Screenshot instructions:
Windows
Mac
Red Hat Linux
Ubuntu
Click URL instructions:
Rightclick on ad, choose "Copy Link", then paste here →
(This may not be possible with some types of ads)
From: SourceForge.net <noreply@so...>  20081021 13:05:15

Bugs item #2184396, was opened at 20081021 22:05 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=2184396&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 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
From: SourceForge.net <noreply@so...>  20090219 03:09:59

Bugs item #2184396, was opened at 20081021 13:05 Message generated for change (Comment added) made by boud1 You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&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 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  Comment By: boud (boud1) Date: 20090219 02:31 Message: There's another bug related to this one IMHO: [ 2202764 ] Taylor series of sqrt(1+xy) http://sourceforge.net/tracker/index.php?func=detail&aid=2202764&group_id=4933&atid=104933 [This is why i came here  i had a Taylor series bug that i think is equivalent.] HACK SOLUTION: The bug is solved for me (maxima 5.10.0, debianetch) by setting radexpand : false; ANALYSIS: However, i'm not convinced that this is a sufficient response to the bug. i don't really know maxima well enough to know what would be most reasonable. (1) Set radexpand to false by default? And add more warnings in the documentation (or do we expect users to learn mathematics elsewhere than in software documentation?) (2) Tell maxima not to rewrite sqrt(X) as %i sqrt(X) when domain:real ? (3) Extend the "is X positive, negative or zero?" question to the cases where it still needs to be asked but so far does not get asked, i.e. when deciding whether sqrt(X*Y) = sqrt(X)*sqrt(Y) or sqrt(X*Y) =  sqrt(X)*sqrt(Y) ? (4) Decide not to invert the order of an expression inside sqrt( ... ) if domain:real, except when it's sure that the expression is positive?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
From: SourceForge.net <noreply@so...>  20091007 22:10:55

Bugs item #2184396, was opened at 20081021 15:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&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 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  >Comment By: Dieter Kaiser (crategus) Date: 20091008 00:10 Message: Maxima can simplify the sqrt function correctly. No simplification, when the sign of a is not known: (%i1) sqrt(a*z); (%o1) sqrt(a*z) Simplification for a a positive or b a negative value: (%i2) assume(a>0)$ (%i3) sqrt(a*z); (%o3) sqrt(a)*sqrt(z) (%i4) assume(b<0)$ (%i5) sqrt(b*z); (%o5) sqrt(b)*sqrt(z) The problem of this bug report is one of the factors of the example. The sign is wrongly determined to be negative: (%i8) sign(1(2sqrt(2))/x); (%o8) neg Therefore Maxima does the above simplification, which is wrong. Dieter Kaiser  Comment By: boud (boud1) Date: 20090219 03:31 Message: There's another bug related to this one IMHO: [ 2202764 ] Taylor series of sqrt(1+xy) http://sourceforge.net/tracker/index.php?func=detail&aid=2202764&group_id=4933&atid=104933 [This is why i came here  i had a Taylor series bug that i think is equivalent.] HACK SOLUTION: The bug is solved for me (maxima 5.10.0, debianetch) by setting radexpand : false; ANALYSIS: However, i'm not convinced that this is a sufficient response to the bug. i don't really know maxima well enough to know what would be most reasonable. (1) Set radexpand to false by default? And add more warnings in the documentation (or do we expect users to learn mathematics elsewhere than in software documentation?) (2) Tell maxima not to rewrite sqrt(X) as %i sqrt(X) when domain:real ? (3) Extend the "is X positive, negative or zero?" question to the cases where it still needs to be asked but so far does not get asked, i.e. when deciding whether sqrt(X*Y) = sqrt(X)*sqrt(Y) or sqrt(X*Y) =  sqrt(X)*sqrt(Y) ? (4) Decide not to invert the order of an expression inside sqrt( ... ) if domain:real, except when it's sure that the expression is positive?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
From: SourceForge.net <noreply@so...>  20091111 00:28:03

Bugs item #2184396, was opened at 20081021 15:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&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 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  >Comment By: Dieter Kaiser (crategus) Date: 20091111 01:27 Message: For the record. Again two example for a wrong sign: (%i3) sign(1(1+sqrt(2))/x); (%o3) neg (%i4) sign(1(1+sqrt(2))*x); (%o4) neg For these expressions the functions splitprod and splitsum are called. I have not figured out up to now the reason for the bug, but the variable x is lost somewhere and not taken into account to determine the sign. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091008 00:10 Message: Maxima can simplify the sqrt function correctly. No simplification, when the sign of a is not known: (%i1) sqrt(a*z); (%o1) sqrt(a*z) Simplification for a a positive or b a negative value: (%i2) assume(a>0)$ (%i3) sqrt(a*z); (%o3) sqrt(a)*sqrt(z) (%i4) assume(b<0)$ (%i5) sqrt(b*z); (%o5) sqrt(b)*sqrt(z) The problem of this bug report is one of the factors of the example. The sign is wrongly determined to be negative: (%i8) sign(1(2sqrt(2))/x); (%o8) neg Therefore Maxima does the above simplification, which is wrong. Dieter Kaiser  Comment By: boud (boud1) Date: 20090219 03:31 Message: There's another bug related to this one IMHO: [ 2202764 ] Taylor series of sqrt(1+xy) http://sourceforge.net/tracker/index.php?func=detail&aid=2202764&group_id=4933&atid=104933 [This is why i came here  i had a Taylor series bug that i think is equivalent.] HACK SOLUTION: The bug is solved for me (maxima 5.10.0, debianetch) by setting radexpand : false; ANALYSIS: However, i'm not convinced that this is a sufficient response to the bug. i don't really know maxima well enough to know what would be most reasonable. (1) Set radexpand to false by default? And add more warnings in the documentation (or do we expect users to learn mathematics elsewhere than in software documentation?) (2) Tell maxima not to rewrite sqrt(X) as %i sqrt(X) when domain:real ? (3) Extend the "is X positive, negative or zero?" question to the cases where it still needs to be asked but so far does not get asked, i.e. when deciding whether sqrt(X*Y) = sqrt(X)*sqrt(Y) or sqrt(X*Y) =  sqrt(X)*sqrt(Y) ? (4) Decide not to invert the order of an expression inside sqrt( ... ) if domain:real, except when it's sure that the expression is positive?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
From: SourceForge.net <noreply@so...>  20091111 22:43:52

Bugs item #2184396, was opened at 20081021 15:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&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 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  >Comment By: Dieter Kaiser (crategus) Date: 20091111 23:43 Message: I think I have found the bug in the routine compsplt. (defun compsplt (x) (cond ((atom x) (setq lhs x rhs 0)) ((atom (car x)) (setq lhs x rhs 0)) > ((not (null (cdr (symbols x)))) (compsplt2 x)) (t (compsplt1 x)))) At the marked line Maxima tests the CDR of the result of the function SYMBOLS. SYMBOLS returns a list of all variables of an expression. The list is of the form '($X $Y ...), where $X, $Y are the variables. Because COMPSPLT takes the CDR of SYMBOLS, one symbol in an expression is not recognized. Later in the algorithm the sign of this variable is not taken into account. For almost all expression this behavior seems to be no problem, but not for the examples of this bug report. When we change the test of the marked line: ((not (null (symbols x))) ... the sign of the given examples of this bug report are correct: (%i3) sign(1(2+sqrt(2))*x); (%o3) pnz (%i4) sign(1(2+sqrt(2))/x); (%o4) pnz and the reported expression does not longer factorize wrongly: (%i5) sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); (%o5) sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) One example of the testsuite no longer works. It is one of the new examples for the sign of the abs function. This is the example: (%i2) assume(abs(x)<%e/2+sin(1)); (%o2) [sin(1)+%e/2 > abs(x)] (%i3) is(x>2*%e); (%o3) true This will be the new result: (%i6) assume(abs(x)<%e/2+sin(1)); (%o6) [abs(x)+sin(1)+%e/2 > 0] (%i7) is(x>2*%e); (%o7) unknown This test no longer works, because the ordering of the terms will change. The reason is that COMPSPLT calls splitsum for one variable x in the expression too. So, with one exception the testsuite and the share_testsuite have no problems with the suggested change in COMPSPLT. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091111 01:27 Message: For the record. Again two example for a wrong sign: (%i3) sign(1(1+sqrt(2))/x); (%o3) neg (%i4) sign(1(1+sqrt(2))*x); (%o4) neg For these expressions the functions splitprod and splitsum are called. I have not figured out up to now the reason for the bug, but the variable x is lost somewhere and not taken into account to determine the sign. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091008 00:10 Message: Maxima can simplify the sqrt function correctly. No simplification, when the sign of a is not known: (%i1) sqrt(a*z); (%o1) sqrt(a*z) Simplification for a a positive or b a negative value: (%i2) assume(a>0)$ (%i3) sqrt(a*z); (%o3) sqrt(a)*sqrt(z) (%i4) assume(b<0)$ (%i5) sqrt(b*z); (%o5) sqrt(b)*sqrt(z) The problem of this bug report is one of the factors of the example. The sign is wrongly determined to be negative: (%i8) sign(1(2sqrt(2))/x); (%o8) neg Therefore Maxima does the above simplification, which is wrong. Dieter Kaiser  Comment By: boud (boud1) Date: 20090219 03:31 Message: There's another bug related to this one IMHO: [ 2202764 ] Taylor series of sqrt(1+xy) http://sourceforge.net/tracker/index.php?func=detail&aid=2202764&group_id=4933&atid=104933 [This is why i came here  i had a Taylor series bug that i think is equivalent.] HACK SOLUTION: The bug is solved for me (maxima 5.10.0, debianetch) by setting radexpand : false; ANALYSIS: However, i'm not convinced that this is a sufficient response to the bug. i don't really know maxima well enough to know what would be most reasonable. (1) Set radexpand to false by default? And add more warnings in the documentation (or do we expect users to learn mathematics elsewhere than in software documentation?) (2) Tell maxima not to rewrite sqrt(X) as %i sqrt(X) when domain:real ? (3) Extend the "is X positive, negative or zero?" question to the cases where it still needs to be asked but so far does not get asked, i.e. when deciding whether sqrt(X*Y) = sqrt(X)*sqrt(Y) or sqrt(X*Y) =  sqrt(X)*sqrt(Y) ? (4) Decide not to invert the order of an expression inside sqrt( ... ) if domain:real, except when it's sure that the expression is positive?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
From: SourceForge.net <noreply@so...>  20091114 18:37:54

Bugs item #2184396, was opened at 20081021 15:05 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&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: Closed >Resolution: Fixed Priority: 5 Private: No Submitted By: Satoshi Adachi (satoshi_adachi) Assigned to: Nobody/Anonymous (nobody) Summary: Wrong factorization of sqrt() Initial Comment: Dear Developers of Maxima, I found a wrong behavihor of sqrt(). It is a principle that sqrt(X*Y) should not be factorized to sqrt(X)*sqrt(Y) unless X and Y can be judged to be nonnegative. I found a case in which this principle is broken. Here is a program for demonstration:  /* * wrong_factorization_of_sqrt.maxima: * * S.Adachi 2008/10/01 */ display2d:false; /* real for 1 <= x <= 2 */ correct:sqrt((11/x)*(2/x1)); /* real for 2sqrt(2) <= x <= 2+sqrt(2) */ INCORRECT:sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); INCORRECT_AT_2:at(INCORRECT,[x=2]); SHOULD_BE_POSITIVE:float(INCORRECT_AT_2); /* END */  The result of execution is as follows:  Maxima 5.14.0cvs http://maxima.sourceforge.net Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL) Distributed under the GNU Public License. See the file COPYING. Dedicated to the memory of William Schelter. The function bug_report() provides bug reporting information. (%i1) batch(wrong_factorization_of_sqrt.maxima) batching #p/Volumes/HFS+2/home/adachi/work/307/wrong_factorization_of_sqrt.maxima (%i2) display2d : false (%o2) false (%i3) correct:sqrt((11/x)*(2/x1)) (%o3) sqrt((11/x)*(2/x1)) (%i4) INCORRECT:sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) (%o4) sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) (%i5) INCORRECT_AT_2:at(INCORRECT,[x = 2]) (%o5) sqrt((2sqrt(2))/21)*sqrt(1(sqrt(2)+2)/2) (%i6) SHOULD_BE_POSITIVE:float(INCORRECT_AT_2) (%o6) 0.70710678118655 (%o7) "wrong_factorization_of_sqrt.maxima"  At first, as is seen from (%i2) and (%o2), sqrt(11/x)*(2/x1)) is not factorized to sqrt(...)*sqrt(...) in any automatic way. This is the correct behavihor. Next, as is seen from (%i3) and (%o3), sqrt(1(2sqrt(2))/x)*((2+sqrt(2))/x1)) is factorized to sqrt((2sqrt(2))/x1)*sqrt(1(sqrt(2)+2)/x) in an automatic way. THIS IS AN INCORRECT BEHAVIOR. This expression is nonnegative for 2sqrt(2) <= x <= 2+sqrt(2). However, as is demonstrated by (%i4)(%o5), the calculated expression takes a negative value at x=2. Please stop the incorrect factorization of sqrt(X*Y) to sqrt(X)*sqrt(Y). Sincerely yours, Satoshi Adachi  >Comment By: Dieter Kaiser (crategus) Date: 20091114 19:37 Message: Fixed in compar.lisp revision 1.62. Closing this bug report as fixed. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091111 23:43 Message: I think I have found the bug in the routine compsplt. (defun compsplt (x) (cond ((atom x) (setq lhs x rhs 0)) ((atom (car x)) (setq lhs x rhs 0)) > ((not (null (cdr (symbols x)))) (compsplt2 x)) (t (compsplt1 x)))) At the marked line Maxima tests the CDR of the result of the function SYMBOLS. SYMBOLS returns a list of all variables of an expression. The list is of the form '($X $Y ...), where $X, $Y are the variables. Because COMPSPLT takes the CDR of SYMBOLS, one symbol in an expression is not recognized. Later in the algorithm the sign of this variable is not taken into account. For almost all expression this behavior seems to be no problem, but not for the examples of this bug report. When we change the test of the marked line: ((not (null (symbols x))) ... the sign of the given examples of this bug report are correct: (%i3) sign(1(2+sqrt(2))*x); (%o3) pnz (%i4) sign(1(2+sqrt(2))/x); (%o4) pnz and the reported expression does not longer factorize wrongly: (%i5) sqrt((1(2sqrt(2))/x)*((2+sqrt(2))/x1)); (%o5) sqrt((1(2sqrt(2))/x)*((sqrt(2)+2)/x1)) One example of the testsuite no longer works. It is one of the new examples for the sign of the abs function. This is the example: (%i2) assume(abs(x)<%e/2+sin(1)); (%o2) [sin(1)+%e/2 > abs(x)] (%i3) is(x>2*%e); (%o3) true This will be the new result: (%i6) assume(abs(x)<%e/2+sin(1)); (%o6) [abs(x)+sin(1)+%e/2 > 0] (%i7) is(x>2*%e); (%o7) unknown This test no longer works, because the ordering of the terms will change. The reason is that COMPSPLT calls splitsum for one variable x in the expression too. So, with one exception the testsuite and the share_testsuite have no problems with the suggested change in COMPSPLT. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091111 01:27 Message: For the record. Again two example for a wrong sign: (%i3) sign(1(1+sqrt(2))/x); (%o3) neg (%i4) sign(1(1+sqrt(2))*x); (%o4) neg For these expressions the functions splitprod and splitsum are called. I have not figured out up to now the reason for the bug, but the variable x is lost somewhere and not taken into account to determine the sign. Dieter Kaiser  Comment By: Dieter Kaiser (crategus) Date: 20091008 00:10 Message: Maxima can simplify the sqrt function correctly. No simplification, when the sign of a is not known: (%i1) sqrt(a*z); (%o1) sqrt(a*z) Simplification for a a positive or b a negative value: (%i2) assume(a>0)$ (%i3) sqrt(a*z); (%o3) sqrt(a)*sqrt(z) (%i4) assume(b<0)$ (%i5) sqrt(b*z); (%o5) sqrt(b)*sqrt(z) The problem of this bug report is one of the factors of the example. The sign is wrongly determined to be negative: (%i8) sign(1(2sqrt(2))/x); (%o8) neg Therefore Maxima does the above simplification, which is wrong. Dieter Kaiser  Comment By: boud (boud1) Date: 20090219 03:31 Message: There's another bug related to this one IMHO: [ 2202764 ] Taylor series of sqrt(1+xy) http://sourceforge.net/tracker/index.php?func=detail&aid=2202764&group_id=4933&atid=104933 [This is why i came here  i had a Taylor series bug that i think is equivalent.] HACK SOLUTION: The bug is solved for me (maxima 5.10.0, debianetch) by setting radexpand : false; ANALYSIS: However, i'm not convinced that this is a sufficient response to the bug. i don't really know maxima well enough to know what would be most reasonable. (1) Set radexpand to false by default? And add more warnings in the documentation (or do we expect users to learn mathematics elsewhere than in software documentation?) (2) Tell maxima not to rewrite sqrt(X) as %i sqrt(X) when domain:real ? (3) Extend the "is X positive, negative or zero?" question to the cases where it still needs to be asked but so far does not get asked, i.e. when deciding whether sqrt(X*Y) = sqrt(X)*sqrt(Y) or sqrt(X*Y) =  sqrt(X)*sqrt(Y) ? (4) Decide not to invert the order of an expression inside sqrt( ... ) if domain:real, except when it's sure that the expression is positive?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2184396&group_id=4933 
Sign up for the SourceForge newsletter:
No, thanks