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last edited 10 years ago by Bill page |
Edit detail for SandBoxDoublePowerSeries revision 12 of 19
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Editor: Bill Page
Time: 2014/08/29 21:06:53 GMT+0 |
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| Note: GSERIES | ||
added:
From BillPage Fri Aug 29 21:06:52 +0000 2014
From: Bill Page
Date: Fri, 29 Aug 2014 21:06:52 +0000
Subject: GSERIES
Message-ID: <20140829210652+0000@axiom-wiki.newsynthesis.org>
\begin{axiom}
x:GeneralUnivariatePowerSeries(FRAC INT,'x,0)
cosh(sqrt x)
y:GeneralUnivariatePowerSeries(GeneralUnivariatePowerSeries(FRAC INT,'x,0),'y,0)
cosh(sqrt x)*sinh(y)
\end{axiom}
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a!
 | (1) |
Type: Variable(a!)
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!:=operator '!
 | (2) |
Type: BasicOperator?
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a(i,j)==(1+(j-1)*i)/!(2*i+4*j)
Type: Void
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a0:=matrix [[a(i,j)*k^i*l^j for i in 0..5] for j in 1..4]
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Compiling function a with type (NonNegativeInteger,PositiveInteger) -> Expression(Integer)
![\label{eq3}\left[
\begin{array}{cccccc}
{l \over{! \left({4}\right)}}&{{k \ l}\over{! \left({6}\right)}}&{{{{k}^{2}}\ l}\over{! \left({8}\right)}}&{{{{k}^{3}}\ l}\over{! \left({1
0}\right)}}&{{{{k}^{4}}\ l}\over{! \left({12}\right)}}&{{{{k}^{5}}\ l}\over{! \left({14}\right)}}
\
{{{l}^{2}}\over{! \left({8}\right)}}&{{2 \ k \ {{l}^{2}}}\over{! \left({10}\right)}}&{{3 \ {{k}^{2}}\ {{l}^{2}}}\over{! \left({1
2}\right)}}&{{4 \ {{k}^{3}}\ {{l}^{2}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{4}}\ {{l}^{2}}}\over{! \left({16}\right)}}&{{6 \ {{k}^{5}}\ {{l}^{2}}}\over{! \left({18}\right)}}
\
{{{l}^{3}}\over{! \left({12}\right)}}&{{3 \ k \ {{l}^{3}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{2}}\ {{l}^{3}}}\over{! \left({1
6}\right)}}&{{7 \ {{k}^{3}}\ {{l}^{3}}}\over{! \left({18}\right)}}&{{9 \ {{k}^{4}}\ {{l}^{3}}}\over{! \left({20}\right)}}&{{{11}\ {{k}^{5}}\ {{l}^{3}}}\over{! \left({22}\right)}}
\
{{{l}^{4}}\over{! \left({16}\right)}}&{{4 \ k \ {{l}^{4}}}\over{! \left({18}\right)}}&{{7 \ {{k}^{2}}\ {{l}^{4}}}\over{! \left({2
0}\right)}}&{{{10}\ {{k}^{3}}\ {{l}^{4}}}\over{! \left({22}\right)}}&{{{1
3}\ {{k}^{4}}\ {{l}^{4}}}\over{! \left({24}\right)}}&{{{16}\ {{k}^{5}}\ {{l}^{4}}}\over{! \left({26}\right)}}](images/8467506247718380201-16.0px.png "\label{eq3}\left[
\begin{array}{cccccc}
{l \over{! \left({4}\right)}}&{{k \ l}\over{! \left({6}\right)}}&{{{{k}^{2}}\ l}\over{! \left({8}\right)}}&{{{{k}^{3}}\ l}\over{! \left({1
0}\right)}}&{{{{k}^{4}}\ l}\over{! \left({12}\right)}}&{{{{k}^{5}}\ l}\over{! \left({14}\right)}}
\
{{{l}^{2}}\over{! \left({8}\right)}}&{{2 \ k \ {{l}^{2}}}\over{! \left({10}\right)}}&{{3 \ {{k}^{2}}\ {{l}^{2}}}\over{! \left({1
2}\right)}}&{{4 \ {{k}^{3}}\ {{l}^{2}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{4}}\ {{l}^{2}}}\over{! \left({16}\right)}}&{{6 \ {{k}^{5}}\ {{l}^{2}}}\over{! \left({18}\right)}}
\
{{{l}^{3}}\over{! \left({12}\right)}}&{{3 \ k \ {{l}^{3}}}\over{! \left({14}\right)}}&{{5 \ {{k}^{2}}\ {{l}^{3}}}\over{! \left({1
6}\right)}}&{{7 \ {{k}^{3}}\ {{l}^{3}}}\over{! \left({18}\right)}}&{{9 \ {{k}^{4}}\ {{l}^{3}}}\over{! \left({20}\right)}}&{{{11}\ {{k}^{5}}\ {{l}^{3}}}\over{! \left({22}\right)}}
\
{{{l}^{4}}\over{! \left({16}\right)}}&{{4 \ k \ {{l}^{4}}}\over{! \left({18}\right)}}&{{7 \ {{k}^{2}}\ {{l}^{4}}}\over{! \left({2
0}\right)}}&{{{10}\ {{k}^{3}}\ {{l}^{4}}}\over{! \left({22}\right)}}&{{{1
3}\ {{k}^{4}}\ {{l}^{4}}}\over{! \left({24}\right)}}&{{{16}\ {{k}^{5}}\ {{l}^{4}}}\over{! \left({26}\right)}}") | (3) |
Type: Matrix(Expression(Integer))
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a(i:INT,j:INT):FRAC INT == (1+(j-1)*i)/Gamma(1+2*i+4*j)
Function declaration a : (Integer,Integer) -> Fraction(Integer) has been added to workspace. Compiled code for a has been cleared. 1 old definition(s) deleted for function or rule a
Type: Void
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aa:DMP([k,l], FRAC INT) := 1+reduce(+, concat [[a(i, j)*k^i*l^j for i in 0..2] for j in 1..2])
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Compiling function a with type (Integer,Integer) -> Fraction(Integer )
![\label{eq4}\begin{array}{@{}l}
\displaystyle
{{1 \over{159667200}}\ {{k}^{2}}\ {{l}^{2}}}+{{1 \over{40320}}\ {{k}^{2}}\ l}+{{1 \over{1814400}}\ k \ {{l}^{2}}}+{{1 \over{720}}\ k \ l}+
\
\
\displaystyle
{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1](images/8577108218012271322-16.0px.png "\label{eq4}\begin{array}{@{}l}
\displaystyle
{{1 \over{159667200}}\ {{k}^{2}}\ {{l}^{2}}}+{{1 \over{40320}}\ {{k}^{2}}\ l}+{{1 \over{1814400}}\ k \ {{l}^{2}}}+{{1 \over{720}}\ k \ l}+
\
\
\displaystyle
{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1") | (4) |
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eval(aa,[k=0, l=l])
 | (5) |
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eval(aa,[k=k, l=0])
 | (6) |
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eval(aa,[k=1.0, l=1.0])
 | (7) |
Type: Polynomial(Float)
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eval(aa,[k=0, l=0])
 | (8) |
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eval(aa,[k=-1, l=-1])::Float
 | (9) |
Type: Float
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)lib GDRAW
GnuDraw is now explicitly exposed in frame initial GnuDraw will be automatically loaded when needed from /var/aw/var/LatexWiki/GDRAW.NRLIB/GDRAW gnuDraw(aa,k=-30..60, l=-30..30, "SandBoxDoublePowerSeries1.dat", title=="Generating Function")
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Compiling function %B with type (DoubleFloat,DoubleFloat) -> DoubleFloat Transmitting data...
Type: Void
![[terminal=pslatex,terminaloptions=color,scale=1.3]
set view 60, 30, 0.85, 1.1
set samples 20, 20
set isosamples 21, 21
set contour base
set cntrparam levels auto 20
set xlabel "k axis"
set ylabel "l axis"
load "SandBoxDoublePowerSeries1.dat"](images/6212032351234159128-16.0px.png "[terminal=pslatex,terminaloptions=color,scale=1.3]
set view 60, 30, 0.85, 1.1
set samples 20, 20
set isosamples 21, 21
set contour base
set cntrparam levels auto 20
set xlabel \"k axis\"
set ylabel \"l axis\"
load \"SandBoxDoublePowerSeries1.dat\"")
Why? --Bill Page, Mon, 25 Aug 2014 01:03:16 +0000 reply
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x:TaylorSeries FRAC INT
Type: Void
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y:TaylorSeries FRAC INT
Type: Void
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cosh(sqrt x)
>> Error detected within library code: ^: rational power does not exist
![\label{eq2}\begin{array}{@{}l}
\displaystyle
{{\left({
\begin{array}{@{}l}
\displaystyle
1 +{{1 \over 2}\ x}+{{1 \over{24}}\ {{x}^{2}}}+{{1 \over{720}}\ {{x}^{3}}}+{{1 \over{40320}}\ {{x}^{4}}}+
\
\
\displaystyle
{{1 \over{3628800}}\ {{x}^{5}}}+{O \left({{x}^{{11}\over 2}}\right)}](images/2536876323736846495-16.0px.png "\label{eq2}\begin{array}{@{}l}
\displaystyle
{{\left({
\begin{array}{@{}l}
\displaystyle
1 +{{1 \over 2}\ x}+{{1 \over{24}}\ {{x}^{2}}}+{{1 \over{720}}\ {{x}^{3}}}+{{1 \over{40320}}\ {{x}^{4}}}+
\
\
\displaystyle
{{1 \over{3628800}}\ {{x}^{5}}}+{O \left({{x}^{{11}\over 2}}\right)}")