diff options
Diffstat (limited to 'src/algebra/poly.spad.pamphlet')
| -rw-r--r-- | src/algebra/poly.spad.pamphlet | 24 |
1 files changed, 8 insertions, 16 deletions
diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index ff21510e..077ba898 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -44,29 +44,25 @@ FreeModule(R:Ring,S:OrderedSet): if R has EntireRing then r * x == zero? r => 0 --- one? r => x - (r = 1) => x + one? r => x --map(r*#1,x) [[u.k,r*u.c] for u in x ] else r * x == zero? r => 0 --- one? r => x - (r = 1) => x + one? r => x --map(r*#1,x) [[u.k,a] for u in x | (a:=r*u.c) ~= 0$R] if R has EntireRing then x * r == zero? r => 0 --- one? r => x - (r = 1) => x + one? r => x --map(r*#1,x) [[u.k,u.c*r] for u in x ] else x * r == zero? r => 0 --- one? r => x - (r = 1) => x + one? r => x --map(r*#1,x) [[u.k,a] for u in x | (a:=u.c*r) ~= 0$R] @@ -298,8 +294,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C p ** nn == null p => 0 zero? nn => 1 --- one? nn => p - (nn = 1) => p + one? nn => p empty? p.rest => zero?(cc:=p.first.c ** nn) => 0 [[nn * p.first.k, cc]] @@ -438,8 +433,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with p ** n == null p => 0 zero? n => 1 --- one? n => p - (n = 1) => p + one? n => p empty? p.rest => zero?(cc:=p.first.c ** n) => 0 [[n * p.first.k, cc]] @@ -465,8 +459,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with zero?(p): Boolean == empty?(p) --- one?(p):Boolean == not empty? p and (empty? rest p and zero? first(p).k and one? first(p).c) - one?(p):Boolean == not empty? p and (empty? rest p and zero? first(p).k and (first(p).c = 1)) + one?(p):Boolean == not empty? p and (empty? rest p and zero? first(p).k and one? first(p).c) ground?(p): Boolean == empty? p or (empty? rest p and zero? first(p).k) multiplyExponents(p,n) == [ [u.k*n,u.c] for u in p] divideExponents(p,n) == @@ -720,8 +713,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with if R has Field then divide( p1, p2) == zero? p2 => error "Division by 0" --- one? p2 => [p1,0] - (p2 = 1) => [p1,0] + one? p2 => [p1,0] ct:=inv(p2.first.c) n:=p2.first.k p2:=p2.rest |