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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
  
last edited 15 years ago by japp

Edit detail for #301 seriesSolve - generates bad fixedPointExquo revision 2 of 5
1 2 3 4 5
Editor: Bill Page
Time: 2008/10/21 18:50:16 GMT-7
Note: Why isn't UnivariateTaylorSeriesODESolver exposed? 
added:

From BillPage Tue Oct 21 18:50:10 -0700 2008
From: Bill Page
Date: Tue, 21 Oct 2008 18:50:10 -0700
Subject: Why isn't UnivariateTaylorSeriesODESolver exposed?
Message-ID: <20081021185010-0700@axiom-wiki.newsynthesis.org>

UnivariateTaylorSeriesODESolver is part of the 'Hidden' group in
'exposed.lsp.pamphlet'. Exposing this package prevents the error:
\begin{axiom}
)clear completely
)expose UnivariateTaylorSeriesODESolver
\end{axiom}

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

Submitted by : (unknown) at: 2007-11-17T22:23:33-08:00 (16 years ago)
Name :
Axiom Version :
Category : Severity : Status :
Optional subject :  
Optional comment :

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

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:
axiom
)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.
axiom
)expose UnivariateTaylorSeriesODESolver

   UnivariateTaylorSeriesODESolver is now explicitly exposed in frame 
      initial

axiom
a := operator 'a
\label{eq6}a(6)
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{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)