diff --git a/changelog b/changelog index ea59a92..7639d25 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,5 @@ +20101209 tpd src/axiom-website/patches.html 20101209.01.tpd.patch +20101209 tpd src/input/series.input add series to polynomial example 20101208 tpd src/axiom-website/patches.html 20101208.01.tpd.patch 20101208 tpd src/interp/vmlisp.lisp treeshake compiler 20101208 tpd src/interp/parsing.lisp treeshake compiler diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 0c44112..643deb6 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -3307,5 +3307,7 @@ books/bookvol9 merge and remove postprop.lisp
books/bookvol9 treeshake compiler
20101208.01.tpd.patch books/bookvol9 treeshake compiler
+20101209.01.tpd.patch +src/input/series.input add series to polynomial example
diff --git a/src/input/series.input.pamphlet b/src/input/series.input.pamphlet index f64bddb..8d79430 100644 --- a/src/input/series.input.pamphlet +++ b/src/input/series.input.pamphlet @@ -26,7 +26,7 @@ We compute series expansions of various functions using EXPR2UPS. Test functions in EXPR2UPS: \begin{chunk}{*} ---S 1 of 17 +--S 1 of 20 xT := taylor(x) --R --R @@ -34,7 +34,7 @@ xT := taylor(x) --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 1 ---S 2 of 17 +--S 2 of 20 sin(tan(xT)) --R --R @@ -44,7 +44,7 @@ sin(tan(xT)) --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 2 ---S 3 of 17 +--S 3 of 20 taylor(asec(2+x)) --R --R @@ -66,7 +66,7 @@ taylor(asec(2+x)) --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 3 ---S 4 of 17 +--S 4 of 20 sec % --R --R @@ -75,7 +75,7 @@ sec % --R Type: UnivariateTaylorSeries(Expression Integer,x,0) --E 4 ---S 5 of 17 +--S 5 of 20 taylor(sin(x),x = %pi/4) --R --R @@ -97,7 +97,7 @@ taylor(sin(x),x = %pi/4) --R Type: UnivariateTaylorSeries(Expression Integer,x,pi/4) --E 5 ---S 6 of 17 +--S 6 of 20 xL := laurent(x) --R --R @@ -105,7 +105,7 @@ xL := laurent(x) --R Type: UnivariateLaurentSeries(Expression Integer,x,0) --E 6 ---S 7 of 17 +--S 7 of 20 1/xL - cot(xL) --R --R @@ -115,7 +115,7 @@ xL := laurent(x) --R Type: UnivariateLaurentSeries(Expression Integer,x,0) --E 7 ---S 8 of 17 +--S 8 of 20 laurent(csc(x)) --R --R @@ -125,7 +125,7 @@ laurent(csc(x)) --R Type: UnivariateLaurentSeries(Expression Integer,x,0) --E 8 ---S 9 of 17 +--S 9 of 20 laurent(1/log(x),x = 1) --R --R @@ -144,7 +144,7 @@ laurent(1/log(x),x = 1) --R Type: UnivariateLaurentSeries(Expression Integer,x,1) --E 9 ---S 10 of 17 +--S 10 of 20 xP := puiseux(x) --R --R @@ -152,7 +152,7 @@ xP := puiseux(x) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 10 ---S 11 of 17 +--S 11 of 20 sqrt(xP) - sqrt(sin(xP)) --R --R @@ -164,7 +164,7 @@ sqrt(xP) - sqrt(sin(xP)) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 11 ---S 12 of 17 +--S 12 of 20 puiseux(sqrt(1 - cos(x))/x) --R --R @@ -181,7 +181,7 @@ puiseux(sqrt(1 - cos(x))/x) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 12 ---S 13 of 17 +--S 13 of 20 puiseux(sqrt(1 - tan(x)),x = %pi/2) --R --R @@ -200,7 +200,7 @@ puiseux(sqrt(1 - tan(x)),x = %pi/2) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,pi/2) --E 13 ---S 14 of 17 +--S 14 of 20 xS := series(x) --R --R @@ -208,7 +208,7 @@ xS := series(x) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 14 ---S 15 of 17 +--S 15 of 20 sin(xS)**(1/3) - sin(xS**(1/3)) --R --R @@ -221,7 +221,7 @@ sin(xS)**(1/3) - sin(xS**(1/3)) --R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) --E 15 ---S 16 of 17 +--S 16 of 20 series(log(tan(x))) --R --R @@ -231,7 +231,7 @@ series(log(tan(x))) --R Type: GeneralUnivariatePowerSeries(Expression Integer,x,0) --E 16 ---S 17 of 17 +--S 17 of 20 series(log(cot(x)),x = %pi/2) --R --R @@ -245,6 +245,44 @@ series(log(cot(x)),x = %pi/2) --R 18900 2 66825 2 2 --R Type: GeneralUnivariatePowerSeries(Expression Integer,x,pi/2) --E 17 + +\end{chunk} + +Series can be converted to polynomials: + +\begin{chunk}{*} +--S 18 of 20 +a:=series(sin x, x=0) +--R +--R +--R 1 3 1 5 1 7 1 9 1 11 12 +--R (18) x - - x + --- x - ---- x + ------ x - -------- x + O(x ) +--R 6 120 5040 362880 39916800 +--R Type: UnivariatePuiseuxSeries(Expression Integer,x,0) +--E 18 + +--S 19 of 20 +b:UnivariateTaylorSeries(Fraction Integer,x,0) := a +--R +--R +--R 1 3 1 5 1 7 1 9 11 +--R (19) x - - x + --- x - ---- x + ------ x + O(x ) +--R 6 120 5040 362880 +--R Type: UnivariateTaylorSeries(Fraction Integer,x,0) +--E 19 + +--S 20 of 20 +univariatePolynomial(b,9) +--R +--R +--R 1 9 1 7 1 5 1 3 +--R (20) ------ x - ---- x + --- x - - x + x +--R 362880 5040 120 6 +--R Type: UnivariatePolynomial(x,Fraction Integer) +--E 20 +)spool + + )spool )lisp (bye)