Re: repeated series expansion
Raymond Rogers <[email protected]> Fri, 16 Jul 2010 16:47:29 -0500
| Newsgroups | gmane.comp.mathematics.axiom.general |
|---|---|
| Organization | A constant variable |
| Message-ID | <[email protected]> |
This is a multi-part message in MIME format. --===============0332802755== Content-Type: multipart/alternative; boundary="------------060700070804000303040308" This is a multi-part message in MIME format. --------------060700070804000303040308 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Martin Rubey wrote: > Vladimir Skokov <[email protected]> writes: > > >> Dear all, >> >> I have only started to learn axiom. Could you help me please? >> I have an expression, say sin(x+y). How could I perform expansion >> withe respect ot x and than to y? >> >> i.e. >> >> series( series( sin(x+y),x=0 ),y=0 ) >> >> thank you in advance >> > > In axiom there is another option: > > (1) -> x := 'X::TS FRAC INT; y := 'Y::TS FRAC INT; > > Type: TaylorSeries(Fraction(Integer)) > (2) -> sin(x+y) > > 1 3 1 2 1 2 1 3 > (2) (Y + X) + (- - Y - - X Y - - X Y - - X ) + O(5) > 6 2 2 6 > Type: TaylorSeries(Fraction(Integer)) > > However, currently there is no domain for generalised multivariate > Taylor series. I don't know how difficult that would be, and I didn't > think the maths through either. > > That's interesting. How does "MultivariateTaylorSeriesCategory()" from bookvol 10.2 page 1026 fall short? I have never used it; but it seemed relevant to the above. Ray --------------060700070804000303040308 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: 8bit <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> <meta content="text/html;charset=UTF-8" http-equiv="Content-Type"> <title></title> </head> <body bgcolor="#ffffff" text="#000000"> Martin Rubey wrote: <blockquote cite="mid:[email protected]" type="cite"> <pre wrap="">Vladimir Skokov <a class="moz-txt-link-rfc2396E" href="mailto:[email protected]"><[email protected]></a> writes: </pre> <blockquote type="cite"> <pre wrap="">Dear all, I have only started to learn axiom. Could you help me please? I have an expression, say sin(x+y). How could I perform expansion withe respect ot x and than to y? i.e. series( series( sin(x+y),x=0 ),y=0 ) thank you in advance </pre> </blockquote> <pre wrap=""><!----> In axiom there is another option: (1) -> x := 'X::TS FRAC INT; y := 'Y::TS FRAC INT; Type: TaylorSeries(Fraction(Integer)) (2) -> sin(x+y) 1 3 1 2 1 2 1 3 (2) (Y + X) + (- - Y - - X Y - - X Y - - X ) + O(5) 6 2 2 6 Type: TaylorSeries(Fraction(Integer)) However, currently there is no domain for generalised multivariate Taylor series. I don't know how difficult that would be, and I didn't think the maths through either. </pre> </blockquote> That's interesting. How does "MultivariateTaylorSeriesCategory()" from bookvol 10.2 page 1026 fall short?<br> I have never used it; but it seemed relevant to the above.<br> <br> Ray <br> </body> </html> --------------060700070804000303040308-- --===============0332802755== Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Disposition: inline _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math --===============0332802755==--