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From: SourceForge.net <noreply@so...>  20080516 20:11:09

Bugs item #1965640, was opened at 20080516 22:04 Message generated for change (Comment added) made by crategus You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1965640&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with $specint Initial Comment: I would like to open a bug report to collect the results of investigations of the function $specint. To get an overview of the problems with $specint I have taken the 99 tabulated Laplace transforms from the website of EqWorld. 55 of the 99 examples fail with the original code. I have divided the problems in the following cases: 1. Maxima has no algorithm: In most cases Maxima gives an internal symbol like otherdefinttofollownegtest or arbpowfailed. This is a known problem. In some cases we get a correct noun form of the unevaluated integral. At last there are many problems which gives a wrong answer. A lot of examples include terms like t^(1) ... or t^(1/2) ... Maxima can't calculat these integrals but we know solutions. A simple type of integral Maxima can't evaluate is the division by the sum of constants: (%i7) specint(%e^(s*t)/(x+y),t); (%o7) otherdefinttofollownegtest In this cases the exponential function is hidden in a summation. I have found a correction which works generally and gives the correct result: (%i7) specint(%e^(s*t)/(x+y),t); (%o7) (1/(x+y)*s) 2. Maxima has an algorithm for a special function but don't give the correct result: We get no results for functions like bessel_k, bessel_y, log, erf, erfc etc. For all these functions Laplace transforms are tabulated. Beside the test of EqWorld I tried to get results for the internal functions %l[n,a](x)  the Laguerre function  or %he[n](x)  the Hermite function. But I dont' get the expected result. Here the example for the Laguerre function: (%i6) kill(all); (%o0) done (%i1) assume(s>0,n>0),declare(n,integer); (%o1) [s > 0,n > 0] (%i2) specint(%e^(2*t)*%l[n,0](t),t); Maxima encountered a Lisp error: Error in MACSYMATOPLEVEL [or a callee]: $N is not of type NUMBER. Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. After correction of the code (the correction is not included in the diff appended to the next post): (%i6) kill(all); (%o0) done (%i1) assume(s>0,n>0),declare(n,integer); (%o1) [s > 0,n > 0] (%i2) specint(%e^(s*t)*%l[n,0](t),t); (%o2) (11/s)^n/s In the case of the Laguerre function I have found a bug in the transformation. After correction, Maxima gives the expected result shown above for the Laguerre function. There may be further bugs. Or limitations of the algorithmen prevend the calculation of results. At least, these limitations should be documented for the user. 3. Maxima gets extra factors or terms in the result A simple example is the bessel_i function. Here we get an additional phase factor: %e^(%i*%pi*v/(1)^(v2/2) in all calculations. This factor vanish when we introduce a small correction to the code. In other cases the problem seems to be more difficult. Dieter Kaiser  >Comment By: Crategus (crategus) Date: 20080516 22:11 Message: Logged In: YES user_id=2039760 Originator: YES As a first step to improve the code of $specint I would like to present 7 changes: 1. Function DEFEXEC If we cant't find a parameter, we apply $factor to the expression. Now Maxima finds the result for expressions like t/(x+y) > 1/(s^2(x+y)) where x and y are free of the integration variable. 2. Function ARBPOW1 I have specialized the pattern match to be sure that in the expression c*t^v the parameter c is free of the integration variable. This condition now will fail if we enter $specint with expression like u(t) or t^(1/2)*(a+t)^(1) and with the changes below we get nice and correct noun forms. 3. Function LTSFLOG Because we have specialized the pattern match we add at the end of the function as return value a noun form. 4. Function LTARBPOW A lot of integrals fail at this point. We add as the return value a noun form. 5. Function LTSFLOG, Condition ONEI This is an example how we can avoid additional phase factors. If we use %i directly in the calculation all additional phase factors in the calculations vanish and the results are correct. There are more places we can apply this change to obtain easier results. 6. Bug in LTEXP and F35P147 I have found a bug in the routine ltexp and f35p147. This bug prevents the calculation of integrals with e.g. sin(2*sqrt(a*t)). $SPECINT gives the result 0. Here the output of Maxima after correction: (%i6) radcan(specint(%e^(s*t)*sin(2*sqrt(a*t)),t)); (%o6) sqrt(%pi)*sqrt(a)*%e^(a/s)/s^(3/2) That is perfectly the tabulated expression and $SPECINT now works for a lot of other integrals too. 7. Extension of the algorithm To show how we can extend the algorithm of $SPECINT to calculate further integrals, I have added code to calculate integrals of the form t^1*(%e^(a*t)%e^(b*t)). The code works also for integrals like t^1*sin(a*t). Here an example (%i4) specint(%e^(s*t)*t^1*sin(a*t),t); (%o4) %i*(log(s%i*a)log(s+%i*a))/2 That's equivalent to the tabulated answer atan(a/s). With this changes problems 55, 150 and 157 of rtest14.mac will produce different results. In all cases the noun form is improved and now more correct. The numbers of correct results of the test file test_eqworld.mac is increased to 87. When Maxima can't evaluate the integral but returns a correct noun form I declared the test as "(OK noun form)". There are 12 remaining examples which fails. This examples mostly include the log or erf function. I think there is something wrong with the mathematic. I have added a diff to show the above described changes to the code. Hint: The test file will stop 5 times and ask for the sign of the internal variable psey. That's a known bug. I have this bug not remarked as an error, because the results are correct. I try to find the reason of the bug. Dieter Kaiser File Added: diff_hypgeo.txt  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1965640&group_id=4933 
From: SourceForge.net <noreply@so...>  20080516 20:04:59

Bugs item #1965640, was opened at 20080516 22:04 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=1965640&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: Includes proposed fix Status: Open Resolution: None Priority: 5 Private: No Submitted By: Crategus (crategus) Assigned to: Nobody/Anonymous (nobody) Summary: Problems with $specint Initial Comment: I would like to open a bug report to collect the results of investigations of the function $specint. To get an overview of the problems with $specint I have taken the 99 tabulated Laplace transforms from the website of EqWorld. 55 of the 99 examples fail with the original code. I have divided the problems in the following cases: 1. Maxima has no algorithm: In most cases Maxima gives an internal symbol like otherdefinttofollownegtest or arbpowfailed. This is a known problem. In some cases we get a correct noun form of the unevaluated integral. At last there are many problems which gives a wrong answer. A lot of examples include terms like t^(1) ... or t^(1/2) ... Maxima can't calculat these integrals but we know solutions. A simple type of integral Maxima can't evaluate is the division by the sum of constants: (%i7) specint(%e^(s*t)/(x+y),t); (%o7) otherdefinttofollownegtest In this cases the exponential function is hidden in a summation. I have found a correction which works generally and gives the correct result: (%i7) specint(%e^(s*t)/(x+y),t); (%o7) (1/(x+y)*s) 2. Maxima has an algorithm for a special function but don't give the correct result: We get no results for functions like bessel_k, bessel_y, log, erf, erfc etc. For all these functions Laplace transforms are tabulated. Beside the test of EqWorld I tried to get results for the internal functions %l[n,a](x)  the Laguerre function  or %he[n](x)  the Hermite function. But I dont' get the expected result. Here the example for the Laguerre function: (%i6) kill(all); (%o0) done (%i1) assume(s>0,n>0),declare(n,integer); (%o1) [s > 0,n > 0] (%i2) specint(%e^(2*t)*%l[n,0](t),t); Maxima encountered a Lisp error: Error in MACSYMATOPLEVEL [or a callee]: $N is not of type NUMBER. Automatically continuing. To reenable the Lisp debugger set *debuggerhook* to nil. After correction of the code (the correction is not included in the diff appended to the next post): (%i6) kill(all); (%o0) done (%i1) assume(s>0,n>0),declare(n,integer); (%o1) [s > 0,n > 0] (%i2) specint(%e^(s*t)*%l[n,0](t),t); (%o2) (11/s)^n/s In the case of the Laguerre function I have found a bug in the transformation. After correction, Maxima gives the expected result shown above for the Laguerre function. There may be further bugs. Or limitations of the algorithmen prevend the calculation of results. At least, these limitations should be documented for the user. 3. Maxima gets extra factors or terms in the result A simple example is the bessel_i function. Here we get an additional phase factor: %e^(%i*%pi*v/(1)^(v2/2) in all calculations. This factor vanish when we introduce a small correction to the code. In other cases the problem seems to be more difficult. Dieter Kaiser  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1965640&group_id=4933 
From: SourceForge.net <noreply@so...>  20080516 15:40:53

Bugs item #1686457, was opened at 20070322 18:52 Message generated for change (Comment added) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1686457&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: Share Libraries Group: None >Status: Closed >Resolution: Rejected Priority: 5 Private: No Submitted By: Nobody/Anonymous (nobody) Assigned to: Mario Rodriguez Riotorto (riotorto) Summary: cspline does not work Initial Comment: Maxima version: 5.11.0Maxima build date: 12:25 2/10/2007host type: i686pcmingw32lispimplementationtype: GNU Common Lisp (GCL)lispimplementationversion: GCL 2.6.8 I am running Vista on a pc and using wxMaxima with p:matrix([1,0.8619948],[0.5,0.95802009],[0,1.0986123],[0.5,1.2943767]) cspline(p) gives (%o5) 9.14034523948868*10^22*( (71825435496803423232*x^3+215476306490410269696*x^2+407633004344606888418*x+1207048040965873240689)* charfun2(x,inf,0.5)+(102765973994457923520*x^3+154148960991686885280*x^2+ 376969355089246552430*x+1201937400000985205250)*charfun2(x,0,inf)+ (30940538497654500288*x^3+154148960991686885280*x^2+376969273915256356068*x+1201937400000985205250)* charfun2(x,0.5,0)) This is a free or natural cubic spline and x^2 terms are supposed to be zero for the infinite range parts and the middle part which is indicated by charfun2(x,.5,0) is the same as the part corresponding to charfun2(x,0,inf) is the same except for the x^3 coefficient.  >Comment By: Robert Dodier (robert_dodier) Date: 20080516 09:40 Message: Logged In: YES user_id=501686 Originator: NO Closing this report as "rejected". Mario, thanks for looking at it.  Comment By: Mario Rodriguez Riotorto (riotorto) Date: 20080515 13:54 Message: Logged In: YES user_id=1270759 Originator: NO I don't see any problems. The abscissas from the given points range from a=1 to b=0.5, and according to the definition of natural cubic splines, if p is the interpolation function, the boundary conditions are p''(a)=p''(b)=0; it's easy to check that the result given by cspline fits this restriction. I don't understand why "x^2 terms are supposed to be zero".  Comment By: Robert Dodier (robert_dodier) Date: 20080514 23:07 Message: Logged In: YES user_id=501686 Originator: NO I don't understand what is the problem here. When I try this with cspline I get foo : (.06565092800000027*x^3+.1969527840000008*x^2 +.3725906320000009*x+1.103283576) *charfun2(x,minf,0.5) +(.09393164799999938*x^3+.1408974719999991*x^2 +.3445629760000002*x+1.0986123) *charfun2(x,0,inf) +(.02828071999999911*x^3+.1408974719999991*x^2+0.344562976*x +1.0986123) *charfun2(x,0.5,0) and when I plot that via draw2d (explicit (foo, x, 2, 1), points ([1, 0.5, 0, 0.5], [0.8619948, 0.95802009, 1.0986123, 1.2943767])); I see the spline is a smooth curve which passes through the points. Can someone point out what is wrong here?  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1686457&group_id=4933 