[sage-support] Re: Problem with integrals and assumptions
On Nov 27, 2:16 am, kcrisman kcris...@gmail.com wrote: Here's this in Sage. See the end of this post for a solution you might like better than the ramblings in between :) -- | Sage Version 4.7.2, Release Date: 2011-10-29 | | Type notebook() for the GUI, and license() for information. | -- sage: var('m r a R') (m, r, a, R) sage: assume(2*m-3==0) ^[[A^[ integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r) -2*r^(-2*m + 1)/((2*m - 1)*a^2) - log(r)/a^4 sage: forget() sage: assume(2*m-10) sage: integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r) -2*r^(-2*m + 1)/((2*m - 1)*a^2) + r^(-2*m + 3)/((2*m - 3)*a^4) Just to make the point that this is something we can't really avoid, using Maxima as the default integration engine. Maxima 5.25.0http://maxima.sourceforge.net using Lisp SBCL 1.0.24 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) integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r); Is 2 m - 3 zero or nonzero? zero ; 1 - 2 m 2 r log(r) (%o1) - -- 2 4 a (1 - 2 m) a (%i2) integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r); Is 2 m - 3 zero or nonzero? nonzero; Is 2 m - 1 zero or nonzero? nonzero; 1 - 2 m 3 - 2 m 2 r r (%o2) - 2 4 a (1 - 2 m) a (3 - 2 m) Bottom line, sage currently has to be coddled excessively via assumptions into giving any result at all, verses system which give results which may happen to be incorrect for certain values. But that sounds dangerous to me, at least for this particular example. How is it different from this example? sage: var('n') n sage: integrate(x^n,x) ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before integral evaluation *may* help (example of legal syntax is 'assume(n+10)', see `assume?` for more details) Is n+1 zero or nonzero? If anything, we've probably been too cavalier with our use of Maxima's fine-grained simplification and other routines at times; it seems dangerous to go the other way. At the same time, we have sage: integrate(x^n,x,algorithm='sympy') x^(n + 1)/(n + 1) which will at least sometimes do what you are interested in. See the PS for the fact that it doesn't always do so. - kcrisman PS to devs: However sage: integrate(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4),r,algorithm='sympy') --- AttributeError Traceback (most recent call last) v, a, b) 37 else: 38 result = sympy.integrate(ex, (v, a._sympy_(), b._sympy_())) --- 39 return result._sage_() 40 41 def mma_free_integrator(expression, v, a=None, b=None): AttributeError: 'Integral' object has no attribute '_sage_' That looks like a bug in our sympy interface. Any takers? Note that: sage: var('m r a') (m, r, a) sage: f=expand(1/r^(2*m+2)*(2*(r/a)^2-(r/a)^4)) sage: f.integrate(r,algorithm=sympy) -2*r^(-2*m + 1)/((2*m - 1)*a^2) + r^(-2*m + 3)/((2*m - 3)*a^4) Andrzej Chrzeszczyk -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Sage problem
Dear Sage Gurus, I was installed Virtual Box and later sage, when I execute SAGE ver last line on screen is writen automatically by SAGE is Starting factory twisted... and later I can write I was write SAGE: 2+2 and how execute this ? Sage treated user as enemy?!? Answer me privately and I'm apologize for my ignorance. Best wishes Artur -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Sage problem
Hi Artur, my first impression of your post was: Not enough information (thus, virtually impossible to answer), and rather rude. Perhaps you find http://catb.org/~esr/faqs/smart-questions.html worth reading. On 27 Nov., 15:15, Artur gra...@csl.pl wrote: I was installed Virtual Box and later sage, when I execute SAGE ver last line on screen is writen automatically by SAGE is Starting factory twisted... and later I can write I was write SAGE: 2+2 and how execute this ? In general, if one has problems with any piece of software and asks for help, one should at least provide some information about the machine: * What CPU? * What operating system (apparently Windows, since you mention vmware)? * What version of Sage did you download? * Are you using Sage on the command line or in your browser (and also: What browser?)? * Does Sage start? If it doesn't: What is the error message? * What exactly is the problem? From the little what you say, I conclude that you use Sage on a Windows machine, you are able to start Sage, a Sage notebook starts in your browser, you write 2+2 and then you don't know how to continue. Did you try to read some documentation?You would certainly learn that in the commandline version, you simply press the Enter key to execute 2+2. But in the notebook version (i.e., when you work with your browser), there are two ways to execute 2+2: Pressing Shift+Enter on your keyboard, or clicking on the evaluate link at the bottom of the cell you were editing. If you just hit Enter (not Shift+Enter), then you remain in the same cell end can put several lines in a single cell. Sage treated user as enemy?!? That's what I mean by rather rude. It feels as if you treat the Sage developers as enemy, which is not a wise attitude for getting help. Answer me privately... No. At least I've put you as Cc to my post. But I think it is a good idea to have a public support forum. After all, if one user has a problem that is solved here, then other users with similar problems can easily find that answer by a little Google search. But I think help will only be possible if you clearly explain the problem. Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
P.S. and Fedora version is 14 W dniu 2011-11-27 18:18, Simon King pisze: Hi Artur, my first impression of your post was: Not enough information (thus, virtually impossible to answer), and rather rude. Perhaps you find http://catb.org/~esr/faqs/smart-questions.html worth reading. On 27 Nov., 15:15, Arturgra...@csl.pl wrote: I was installed Virtual Box and later sage, when I execute SAGE ver last line on screen is writen automatically by SAGE is Starting factorytwisted... and later I can write I was write SAGE: 2+2 and how execute this ? In general, if one has problems with any piece of software and asks for help, one should at least provide some information about the machine: * What CPU? * What operating system (apparently Windows, since you mention vmware)? * What version of Sage did you download? * Are you using Sage on the command line or in your browser (and also: What browser?)? * Does Sage start? If it doesn't: What is the error message? * What exactly is the problem? From the little what you say, I conclude that you use Sage on a Windows machine, you are able to start Sage, a Sage notebook starts in your browser, you write 2+2 and then you don't know how to continue. Did you try to read some documentation?You would certainly learn that in the commandline version, you simply press the Enter key to execute 2+2. But in the notebook version (i.e., when you work with your browser), there are two ways to execute 2+2: Pressing Shift+Enter on your keyboard, or clicking on the evaluate link at the bottom of the cell you were editing. If you just hit Enter (not Shift+Enter), then you remain in the same cell end can put several lines in a single cell. Sage treated user as enemy?!? That's what I mean by rather rude. It feels as if you treat the Sage developers as enemy, which is not a wise attitude for getting help. Answer me privately... No. At least I've put you as Cc to my post. But I think it is a good idea to have a public support forum. After all, if one user has a problem that is solved here, then other users with similar problems can easily find that answer by a little Google search. But I think help will only be possible if you clearly explain the problem. Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
Shift + Enter doesn't work no button evaluate W dniu 2011-11-27 18:18, Simon King pisze: Hi Artur, my first impression of your post was: Not enough information (thus, virtually impossible to answer), and rather rude. Perhaps you find http://catb.org/~esr/faqs/smart-questions.html worth reading. On 27 Nov., 15:15, Arturgra...@csl.pl wrote: I was installed Virtual Box and later sage, when I execute SAGE ver last line on screen is writen automatically by SAGE is Starting factorytwisted... and later I can write I was write SAGE: 2+2 and how execute this ? In general, if one has problems with any piece of software and asks for help, one should at least provide some information about the machine: * What CPU? * What operating system (apparently Windows, since you mention vmware)? * What version of Sage did you download? * Are you using Sage on the command line or in your browser (and also: What browser?)? * Does Sage start? If it doesn't: What is the error message? * What exactly is the problem? From the little what you say, I conclude that you use Sage on a Windows machine, you are able to start Sage, a Sage notebook starts in your browser, you write 2+2 and then you don't know how to continue. Did you try to read some documentation?You would certainly learn that in the commandline version, you simply press the Enter key to execute 2+2. But in the notebook version (i.e., when you work with your browser), there are two ways to execute 2+2: Pressing Shift+Enter on your keyboard, or clicking on the evaluate link at the bottom of the cell you were editing. If you just hit Enter (not Shift+Enter), then you remain in the same cell end can put several lines in a single cell. Sage treated user as enemy?!? That's what I mean by rather rude. It feels as if you treat the Sage developers as enemy, which is not a wise attitude for getting help. Answer me privately... No. At least I've put you as Cc to my post. But I think it is a good idea to have a public support forum. After all, if one user has a problem that is solved here, then other users with similar problems can easily find that answer by a little Google search. But I think help will only be possible if you clearly explain the problem. Best regards, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
You want to open http://localhost:8000 in a web browser on the host machine. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field E.points() Traceback (click to the left of this block for traceback) ... AttributeError: 'EllipticCurve_rational_field' object has no attribute 'points' Best wishes Artur W dniu 2011-11-27 20:00, Volker Braun pisze: You want to open http://localhost:8000 in a web browser on the host machine. -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
On Sunday, November 27, 2011 11:16:10 AM UTC-8, Artur wrote: 2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field Now type E. and hit the TAB key; you'll see many choices. One of them is integral_points. -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
After Tab key on E I have following: E ECM EOFError Ei EisensteinForms ElementWrapper Elements Ellipsis EllipticCurve EllipticCurveIsogeny EllipticCurve_from_c4c6 EllipticCurve_from_cubic EllipticCurve_from_j EllipticCurve_from_plane_curve EllipticCurves_with_good_reduction_outside_S EmptySetError End EnumeratedSet EnumeratedSets EnvironmentError EquationOrder EtaGroup EtaGroupElement EtaGroup_class EllipticCurve_from_j EllipticCurve_from_plane_curve EllipticCurves_with_good_reduction_outside_S EmptySetError End EnumeratedSet EnumeratedSets EnvironmentError EquationOrder EtaGroup EtaGroupElement EtaGroup_class EtaProduct EuclideanDomain EuclideanDomainElement EuclideanDomains Euler_Phi Exception Expression ExtendedBinaryGolayCode ExtendedQuadraticResidueCode ExtendedTernaryGolayCode no integral_points W dniu 2011-11-27 20:21, John H Palmieri pisze: On Sunday, November 27, 2011 11:16:10 AM UTC-8, Artur wrote: 2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field Now type E. and hit the TAB key; you'll see many choices. One of them is integral_points. -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
2011/11/27 Artur gra...@csl.pl ** After Tab key on E I have following: snip You forgot the point. Try E. tab (that is E, dot, then press tab). Renan -- Renan Birck Pinheiro - Grupo de Microeletrônica http://www.ufsm.br/gmicro- Engenharia Elétrica http://www.ufsm.br/cee/UFSM http://www.ufsm.br http://renanbirck.blogspot.com / skype: renan.ee.ufsm -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
Dear John, Mayby in manual will be all options connected in Elliptic curve E.conductor() work properly Best wishes Artur W dniu 2011-11-27 20:21, John H Palmieri pisze: On Sunday, November 27, 2011 11:16:10 AM UTC-8, Artur wrote: 2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field Now type E. and hit the TAB key; you'll see many choices. One of them is integral_points. -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
OK ! I was forgot add () E=EllipticCurve([0,297]) E E.conductor() E.integral_points() work perfect . Thank You for proffessional assist! Best wishes Artur W dniu 2011-11-27 20:21, John H Palmieri pisze: On Sunday, November 27, 2011 11:16:10 AM UTC-8, Artur wrote: 2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field Now type E. and hit the TAB key; you'll see many choices. One of them is integral_points. -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
WOW! As many options! Wonderfull !!! I like SAGE! Best wishes Artur P.S. Have Sage Prime factorization algorhitms? W dniu 2011-11-27 20:29, Renan Birck Pinheiro pisze: 2011/11/27 Artur gra...@csl.pl mailto:gra...@csl.pl After Tab key on E I have following: snip You forgot the point. Try E. tab (that is E, dot, then press tab). Renan -- Renan Birck Pinheiro - Grupo de Microeletrônica http://www.ufsm.br/gmicro - Engenharia Elétrica http://www.ufsm.br/cee/UFSM http://www.ufsm.br http://renanbirck.blogspot.com / skype: renan.ee.ufsm -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
John Tell me yet is possible to count rank of my curve over rational field I was try E.mwrank bound method EllipticCurve_rational_field.mwrank of Elliptic Curve defined by y^2 W dniu 2011-11-27 20:21, John H Palmieri pisze: On Sunday, November 27, 2011 11:16:10 AM UTC-8, Artur wrote: 2+2 Work, Hurah!!! Thank You very much! Tell me how to find integral points on elliptic curve x^3-y^2=-297 Im start E=EllipticCurve([0,297]) E Elliptic Curve defined by y^2 = x^3 + 297 over Rational Field Now type E. and hit the TAB key; you'll see many choices. One of them is integral_points. -- John -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
On Nov 27, 2011, at 12:24 , Artur wrote: John Tell me yet is possible to count rank of my curve over rational field I was try E.mwrank bound method EllipticCurve_rational_field.mwrank of Elliptic Curve defined by y^2 It might help you to know the following: The TAB key can provide information about what possibilities are available from the string that you have just typed. As you have discovered, if you type a partial string, TAB will give you completions that are known. TAB following the . will give you names of both methods (functions) and variables associated to the name you have just typed, as for E.. Not all names will work for a given instance; what will actually work depends on exactly how the instance was created (Sage is based on Python [see below], which has a good object structure underlying it). Also, once you have a complete name, ? and ?? will give you documentation (?) or documentation + implementation (if possible) (??) for the name. Try typing E?, once you have defined E as an elliptic curve (you get the same with Elliptic_Curcve?). It may also be helpful to review documentation on Python, and its class structures (see the documentation link on http://www.python.org). Python is the underlying language for both the Sage system and the Sage interpreter, so understanding that will help you to understand Sage. We don't put all of the possible details for all of Sage's functions and classes into documentation at any one time; Sage is dynamically changing, and to do so would be a lot of work. Instead, we rely on the above on-line mechanisms to supplement the documentation. A fair amount is automatically culled from source and put into various manuals (cf the documentation available in your installation, or on-line at http://sagemath.org). Finally (if you've gotten this far), your experience with mwrank shows that this is a method, i.e., a function/procedure. Typing E.mwrank? will give you information about how to use it. HTH Justin -- Justin C. Walker, Curmudgeon-At-Large Institute for the Enhancement of the Director's Income When LuteFisk is outlawed, Only outlaws will have LuteFisk -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
John, Many Thanks for support! Now I have all information which I need on the start. About Integer factorizations Will be worthy to implemented to SAGE probe factorization with prime base to safe computer time. best wishes Artur W dniu 2011-11-27 21:41, Justin C. Walker pisze: On Nov 27, 2011, at 12:24 , Artur wrote: John Tell me yet is possible to count rank of my curve over rational field I was try E.mwrank bound method EllipticCurve_rational_field.mwrank of Elliptic Curve defined by y^2 It might help you to know the following: The TAB key can provide information about what possibilities are available from the string that you have just typed. As you have discovered, if you type a partial string, TAB will give you completions that are known. TAB following the . will give you names of both methods (functions) and variables associated to the name you have just typed, as for E.. Not all names will work for a given instance; what will actually work depends on exactly how the instance was created (Sage is based on Python [see below], which has a good object structure underlying it). Also, once you have a complete name, ? and ?? will give you documentation (?) or documentation + implementation (if possible) (??) for the name. Try typing E?, once you have defined E as an elliptic curve (you get the same with Elliptic_Curcve?). It may also be helpful to review documentation on Python, and its class structures (see the documentation link onhttp://www.python.org). Python is the underlying language for both the Sage system and the Sage interpreter, so understanding that will help you to understand Sage. We don't put all of the possible details for all of Sage's functions and classes into documentation at any one time; Sage is dynamically changing, and to do so would be a lot of work. Instead, we rely on the above on-line mechanisms to supplement the documentation. A fair amount is automatically culled from source and put into various manuals (cf the documentation available in your installation, or on-line athttp://sagemath.org). Finally (if you've gotten this far), your experience with mwrank shows that this is a method, i.e., a function/procedure. Typing E.mwrank? will give you information about how to use it. HTH Justin -- Justin C. Walker, Curmudgeon-At-Large Institute for the Enhancement of the Director's Income When LuteFisk is outlawed, Only outlaws will have LuteFisk -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Sage problem
Hi Artur, On 27 Nov., 22:08, Artur gra...@csl.pl wrote: John, Many Thanks for support! Now I have all information which I need on the start. Good! I think tab completion and the possibility to see documentation and even the source code of the stuff is a big plus. About Integer factorizations Will be worthy to implemented to SAGE probe factorization with prime base to safe computer time. At least according to the benchmarks at http://sagemath.org/tour-benchmarks.html (factorization of 2^512-1), Sage is not bad at factoring integers. So, I guess using the existing implementation of factorization algorithms is a good starting point. Of course, if you observe that in some applications factorization is too slow and you know how to improve it, then you are welcome to demonstrate how. Cheers, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] Re: Sage problem
Dear Simon, I have base about 1 MB prime factors which occured in many factorizations x^n-1 , Lucas, Fibonacci etc. I don't adding any successive primes only primes which occured in siome factorizations (my base also contained Cunningham base and 100 others) Algorhithm of probe factorziation is very simply. Take successive primes from base smaller as factorized number and by GCD method checked that this prime divisor occured in factorized number. GCD algorhitm is very quick that scan whole baseneed few seconds but finding big factors even with NFS method (not implemented in SAGE yet) need lot of time. That is worth lost 5 second on the start and lot of very big numbers can be factorized completely on this method during 5 seconds only. Best wishes Artur W dniu 2011-11-27 22:33, Simon King pisze: Hi Artur, On 27 Nov., 22:08, Arturgra...@csl.pl wrote: John, Many Thanks for support! Now I have all information which I need on the start. Good! I think tab completion and the possibility to see documentation and even the source code of the stuff is a big plus. About Integer factorizations Will be worthy to implemented to SAGE probe factorization with prime base to safe computer time. At least according to the benchmarks at http://sagemath.org/tour-benchmarks.html (factorization of 2^512-1), Sage is not bad at factoring integers. So, I guess using the existing implementation of factorization algorithms is a good starting point. Of course, if you observe that in some applications factorization is too slow and you know how to improve it, then you are welcome to demonstrate how. Cheers, Simon -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org