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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 5 of 5

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Editor: japp Time: 2009/02/04 17:17:32 GMT-8
Note:

added:

From japp Wed Feb 4 17:17:32 -0800 2009
From: japp
Date: Wed, 04 Feb 2009 17:17:32 -0800
Subject: 
Message-ID: <20090204171732-0800@axiom-wiki.newsynthesis.org>

Status: fixed somewhere => fix proposed

fricas

a := operator 'a

$\label{eq1}a$

(1)

Type: BasicOperator?

fricas

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

fricas

Compiling function %D 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

fricas

a := operator 'a

$\label{eq3}a$

(3)

Type: BasicOperator?

fricas

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

Type: Void

fricas

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

fricas

Compiling function %H 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)

fricas

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

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

(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

Why isn't UnivariateTaylorSeriesODESolver? exposed? --Bill Page, Tue, 21 Oct 2008 18:50:10 -0700 reply

UnivariateTaylorSeriesODESolver? is part of the Hidden group in exposed.lsp.pamphlet. Exposing this package prevents the error:

fricas

)clear completely

   All user variables and function definitions have been cleared.
   All )browse facility databases have been cleared.
   Internally cached functions and constructors have been cleared.
   )clear completely is finished.

fricas

)expose UnivariateTaylorSeriesODESolver

   UnivariateTaylorSeriesODESolver is now explicitly exposed in frame 
      initial

fricas

a := operator 'a

$\label{eq6}a$

(6)

Type: BasicOperator?

fricas

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

fricas

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

$\label{eq7}\begin{array}{@{}l} \displaystyle 1 +{2 \ x}+{3 \ {{x}^{2}}}+{4 \ {{x}^{3}}}+{5 \ {{x}^{4}}}+{6 \ {{x}^{5}}}+{7 \ {{x}^{6}}}+{8 \ {{x}^{7}}}+{9 \ {{x}^{8}}}+ \ \ \displaystyle {{10}\ {{x}^{9}}}+{{11}\ {{x}^{10}}}+{O \left({{x}^{11}}\right)}$

(7)

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

fixed in FriCAS revision 423 --kratt6, Tue, 13 Jan 2009 02:05:24 -0800 reply