diff --git a/books/bookvol10.3.pamphlet b/books/bookvol10.3.pamphlet index a4fb558..30f0835 100644 --- a/books/bookvol10.3.pamphlet +++ b/books/bookvol10.3.pamphlet @@ -71242,7 +71242,8 @@ ParametricSurface(ComponentFunction): Exports == Implementation where )set message test on )set message auto off )clear all ---S 1 of 10 + +--S 1 of 22 partialFraction(1,factorial 10) --R --R @@ -71253,7 +71254,7 @@ partialFraction(1,factorial 10) --R Type: PartialFraction Integer --E 1 ---S 2 of 10 +--S 2 of 22 f := padicFraction(%) --R --R @@ -71264,7 +71265,7 @@ f := padicFraction(%) --R Type: PartialFraction Integer --E 2 ---S 3 of 10 +--S 3 of 22 compactFraction(f) --R --R @@ -71275,7 +71276,7 @@ compactFraction(f) --R Type: PartialFraction Integer --E 3 ---S 4 of 10 +--S 4 of 22 numberOfFractionalTerms(f) --R --R @@ -71283,7 +71284,7 @@ numberOfFractionalTerms(f) --R Type: PositiveInteger --E 4 ---S 5 of 10 +--S 5 of 22 nthFractionalTerm(f,3) --R --R @@ -71294,7 +71295,7 @@ nthFractionalTerm(f,3) --R Type: PartialFraction Integer --E 5 ---S 6 of 10 +--S 6 of 22 partialFraction(1,- 13 + 14 * %i) --R --R @@ -71304,7 +71305,7 @@ partialFraction(1,- 13 + 14 * %i) --R Type: PartialFraction Complex Integer --E 6 ---S 7 of 10 +--S 7 of 22 % :: Fraction Complex Integer --R --R @@ -71314,7 +71315,7 @@ partialFraction(1,- 13 + 14 * %i) --R Type: Fraction Complex Integer --E 7 ---S 8 of 10 +--S 8 of 22 u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4]) --R --R @@ -71323,7 +71324,7 @@ u : FR UP(x, FRAC INT) := reduce(*,[primeFactor(x+i,i) for i in 1..4]) --R Type: Factored UnivariatePolynomial(x,Fraction Integer) --E 8 ---S 9 of 10 +--S 9 of 22 partialFraction(1,u) --R --R @@ -71337,7 +71338,7 @@ partialFraction(1,u) --R Type: PartialFraction UnivariatePolynomial(x,Fraction Integer) --E 9 ---S 10 of 10 +--S 10 of 22 padicFraction % --R --R @@ -71357,6 +71358,117 @@ padicFraction % --R (x + 4) (x + 4) --R Type: PartialFraction UnivariatePolynomial(x,Fraction Integer) --E 10 + +--S 11 of 22 +fraction:=Fraction(Polynomial(Integer)) +--R +--R +--R (11) Fraction Polynomial Integer +--R Type: Domain +--E 11 + +--S 12 of 22 +up:=UnivariatePolynomial(y,fraction) +--R +--R +--R (12) UnivariatePolynomial(y,Fraction Polynomial Integer) +--R Type: Domain +--E 12 + +--S 13 of 22 +pfup:=PartialFraction(up) +--R +--R +--R (13) PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--R Type: Domain +--E 13 + +--S 14 of 22 +a:=x+1/(y+1) +--R +--R +--R x y + x + 1 +--R (14) ----------- +--R y + 1 +--R Type: Fraction Polynomial Integer +--E 14 + +--S 15 of 22 +b:=partialFraction(a,y)$PartialFractionPackage(Integer) +--R +--R +--R 1 +--R (15) x + ----- +--R y + 1 +--R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--E 15 + +--S 16 of 22 +c:=b::pfup +--R +--R +--R 1 +--R (16) x + ----- +--R y + 1 +--R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--E 16 + +--S 17 of 22 +cw:=(wholePart c)::Expression(Integer) +--R +--R +--R (17) x +--R Type: Expression Integer +--E 17 + +--S 18 of 22 +m:=numberOfFractionalTerms(c) +--R +--R +--R (18) 1 +--R Type: PositiveInteger +--E 18 + +--S 19 of 22 +crList:=[nthFractionalTerm(c,i) for i in 1..m] +--R +--R +--R 1 +--R (19) [-----] +--R y + 1 +--RType: List PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--E 19 + +--S 20 of 22 +cc:=reduce(+,crList) +--R +--R +--R 1 +--R (20) ----- +--R y + 1 +--R Type: PartialFraction UnivariatePolynomial(y,Fraction Polynomial Integer) +--E 20 + +--S 21 of 22 +ccx:=cc::(Fraction(up))::(Expression(Integer)) +--R +--R +--R 1 +--R (21) ----- +--R y + 1 +--R Type: Expression Integer +--E 21 + +--S 22 of 22 +sin(cw)*cos(ccx)+sin(ccx)*cos(cw) +--R +--R +--R 1 1 +--R (22) cos(-----)sin(x) + cos(x)sin(-----) +--R y + 1 y + 1 +--R Type: Expression Integer +--E 22 + )spool )lisp (bye) @ diff --git a/changelog b/changelog index e096256..2ebe8cc 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20091030 tpd src/axiom-website/patches.html 20091030.05.tpd.patch +20091030 tpd books/bookvol10.3 more PartialFraction documentation 20091030 tpd src/axiom-website/patches.html 20091030.04.tpd.patch 20091030 tpd books/bookvol10.3 partial fix OrderedFreeMonoid 20091030 tpd src/axiom-website/patches.html 20091030.03.tpd.patch diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 208e80a..79a6efd 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2205,5 +2205,7 @@ books/bookvol10.3 document OrderedFreeMonoid
books/bookvol10.4 document PartialFractionPackage
20091030.04.tpd.patch books/bookvol10.3 partial fix OrderedFreeMonoid
+20091030.05.tpd.patch +books/bookvol10.3 more PartialFraction documentation