MathAction #301 seriesSolve - generates bad fixedPointExquo

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  - #301 seriesSolve - generates bad fixedPointExquo <-- You are here.

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(1) -> a := operator 'a

$\label{eq1}a$

(1)

Type: BasicOperator?

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

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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

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a := operator 'a

$\label{eq3}a$

(3)

Type: BasicOperator?

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

Type: Void

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

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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)

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(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:

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)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.

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)expose UnivariateTaylorSeriesODESolver

   UnivariateTaylorSeriesODESolver is now explicitly exposed in frame 
      initial

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a := operator 'a

$\label{eq6}a$

(6)

Type: BasicOperator?

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

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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

Subject: Be Bold !!

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