MathAction #132 Series expansion with complex doesn't print expansion point in type expression

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Original Date: Sun, 13 Mar 2005 08:44:43 -0600

axiom

series(sin(x),x=%i)

$\label{eq1}\begin{array}{@{}l} \displaystyle {\sin \left({i}\right)}+{{\cos \left({i}\right)}\ {\left(x - i \right)}}-{{{\sin \left({i}\right)}\over 2}\ {{\left(x - i \right)}^2}}-{{{\cos \left({i}\right)}\over 6}\ {{\left(x - i \right)}^3}}+ \ \ \displaystyle {{{\sin \left({i}\right)}\over{24}}\ {{\left(x - i \right)}^4}}+{{{\cos \left({i}\right)}\over{120}}\ {{\left(x - i \right)}^5}}-{{{\sin \left({i}\right)}\over{720}}\ {{\left(x - i \right)}^6}}- \ \ \displaystyle {{{\cos \left({i}\right)}\over{5040}}\ {{\left(x - i \right)}^7}}+{{{\sin \left({i}\right)}\over{40320}}\ {{\left(x - i \right)}^8}}+{{{\cos \left({i}\right)}\over{362880}}\ {{\left(x - i \right)}^9}}- \ \ \displaystyle {{{\sin \left({i}\right)}\over{3628800}}\ {{\left(x - i \right)}^{10}}}+{O \left({{\left(x - i \right)}^{11}}\right)}$

(1)

Type: UnivariatePuiseuxSeries(Expression(Complex(Integer)),x,)

Type: UnivariatePuiseuxSeries?(Expression Complex Integer,x,)
                                                           ^^

but for Integer for example

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

With complex doesn't print expansion point (type): Sun, 20 Mar 2005 14:30:14 -0600 reply

file: msgdb.boot.pamphlet function: brightPrint0

x = '"%i" => MARG + 3 ------------------------ Each message may contain formatting codes and and parameter codes. The formatting codes are: %b turn on bright printing %ceoff turn off centering %ceon turn on centering %d turn off bright printing %f user defined printing %i start indentation of 3 more spaces %l start a new line %m math-print an expression %rjoff turn off right justification (actually ragged left) %rjon turn on right justification (actually ragged left) %s pretty-print as an S-expression %u unindent 3 spaces %x# insert # spaces

With binary infix operator in expansion point, transform it to fortran (displayed type) -- Sun, 20 Mar 2005 14:33:53 -0600 reply

axiom

series(sin(x),x=%pi/2)

$\label{eq2}\begin{array}{@{}l} \displaystyle 1 -{{1 \over 2}\ {{\left(x -{\pi \over 2}\right)}^2}}+{{1 \over{2 4}}\ {{\left(x -{\pi \over 2}\right)}^4}}-{{1 \over{720}}\ {{\left(x -{\pi \over 2}\right)}^6}}+ \ \ \displaystyle {{1 \over{40320}}\ {{\left(x -{\pi \over 2}\right)}^8}}-{{1 \over{3 628800}}\ {{\left(x -{\pi \over 2}\right)}^{10}}}+{O \left({{\left(x -{\pi \over 2}\right)}^{11}}\right)}$

(2)

Type: UnivariatePuiseuxSeries(Expression(Integer),x,%pi/2)

axiom

series(sin(x),x=%e)

$\label{eq3}\begin{array}{@{}l} \displaystyle {\sin \left({e}\right)}+{{\cos \left({e}\right)}\ {\left(x - e \right)}}-{{{\sin \left({e}\right)}\over 2}\ {{\left(x - e \right)}^2}}-{{{\cos \left({e}\right)}\over 6}\ {{\left(x - e \right)}^3}}+ \ \ \displaystyle {{{\sin \left({e}\right)}\over{24}}\ {{\left(x - e \right)}^4}}+{{{\cos \left({e}\right)}\over{120}}\ {{\left(x - e \right)}^5}}-{{{\sin \left({e}\right)}\over{720}}\ {{\left(x - e \right)}^6}}- \ \ \displaystyle {{{\cos \left({e}\right)}\over{5040}}\ {{\left(x - e \right)}^7}}+{{{\sin \left({e}\right)}\over{40320}}\ {{\left(x - e \right)}^8}}+{{{\cos \left({e}\right)}\over{362880}}\ {{\left(x - e \right)}^9}}- \ \ \displaystyle {{{\sin \left({e}\right)}\over{3628800}}\ {{\left(x - e \right)}^{10}}}+{O \left({{\left(x - e \right)}^{11}}\right)}$

(3)

Type: UnivariatePuiseuxSeries(Expression(Integer),x,%e)

axiom

series(sin(x),x=%e+3)

$\label{eq4}\begin{array}{@{}l} \displaystyle {\sin \left({e + 3}\right)}+{{\cos \left({e + 3}\right)}\ {\left(x -{e + 3}\right)}}-{{{\sin \left({e + 3}\right)}\over 2}\ {{\left(x -{e + 3}\right)}^2}}- \ \ \displaystyle {{{\cos \left({e + 3}\right)}\over 6}\ {{\left(x -{e + 3}\right)}^3}}+{{{\sin \left({e + 3}\right)}\over{24}}\ {{\left(x -{e + 3}\right)}^4}}+ \ \ \displaystyle {{{\cos \left({e + 3}\right)}\over{120}}\ {{\left(x -{e + 3}\right)}^5}}-{{{\sin \left({e + 3}\right)}\over{720}}\ {{\left(x -{e + 3}\right)}^6}}- \ \ \displaystyle {{{\cos \left({e + 3}\right)}\over{5040}}\ {{\left(x -{e + 3}\right)}^7}}+{{{\sin \left({e + 3}\right)}\over{40320}}\ {{\left(x -{e + 3}\right)}^8}}+ \ \ \displaystyle {{{\cos \left({e + 3}\right)}\over{362880}}\ {{\left(x -{e + 3}\right)}^9}}-{{{\sin \left({e + 3}\right)}\over{3628800}}\ {{\left(x -{e + 3}\right)}^{10}}}+ \ \ \displaystyle {O \left({{\left(x -{e + 3}\right)}^{11}}\right)}$

(4)

Type: UnivariatePuiseuxSeries(Expression(Integer),x,%e+3)

axiom

series(sin(x),x=%i+7)

$\label{eq5}\begin{array}{@{}l} \displaystyle {\sin \left({7 + i}\right)}+{{\cos \left({7 + i}\right)}\ {\left(x -{7 + i}\right)}}-{{{\sin \left({7 + i}\right)}\over 2}\ {{\left(x -{7 + i}\right)}^2}}- \ \ \displaystyle {{{\cos \left({7 + i}\right)}\over 6}\ {{\left(x -{7 + i}\right)}^3}}+{{{\sin \left({7 + i}\right)}\over{24}}\ {{\left(x -{7 + i}\right)}^4}}+ \ \ \displaystyle {{{\cos \left({7 + i}\right)}\over{120}}\ {{\left(x -{7 + i}\right)}^5}}-{{{\sin \left({7 + i}\right)}\over{720}}\ {{\left(x -{7 + i}\right)}^6}}- \ \ \displaystyle {{{\cos \left({7 + i}\right)}\over{5040}}\ {{\left(x -{7 + i}\right)}^7}}+{{{\sin \left({7 + i}\right)}\over{40320}}\ {{\left(x -{7 + i}\right)}^8}}+ \ \ \displaystyle {{{\cos \left({7 + i}\right)}\over{362880}}\ {{\left(x -{7 + i}\right)}^9}}-{{{\sin \left({7 + i}\right)}\over{3628800}}\ {{\left(x -{7 + i}\right)}^{10}}}+ \ \ \displaystyle {O \left({{\left(x -{7 + i}\right)}^{11}}\right)}$

(5)

Type: UnivariatePuiseuxSeries(Expression(Complex(Integer)),x,7+)

file:                  format.boot.pamphlet
Infix Binary Operator: "=" "+" "-" "" "/" "*" "^" (i-output.boot.pamphlet => function isBinaryInfix)
function:              form2String1 call fortexp0   isBinaryInfix op => fortexp0 [op,:argl]

----------------------------------------
In fortPre1 (file:newfort.boot.pamphlet)

  fortPre1 e ==
replace spad function names by Fortran equivalents
    -- where appropriate, replace integers by floats
    -- extract complex numbers
    -- replace powers of %e by calls to EXP
    -- replace x*2 by xx etc.
    -- replace ROOT by either SQRT or **(1./ ... )
    -- replace N-ary by binary functions
    -- strip the % character off objects like %pi etc..

PATCH: Replace %i (indent) by %I --test, Thu, 24 Mar 2005 12:03:22 -0600 reply

This patch replace all %i (format) by %I. Go to src/interp directory and type grep -r %i\> . It's not heavily tested but relatively simple (check it). See above for details.

powerSeries.patch

split form #122 --Bill Page, Thu, 24 Mar 2005 13:42:38 -0600 reply

Severity: normal => critical

Name of this issue --unknown, Fri, 25 Mar 2005 12:39:26 -0600 reply

Bill, I think you can change the name of this issue. The problem concerns expansion point that involve binary operator too (for example 1+3*i).

... --kratt6, Fri, 28 Dec 2007 13:17:46 -0800 reply

Category: Axiom Compiler => Axiom Interpreter

Subject: Be Bold !!

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