## [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error

 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-08-31 18:56:04 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-08-31 14:55 Message: Logged In: YES user_id=28849 What is happening, partially, is that maxima wants to convert the given integral to an equivalent integral from 0 to infinity. I don't know why we get an internal error for 1/(x^8-1). However, we can work around the problem by changing the order in method-radical-poly. The third cond clause could be moved up one more, just before the second clause containing the calls to ratp and ratfnt (which converts the finite integral to an infinite integral). What this does is try to compute the indefinite integral, and if we succeed, we just substitute the limits in. Then all of the examples here work, and the test suite passes. ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```

 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-06-11 22:24:57 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-06-21 03:38:58 ```Bugs item #1504505, was opened at 2006-06-11 16:24 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- >Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 21:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-06-21 05:24:39 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- >Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-08-31 18:49:06 ```Bugs item #1504505, was opened at 2006-06-11 15:24 Message generated for change (Comment added) made by macrakis You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-20 22:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 20:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-08-31 18:56:04 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-08-31 14:55 Message: Logged In: YES user_id=28849 What is happening, partially, is that maxima wants to convert the given integral to an equivalent integral from 0 to infinity. I don't know why we get an internal error for 1/(x^8-1). However, we can work around the problem by changing the order in method-radical-poly. The third cond clause could be moved up one more, just before the second clause containing the calls to ratp and ratfnt (which converts the finite integral to an infinite integral). What this does is try to compute the indefinite integral, and if we succeed, we just substitute the limits in. Then all of the examples here work, and the test suite passes. ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-11-04 16:03:03 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-11-04 11:03 Message: Logged In: YES user_id=28849 For the record, here's is what is happening. The integral is converted to an integral from 0 to inf. Since it's still rational, it uses contour integration over the poles of the rational inside the keyhole contour. To compute this, a partial fraction expansion is done, and all parts are integrated separately. This works until the rational (4*x^2+8*x+4)/(17*x^4+64*x^3+96*x^2+64*x+16) is integrated. At this point the function RES is called and gets a division by zero. Not sure why yet. Perhaps some confusion on computing the residues for the complicated roots of the denominator above? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-08-31 14:55 Message: Logged In: YES user_id=28849 What is happening, partially, is that maxima wants to convert the given integral to an equivalent integral from 0 to infinity. I don't know why we get an internal error for 1/(x^8-1). However, we can work around the problem by changing the order in method-radical-poly. The third cond clause could be moved up one more, just before the second clause containing the calls to ratp and ratfnt (which converts the finite integral to an infinite integral). What this does is try to compute the indefinite integral, and if we succeed, we just substitute the limits in. Then all of the examples here work, and the test suite passes. ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-11-04 16:54:28 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None Status: Open Resolution: None Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-11-04 11:54 Message: Logged In: YES user_id=28849 Not sure if this is right, but the maxima calculates the roots of 17*x^4+64*x^3+96*x^2+16 in a rather messy form. This seems to confuse \$residue (used in RES). If we modify the calls to \$residue to call \$rectform for the pole to simplify it, this integral works. Not exactly sure whether \$residue should do this itself or if RES should do it. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-11-04 11:03 Message: Logged In: YES user_id=28849 For the record, here's is what is happening. The integral is converted to an integral from 0 to inf. Since it's still rational, it uses contour integration over the poles of the rational inside the keyhole contour. To compute this, a partial fraction expansion is done, and all parts are integrated separately. This works until the rational (4*x^2+8*x+4)/(17*x^4+64*x^3+96*x^2+64*x+16) is integrated. At this point the function RES is called and gets a division by zero. Not sure why yet. Perhaps some confusion on computing the residues for the complicated roots of the denominator above? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-08-31 14:55 Message: Logged In: YES user_id=28849 What is happening, partially, is that maxima wants to convert the given integral to an equivalent integral from 0 to infinity. I don't know why we get an internal error for 1/(x^8-1). However, we can work around the problem by changing the order in method-radical-poly. The third cond clause could be moved up one more, just before the second clause containing the calls to ratp and ratfnt (which converts the finite integral to an infinite integral). What this does is try to compute the indefinite integral, and if we succeed, we just substitute the limits in. Then all of the examples here work, and the test suite passes. ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1504505 ] integrate( 1/(x^8-1), x, 0, 1/2) => internal error From: SourceForge.net - 2006-11-05 02:44:57 ```Bugs item #1504505, was opened at 2006-06-11 18:24 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&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 - Integration Group: None >Status: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate( 1/(x^8-1),x,0,1/2) => internal error Initial Comment: integrate( 1/(x^8-1), x, 0, 1/2 ) => Divison by 0 Smaller exponents don't cause problem. Same problem with gcd: spmod. Using the indefinite-integral at the limits works fine. 5.9.3 gcl windows ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-11-04 21:44 Message: Logged In: YES user_id=28849 The bug is really in \$TAYLOR. A workaround is to call \$RATSIMP in RESM1 to simplify the pole somewhat. Closing this bug. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-11-04 11:54 Message: Logged In: YES user_id=28849 Not sure if this is right, but the maxima calculates the roots of 17*x^4+64*x^3+96*x^2+16 in a rather messy form. This seems to confuse \$residue (used in RES). If we modify the calls to \$residue to call \$rectform for the pole to simplify it, this integral works. Not exactly sure whether \$residue should do this itself or if RES should do it. ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-11-04 11:03 Message: Logged In: YES user_id=28849 For the record, here's is what is happening. The integral is converted to an integral from 0 to inf. Since it's still rational, it uses contour integration over the poles of the rational inside the keyhole contour. To compute this, a partial fraction expansion is done, and all parts are integrated separately. This works until the rational (4*x^2+8*x+4)/(17*x^4+64*x^3+96*x^2+64*x+16) is integrated. At this point the function RES is called and gets a division by zero. Not sure why yet. Perhaps some confusion on computing the residues for the complicated roots of the denominator above? ---------------------------------------------------------------------- Comment By: Raymond Toy (rtoy) Date: 2006-08-31 14:55 Message: Logged In: YES user_id=28849 What is happening, partially, is that maxima wants to convert the given integral to an equivalent integral from 0 to infinity. I don't know why we get an internal error for 1/(x^8-1). However, we can work around the problem by changing the order in method-radical-poly. The third cond clause could be moved up one more, just before the second clause containing the calls to ratp and ratfnt (which converts the finite integral to an infinite integral). What this does is try to compute the indefinite integral, and if we succeed, we just substitute the limits in. Then all of the examples here work, and the test suite passes. ---------------------------------------------------------------------- Comment By: Stavros Macrakis (macrakis) Date: 2006-06-21 01:24 Message: Logged In: YES user_id=588346 integrate(1/(x^4+1),x,0,1/2) same problem. This is a subproblem (by partfrac) of previous problem. ---------------------------------------------------------------------- Comment By: Robert Dodier (robert_dodier) Date: 2006-06-20 23:38 Message: Logged In: YES user_id=501686 Assign category (Lisp Core - Integration). I looked at this a little bit but I can't tell what's going on. trace output from :lisp (trace polyform method-by-limits initial-analysis) suggests something interesting is happening but I can't tell what. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1504505&group_id=4933 ```