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last edited 10 years ago by Bill page |
Edit detail for SandBoxDoublePowerSeries revision 9 of 19
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Editor: Bill Page
Time: 2014/08/25 00:50:13 GMT+0 |
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| Note: | ||
changed: -a(i,j)==(1+(j-1)*i)/Gamma(1+2*i+4*j) -aa(k,l)==1+reduce(+,concat [[a(i,j)*k^i*l^j for i in 0..10] for j in 1..11]) -aa(0,l) -aa(k,0) -aa(1,1)::Float -aa(0,0)::Float -aa(-1,-1)::Float a(i:INT,j:INT):FRAC INT == (1+(j-1)*i)/Gamma(1+2*i+4*j) aa:DMP([k,l], FRAC INT) := 1+reduce(+,concat [[a(i,j)*k^i*l^j for i in 0..4] for j in 1..5]) eval(aa,[k=0,l=l]) eval(aa,[k=k,l=0]) eval(aa,[k=1.0,l=1.0]) eval(aa,[k=0,l=0]) eval(aa,[k=-1,l=-1])::Float removed: - -\begin{axiom} -i0:=a(1/2+%i*beta,0)*(-x)^(1/2+%i*beta)/cosh(%pi*beta) -i0':=a(1/2+%i*beta,0)*exp((1/2+%i*beta)*log(-x))/cosh(%pi*beta) -i0'':=htrigs % -i1:=a(0,1/2+%i*delta)*(-y)^(1/2+%i*delta)/cosh(%pi*delta) -i2:=a(1/2+%i*beta,1/2+%i*delta)*(-y)^(1/2+%i*delta)/(cosh(%pi*beta)*cosh(%pi*delta)) -eval(i0,beta=-1) -eval(i0,beta=0) -eval(i0,beta=1) -eval(i0,[beta=1,x=1]) -%::Expression Complex Float -%::Complex Float -Gamma(2+%i*2) -Gamma(2.0+%i*2.0) -eval(i1,delta=-1) -eval(i1,delta=0) -eval(i1,delta=1) -\end{axiom} - -\begin{axiom} -integrate(i0,beta=%minusInfinity..%plusInfinity,"noPole") -\end{axiom} - -\begin{axiom} -integrate(i0'',beta=%minusInfinity..%plusInfinity,"noPole") -\end{axiom} - -\begin{axiom} -integrate(i1,delta=%minusInfinity..%plusInfinity,"noPole") -\end{axiom} - -\begin{axiom} -integrate(x^(t-1)*exp(-x),x=0..%plusInfinity,"noPole") -\end{axiom} - -\begin{axiom} -integrate(x^((2+%i*2)-1)*exp(-x),x=0..%plusInfinity,"noPole") -\end{axiom} changed: -gnuDraw(aa(x,y),x=-30..60,y=-30..30,"SandBoxDoublePowerSeries1.dat",title=="Generating Function") gnuDraw(aa,k=-30..60,l=-30..30,"SandBoxDoublePowerSeries1.dat",title=="Generating Function")
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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..4] for j in 1..5])
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Compiling function a with type (Integer,Integer) -> Fraction(Integer )
![\label{eq4}\begin{array}{@{}l}
\displaystyle
{{1 \over{17934608506571403558912000000}}\ {{k}^{4}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{47726800133326110720000}}\ {{k}^{4}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{270322445352960000}}\ {{k}^{4}}\ {{l}^{3}}}+{{1 \over{4
184557977600}}\ {{k}^{4}}\ {{l}^{2}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{k}^{4}}\ l}+{{1 \over{3102242008666
1971968000000}}\ {{k}^{3}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{112400072777760768000}}\ {{k}^{3}}\ {{l}^{4}}}+{{1 \over{914624815104000}}\ {{k}^{3}}\ {{l}^{3}}}+
\
\
\displaystyle
{{1 \over{21794572800}}\ {{k}^{3}}\ {{l}^{2}}}+{{1 \over{3628
800}}\ {{k}^{3}}\ l}+
\
\
\displaystyle
{{1 \over{68938711303693271040000}}\ {{k}^{2}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{347557429739520000}}\ {{k}^{2}}\ {{l}^{4}}}+{{1 \over{4
184557977600}}\ {{k}^{2}}\ {{l}^{3}}}+
\
\
\displaystyle
{{1 \over{159667200}}\ {{k}^{2}}\ {{l}^{2}}}+{{1 \over{40320}}\ {{k}^{2}}\ l}+
\
\
\displaystyle
{{1 \over{224800145555521536000}}\ k \ {{l}^{5}}}+{{1 \over{1
600593426432000}}\ k \ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{29059430400}}\ k \ {{l}^{3}}}+{{1 \over{1814400}}\ k \ {{l}^{2}}}+{{1 \over{720}}\ k \ l}+
\
\
\displaystyle
{{1 \over{2432902008176640000}}\ {{l}^{5}}}+{{1 \over{2092278
9888000}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{l}^{3}}}+{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1](images/8441551605157855343-16.0px.png "\label{eq4}\begin{array}{@{}l}
\displaystyle
{{1 \over{17934608506571403558912000000}}\ {{k}^{4}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{47726800133326110720000}}\ {{k}^{4}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{270322445352960000}}\ {{k}^{4}}\ {{l}^{3}}}+{{1 \over{4
184557977600}}\ {{k}^{4}}\ {{l}^{2}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{k}^{4}}\ l}+{{1 \over{3102242008666
1971968000000}}\ {{k}^{3}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{112400072777760768000}}\ {{k}^{3}}\ {{l}^{4}}}+{{1 \over{914624815104000}}\ {{k}^{3}}\ {{l}^{3}}}+
\
\
\displaystyle
{{1 \over{21794572800}}\ {{k}^{3}}\ {{l}^{2}}}+{{1 \over{3628
800}}\ {{k}^{3}}\ l}+
\
\
\displaystyle
{{1 \over{68938711303693271040000}}\ {{k}^{2}}\ {{l}^{5}}}+
\
\
\displaystyle
{{1 \over{347557429739520000}}\ {{k}^{2}}\ {{l}^{4}}}+{{1 \over{4
184557977600}}\ {{k}^{2}}\ {{l}^{3}}}+
\
\
\displaystyle
{{1 \over{159667200}}\ {{k}^{2}}\ {{l}^{2}}}+{{1 \over{40320}}\ {{k}^{2}}\ l}+
\
\
\displaystyle
{{1 \over{224800145555521536000}}\ k \ {{l}^{5}}}+{{1 \over{1
600593426432000}}\ k \ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{29059430400}}\ k \ {{l}^{3}}}+{{1 \over{1814400}}\ k \ {{l}^{2}}}+{{1 \over{720}}\ k \ l}+
\
\
\displaystyle
{{1 \over{2432902008176640000}}\ {{l}^{5}}}+{{1 \over{2092278
9888000}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{l}^{3}}}+{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1") | (4) |
fricas
eval(aa,[k=0, l=l])
![\label{eq5}\begin{array}{@{}l}
\displaystyle
{{1 \over{2432902008176640000}}\ {{l}^{5}}}+{{1 \over{2092278
9888000}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{l}^{3}}}+{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1](images/269118148939948445-16.0px.png "\label{eq5}\begin{array}{@{}l}
\displaystyle
{{1 \over{2432902008176640000}}\ {{l}^{5}}}+{{1 \over{2092278
9888000}}\ {{l}^{4}}}+
\
\
\displaystyle
{{1 \over{479001600}}\ {{l}^{3}}}+{{1 \over{40320}}\ {{l}^{2}}}+{{1 \over{24}}\ l}+ 1") | (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")
fricas
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 title "3D gnuplot demo - contour plot"
set xlabel "X axis"
set ylabel "Y axis"
set zlabel "Z axis"
set zlabel offset character 1, 0, 0 font "" textcolor lt -1 norotate
load "SandBoxDoublePowerSeries1.dat"](images/2463187652313621449-16.0px.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 title \"3D gnuplot demo - contour plot\"
set xlabel \"X axis\"
set ylabel \"Y axis\"
set zlabel \"Z axis\"
set zlabel offset character 1, 0, 0 font \"\" textcolor lt -1 norotate
load \"SandBoxDoublePowerSeries1.dat\"")