip::O) *$O (mvar(p))::O) +$O (tp::O)) ((ip)::O *$O ((mvar(p))::O **$O ((mdeg(p)::O))) +$O (tail(p)::O)) @@ -1063,8 +1056,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca primitivePart! p == zero? p => p --- if one?(cp := content(p)) - if ((cp := content(p)) = 1) + if one?(cp := content(p)) then p := unitCanonical p else @@ -1086,8 +1078,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca then gcd(r:R,p:$):R == --- one? r => r - (r = 1) => r + one? r => r zero? p => r ground? p => gcd(r,ground(p))$R gcd(gcd(r,init(p)),tail(p)) @@ -1392,13 +1383,11 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca dpol : NNI := mdeg(pol) tpol: $ := tail(pol) sipol,svpol,sdpol,stpol : String --- if one? ipol - if (ipol = 1) + if one? ipol then sipol := empty()$String else --- if one?(-ipol) - if ((-ipol) = 1) + if one?(-ipol) then sipol := "-" else @@ -1409,8 +1398,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca else sipol := concat(sipol,"*")$String svpol := string(convert(vpol)@Symbol) --- if one? dpol - if (dpol = 1) + if one? dpol then sdpol := empty()$String else @@ -1571,8 +1559,7 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where not ground?(ib)$$ => error"Error in monicModulo from NSMP : #2 is not monic" mM : $ --- if not one?(ib)$$ - if not ((ib) = 1)$$ + if not one?(ib)$$ then r : R := ground(ib)$$ rec : Union(R,"failed"):= recip(r)$R @@ -1703,23 +1690,20 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where LazardQuotient(x:$, y:$, n: N):$ == zero?(n) => error("LazardQuotient$NSMP : n = 0") --- one?(n) => x - (n = 1) => x + one?(n) => x a: N := 1 while n >= (b := 2*a) repeat a := b c: $ := x n := (n - a)::N repeat --- one?(a) => return c - (a = 1) => return c + one?(a) => return c a := a quo 2 c := exactQuo(c*c,y) if n >= a then ( c := exactQuo(c*x,y) ; n := (n - a)::N ) LazardQuotient2(p:$, a:$, b:$, n: N) == zero?(n) => error " in LazardQuotient2$NSMP: bad #4" --- one?(n) => p - (n = 1) => p + one?(n) => p c: $ := LazardQuotient(a,b,(n-1)::N) exactQuo(c*p,b) @@ -1782,14 +1766,12 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where then exactQuotient (a:$,b:R) == --- one? b => a - (b = 1) => a + one? b => a a case R => (a::R quo$R b)::$ ([a.v, map(exactQuotient(#1,b),a.ts)$SUP2]$VPoly)::Rep exactQuotient! (a:$,b:R) == --- one? b => a - (b = 1) => a + one? b => a a case R => (a::R quo$R b)::$ a.ts := map(exactQuotient!(#1,b),a.ts)$SUP2 a @@ -1797,14 +1779,12 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where else exactQuotient (a:$,b:R) == --- one? b => a - (b = 1) => a + one? b => a a case R => ((a::R exquo$R b)::R)::$ ([a.v, map(exactQuotient(#1,b),a.ts)$SUP2]$VPoly)::Rep exactQuotient! (a:$,b:R) == --- one? b => a - (b = 1) => a + one? b => a a case R => ((a::R exquo$R b)::R)::$ a.ts := map(exactQuotient!(#1,b),a.ts)$SUP2 a @@ -1817,8 +1797,7 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where gcd(r,content(p))$R gcd(r:R,p:$):R == --- one? r => r - (r = 1) => r + one? r => r zero? p => r localGcd(r,p) @@ -1826,8 +1805,7 @@ NewSparseMultivariatePolynomial(R,VarSet) : Exports == Implementation where p case R => p up : D := p.ts r := 0$R --- while (not zero? up) and (not one? r) repeat - while (not zero? up) and (not (r = 1)) repeat + while (not zero? up) and (not one? r) repeat r := localGcd(r,leadingCoefficient(up)) up := reductum up r |