## [Maxima-bugs] [ maxima-Bugs-629539 ] taylor(x + sqrt(1+x^2),x,a,2)

 [Maxima-bugs] [ maxima-Bugs-629539 ] taylor(x + sqrt(1+x^2),x,a,2) From: - 2002-10-27 20:40:38 ```Bugs item #629539, was opened at 2002-10-27 14:40 You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Barton Willis (willisb) Assigned to: Nobody/Anonymous (nobody) Summary: taylor(x + sqrt(1+x^2),x,a,2) Initial Comment: (C1) display2d : false; (D1) FALSE (C2) p : x + sqrt(1+x^2); (D2) SQRT(x^2+1)+x With ratfac true, Maxima finds the Taylor polynomial of p centered at a with no problem (C3) ratfac : true; (D3) TRUE (C4) taylor(p,x,a,2); (D4) SQRT(a^2+1)+a+(a^2+SQRT(a^2+1)*a+1)*(x-a)/(a^2+1) +(x-a)^2/(2*SQRT(a^2+1)*(a^2+1)) But setting ratfac to false, we get an error (C5) ratfac : false; (D5) FALSE (C6) taylor(p,x,a,2); Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C7) This same bug may be responsible for the bug (C11) taylor(asin(x),x,a,2), ratfac : false; Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C12) taylor(asin(x),x,a,2), ratfac : true; Is (a-1)*(a+1) positive, negative, or zero? neg; (D12) ATAN2(a,-SQRT(1-a^2))-(a^2+SQRT(a^2-1)*a-1)*%I*(x-a) /((a+SQRT(a^2-1))*(a^2-1)) +(2*a^3+2*SQRT(a^2-1)*a^2-2*a-SQRT(a^2-1))*%I*a *(x-a)^2 /(2*(a+SQRT(a^2-1))^2*(a^2-1)^2) (C13) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-629539 ] taylor(x + sqrt(1+x^2),x,a,2) From: - 2002-10-27 20:40:38 ```Bugs item #629539, was opened at 2002-10-27 14:40 You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Barton Willis (willisb) Assigned to: Nobody/Anonymous (nobody) Summary: taylor(x + sqrt(1+x^2),x,a,2) Initial Comment: (C1) display2d : false; (D1) FALSE (C2) p : x + sqrt(1+x^2); (D2) SQRT(x^2+1)+x With ratfac true, Maxima finds the Taylor polynomial of p centered at a with no problem (C3) ratfac : true; (D3) TRUE (C4) taylor(p,x,a,2); (D4) SQRT(a^2+1)+a+(a^2+SQRT(a^2+1)*a+1)*(x-a)/(a^2+1) +(x-a)^2/(2*SQRT(a^2+1)*(a^2+1)) But setting ratfac to false, we get an error (C5) ratfac : false; (D5) FALSE (C6) taylor(p,x,a,2); Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C7) This same bug may be responsible for the bug (C11) taylor(asin(x),x,a,2), ratfac : false; Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C12) taylor(asin(x),x,a,2), ratfac : true; Is (a-1)*(a+1) positive, negative, or zero? neg; (D12) ATAN2(a,-SQRT(1-a^2))-(a^2+SQRT(a^2-1)*a-1)*%I*(x-a) /((a+SQRT(a^2-1))*(a^2-1)) +(2*a^3+2*SQRT(a^2-1)*a^2-2*a-SQRT(a^2-1))*%I*a *(x-a)^2 /(2*(a+SQRT(a^2-1))^2*(a^2-1)^2) (C13) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-629539 ] taylor(x + sqrt(1+x^2),x,a,2) From: SourceForge.net - 2006-04-09 20:31:02 ```Bugs item #629539, was opened at 2002-10-27 13:40 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. >Category: Lisp Core - Taylor Group: None Status: Open Resolution: None Priority: 5 Submitted By: Barton Willis (willisb) Assigned to: Nobody/Anonymous (nobody) Summary: taylor(x + sqrt(1+x^2),x,a,2) Initial Comment: (C1) display2d : false; (D1) FALSE (C2) p : x + sqrt(1+x^2); (D2) SQRT(x^2+1)+x With ratfac true, Maxima finds the Taylor polynomial of p centered at a with no problem (C3) ratfac : true; (D3) TRUE (C4) taylor(p,x,a,2); (D4) SQRT(a^2+1)+a+(a^2+SQRT(a^2+1)*a+1)*(x-a)/(a^2+1) +(x-a)^2/(2*SQRT(a^2+1)*(a^2+1)) But setting ratfac to false, we get an error (C5) ratfac : false; (D5) FALSE (C6) taylor(p,x,a,2); Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C7) This same bug may be responsible for the bug (C11) taylor(asin(x),x,a,2), ratfac : false; Quotient by a polynomial of higher degree -- an error. Quitting. To debug this try DEBUGMODE(TRUE);) (C12) taylor(asin(x),x,a,2), ratfac : true; Is (a-1)*(a+1) positive, negative, or zero? neg; (D12) ATAN2(a,-SQRT(1-a^2))-(a^2+SQRT(a^2-1)*a-1)*%I*(x-a) /((a+SQRT(a^2-1))*(a^2-1)) +(2*a^3+2*SQRT(a^2-1)*a^2-2*a-SQRT(a^2-1))*%I*a *(x-a)^2 /(2*(a+SQRT(a^2-1))^2*(a^2-1)^2) (C13) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=629539&group_id=4933 ```