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#300 Axiom does not evaluate (a+b)^7 in TEXMAC session ←	↑	→ #302 Cannot rename the file erlib to NRLIB

#301 seriesSolve - generates bad fixedPointExquo

Edit detail for #301 seriesSolve - generates bad fixedPointExquo revision 1 of 5

	1 2 3 4 5
Editor: Time: 2007/11/17 22:23:33 GMT-8
Note:

changed:
-
\begin{axiom}
a := operator 'a
seriesSolve((2*x-2)*D(a(x),x)+4*a(x),a,x=0,[1])
\end{axiom}

does not work. A workaround within the interpreter is to provide a function like::

  fixedPointExquo(s, p) == fixedPointExquo(s, p::UTS(EXPR INT, x, 0))$UTSODE(EXPR INT,UTS(EXPR INT, x, 0))

but that won't work in spad.

From WilliamSit Wed Jul 5 00:34:10 -0500 2006
From: William Sit
Date: Wed, 05 Jul 2006 00:34:10 -0500
Subject: 
Message-ID: <20060705003410-0500@wiki.axiom-developer.org>

\begin{axiom}
a := operator 'a
fixedPointExquo(s, p) == fixedPointExquo(s, p::UTS(EXPR INT, x, 0))$UTSODE(EXPR INT,UTS(EXPR INT, x, 0))
p := seriesSolve((2*x-2)*D(a(x),x)+4*a(x),a,x=0,[1])
(2*x-2)*D(p,x)+4*p
\end{axiom}

Looks like the case of two different x's again.

From unknown Wed Jul 5 01:54:30 -0500 2006
From: unknown
Date: Wed, 05 Jul 2006 01:54:30 -0500
Subject: 
Message-ID: <20060705015430-0500@wiki.axiom-developer.org>

I have a better fix, but I'm still not happy. And 'seriesSolve' still crashes quite often...

I'll send it per mail,

Martin

axiom

a := operator 'a

$\label{eq1}a$

(1)

Type: BasicOperator?

axiom

seriesSolve((2*x-2)*D(a(x),x)+4*a(x),a,x=0,[1])

axiom

Compiling function %B with type List(UnivariateTaylorSeries(
      Expression(Integer),x,0)) -> UnivariateTaylorSeries(Expression(
      Integer),x,0)

$\label{eq2}\begin{array}{@{}l} \displaystyle 1 +{2 \ x}+{3 \ {x^2}}+{4 \ {x^3}}+{5 \ {x^4}}+{6 \ {x^5}}+{7 \ {x^6}}+{8 \ {x^7}}+{9 \ {x^8}}+ \ \ \displaystyle {{10}\ {x^9}}+{{11}\ {x^{10}}}+{O \left({x^{11}}\right)}$

(2)

Type: UnivariateTaylorSeries?(Expression(Integer),x,0)

does not work. A workaround within the interpreter is to provide a function like:

  fixedPointExquo(s, p) == fixedPointExquo(s, p::UTS(EXPR INT, x, 0))$UTSODE(EXPR INT,UTS(EXPR INT, x, 0))

but that won't work in spad.

... --William Sit, Wed, 05 Jul 2006 00:34:10 -0500 reply

axiom

a := operator 'a

$\label{eq3}a$

(3)

Type: BasicOperator?

axiom

fixedPointExquo(s, p) == fixedPointExquo(s, p::UTS(EXPR INT, x, 0))$UTSODE(EXPR INT,UTS(EXPR INT, x, 0))

Type: Void

axiom

p := seriesSolve((2*x-2)*D(a(x),x)+4*a(x),a,x=0,[1])

axiom

Compiling function %D with type List(UnivariateTaylorSeries(
      Expression(Integer),x,0)) -> UnivariateTaylorSeries(Expression(
      Integer),x,0)

$\label{eq4}\begin{array}{@{}l} \displaystyle 1 +{2 \ x}+{3 \ {x^2}}+{4 \ {x^3}}+{5 \ {x^4}}+{6 \ {x^5}}+{7 \ {x^6}}+{8 \ {x^7}}+{9 \ {x^8}}+ \ \ \displaystyle {{10}\ {x^9}}+{{11}\ {x^{10}}}+{O \left({x^{11}}\right)}$

(4)

Type: UnivariateTaylorSeries?(Expression(Integer),x,0)

axiom

(2*x-2)*D(p,x)+4*p

$\label{eq5}\begin{array}{@{}l} \displaystyle {4 \ x}+{{\left({{12}\ x}- 4 \right)}\ x}+{{\left({{24}\ x}-{12}\right)}\ {x^2}}+{{\left({{40}\ x}-{24}\right)}\ {x^3}}+ \ \ \displaystyle {{\left({{60}\ x}-{40}\right)}\ {x^4}}+{{\left({{84}\ x}-{6 0}\right)}\ {x^5}}+{{\left({{112}\ x}-{84}\right)}\ {x^6}}+ \ \ \displaystyle {{\left({{144}\ x}-{112}\right)}\ {x^7}}+{{\left({{180}\ x}-{144}\right)}\ {x^8}}+{{\left({{220}\ x}-{180}\right)}\ {x^9}}+ \ \ \displaystyle {{\left({{264}\ x}-{220}\right)}\ {x^{10}}}+{O \left({x^{11}}\right)}$

(5)

Type: UnivariateTaylorSeries?(Expression(Integer),x,0)

Looks like the case of two different x's again.

... --unknown, Wed, 05 Jul 2006 01:54:30 -0500 reply

I have a better fix, but I'm still not happy. And seriesSolve still crashes quite often...

I'll send it per mail,

Martin