Re: [sage-support] strange n()
Mike Hansen schrieb: On Sat, Apr 10, 2010 at 3:37 AM, bb bblo...@arcor.de wrote: sage: n(sqrt(2.), digits=40) 1.414213562373095145474621858738828450441 sage: n(sqrt(2), digits=40) 1.414213562373095048801688724209698078570 sage: If you wanted this to be more like Maxima, the appropriate thing to do would some something like: sage: RealNumber = RealField(137) sage: sqrt(2.0) 1.414213562373095048801688724209698078570 sage: sqrt(2).n(digits=40) 1.414213562373095048801688724209698078570 Sage is missing the errror forwarding of Mathematica. Yes, Sage does not have a numerical type that does Mathematica's significance arithmetic. An interesting thread about the merits and demerits of significance arithmetic is http://sci.tech-archive.net/Archive/sci.math.symbolic/2008-03/msg00014.html . One could do a little work to get Sage's interval arithmetic to do something similar. --Mike Tnx for helping. I did some more experimentation. I dont want to bother you, but if you have some time and some pation I would be thankfull for one more explanation. Your tip works as expected, but if I use the method n() I still get 53 bit of significant bits??? (see last expression of the snippet.) I argue, that the parameter of n() is set elsewhere in another Variable than RealNumber? sage: RealNumber = RealField(137) sage: sqrt(2.) 1.414213562373095048801688724209698078570 sage: _.prec() 137 sage: sqrt(2.000) 1.414213562373095048801688724209698078570 sage: _.prec() 137 sage: n(sqrt(2.000), digits=60) 1.41421356237309504880168872420969807856967336610324780267484 sage: _.prec() 203 sage: n(sqrt(2.000)) 1.41421356237310 sage: _.prec() 53 sage: Regards BB -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
On Sun, Apr 11, 2010 at 10:01 AM, bb bblo...@arcor.de wrote: Tnx for helping. I did some more experimentation. I dont want to bother you, but if you have some time and some pation I would be thankfull for one more explanation. Your tip works as expected, but if I use the method n() I still get 53 bit of significant bits??? (see last expression of the snippet.) I argue, that the parameter of n() is set elsewhere in another Variable than RealNumber? Yes, in the code for n, we have the following: if prec is None: if digits is None: prec = 53 else: prec = int((digits+1) * 3.32192) + 1 so it just defaults to 53 if nothing is passed in. The RealNumber = RealField(137) just changes the precision for floating point literals entered on the command line. --Mike -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
Mike Hansen schrieb: On Sun, Apr 11, 2010 at 10:01 AM, bb bblo...@arcor.de wrote: Tnx for helping. I did some more experimentation. I dont want to bother you, but if you have some time and some pation I would be thankfull for one more explanation. Your tip works as expected, but if I use the method n() I still get 53 bit of significant bits??? (see last expression of the snippet.) I argue, that the parameter of n() is set elsewhere in another Variable than RealNumber? Yes, in the code for n, we have the following: if prec is None: if digits is None: prec = 53 else: prec = int((digits+1) * 3.32192) + 1 so it just defaults to 53 if nothing is passed in. The RealNumber = RealField(137) just changes the precision for floating point literals entered on the command line. --Mike Tnx for clearing that n()-question! In an earlier posting (I am always thankful for any help!) you wrote: One could do a little work to get Sage's interval arithmetic to do something similar. Would be an interesting experiment. I found an internet page about that topic concerning MPFR from 2/5/2006: http://www.ma.utexas.edu/users/kschalm/mpfr-in-sage.html (MPFR seems to be very broadly used by different Progs under GNU Lesser GPL. Added is a list of related software.) There are used some Sage-examples with a strange line-numbering with underscores? May be that is an outdated Sage-Version? Actual versions do not do any line numbering. I did not find any evidence that MPFR or MAPM is included in Sage? I do not understand if MPFR is compiled with Sage in this examples on that page? I cannot find any evidence that MPFR is loaded? In an extension of the floating point issue I am actually interested in: I found a list of libs to support floating point arithmetics that are not in the list of included libs to Sage. I found some examples to include tools with a CLI via http in the documentatin. I did not find hints how to include C/C++ or other language libs to Sage? (To clear that statement: The fact I could not find it does not mean it is not documented in some place!) Again - please ignore my boring question if you feel bothered - I can understand that! With yor response you opened a door for floting point questions. Tnx anyway - regards BB -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
On Sun, Apr 11, 2010 at 12:47 PM, bb bblo...@arcor.de wrote: In an earlier posting (I am always thankful for any help!) you wrote: One could do a little work to get Sage's interval arithmetic to do something similar. Would be an interesting experiment. Here's a brief example sage: RIF Real Interval Field with 53 bits of precision sage: R = RealIntervalField(200); R Real Interval Field with 200 bits of precision sage: f = RIF(pi) + 0.5; f 3.641592653589794? sage: g = R(f); g 3.641592653589794? sage: g.parent() Real Interval Field with 200 bits of precision Even when you increase the precision, it doesn't print out more digits since it knows the upper and lower bounds. However, this does not currently play nice with the .n() stuff. I found an internet page about that topic concerning MPFR from 2/5/2006: http://www.ma.utexas.edu/users/kschalm/mpfr-in-sage.html (MPFR seems to be very broadly used by different Progs under GNU Lesser GPL. Added is a list of related software.) There are used some Sage-examples with a strange line-numbering with underscores? May be that is an outdated Sage-Version? Actual versions do not do any line numbering. This page is indeed quite outdated. I did not find any evidence that MPFR or MAPM is included in Sage? I do not understand if MPFR is compiled with Sage in this examples on that page? I cannot find any evidence that MPFR is loaded? MPFR is included in Sage by default. Sage's RealNumber class is a wrapper around an MPFR object. Any high-precision floating point arithmetic in Sage uses MPFR. In an extension of the floating point issue I am actually interested in: I found a list of libs to support floating point arithmetics that are not in the list of included libs to Sage. I found some examples to include tools with a CLI via http in the documentatin. I did not find hints how to include C/C++ or other language libs to Sage? (To clear that statement: The fact I could not find it does not mean it is not documented in some place!) If you want to interface with other C/C++ libraries, the easiest way to do so is using Cython [1]. There are also lots of examples in the Sage library; for example, $SAGE_ROOT/devel/sage/sage/rings/real_mpfr.pyx --Mike -- 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 unsubscribe, reply using remove me as the subject.
[sage-support] strange n()
Just experimenting with Sage syntax I found something strange: sage: n(pi) 3.14159265358979 sage: n(pi,20) 3.1416 sage: n(pi,29) 3.1415927 sage: n(pi,59) 3.1415926535897932 sage: n(pi,0x59) 3.1415926535897932384626434 sage: pi.n(digits=17) 3.1415926535897932 sage: Is there any explanation? Regards BB -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
On Sat, Apr 10, 2010 at 1:02 AM, bb bblo...@arcor.de wrote: Is there any explanation? Could you be more specific in your question? Everything there looks normal to me. n(pi, 20) means to compute using 20 bits of precision. --Mike -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
On Sat, 10 Apr 2010 01:08:12 -0700, Mike Hansen mhan...@gmail.com wrote: On Sat, Apr 10, 2010 at 1:02 AM, bb bblo...@arcor.de wrote: Is there any explanation? Could you be more specific in your question? Everything there looks normal to me. n(pi, 20) means to compute using 20 bits of precision. ... which you can figure out from the first two lines of the docstring for n, by typing n? at the Sage prompt :). Best, Alex -- Alex Ghitza -- http://aghitza.org/ Lecturer in Mathematics -- The University of Melbourne -- Australia -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
Mike Hansen schrieb: On Sat, Apr 10, 2010 at 1:02 AM, bb bblo...@arcor.de wrote: Is there any explanation? Could you be more specific in your question? Everything there looks normal to me. n(pi, 20) means to compute using 20 bits of precision. --Mike Ok, I see - the argument defines the number of bits and not of digits! In any other CAS (I know) that parameter describes the number of digits displayed. I. e . Maxima: (%i2) fpprec: 40; (%o2) 40 (%i3) bfloat(sqrt(2.)); (%o3) 1.41421356237309504880168872420969807857b0 (%i4) bfloat(sqrt(2)); (%o4) 1.41421356237309504880168872420969807857b0 (%i4) That are 40 digits (with decimal point) Mathematica: N[sqrt[2], 40] 1.41421356237309504880168872420969807857 delivers 40 decimal places including the decimal point. N[sqrt[2.], 40] 1.414213562373095 (that is because Mathematica assumes a 18 bit machine precision in the number 2.0 and cuts off questionable digits of precision) Sage works a bit different from the main stream with the definition of the number of digits. So one should not wonder about my misinterpretation! But thanks for helping! Now I understand the difference: sage: n(sqrt(2.), digits=40) 1.414213562373095145474621858738828450441 sage: n(sqrt(2), digits=40) 1.414213562373095048801688724209698078570 sage: Sage is missing the errror forwarding of Mathematica. sage: n(sqrt(2.000), digits=40) 1.414213562373095145474621858738828450441 sage: n(sqrt(2.000), digits=40) 1.414213562373095048804445654500039353252 sage: n(sqrt(2.000), digits=40) 1.414213562373095048801688724209698078570 sage: n(sqrt(2.000), digits=41) 1.4142135623730950488016887242096980785697 sage: So one has an assortet collection and a rich choice of different numbers. Where I find the calculation philosophie of maxima not too bad! Regards BB -- 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 unsubscribe, reply using remove me as the subject.
Re: [sage-support] strange n()
On Sat, Apr 10, 2010 at 3:37 AM, bb bblo...@arcor.de wrote: sage: n(sqrt(2.), digits=40) 1.414213562373095145474621858738828450441 sage: n(sqrt(2), digits=40) 1.414213562373095048801688724209698078570 sage: If you wanted this to be more like Maxima, the appropriate thing to do would some something like: sage: RealNumber = RealField(137) sage: sqrt(2.0) 1.414213562373095048801688724209698078570 sage: sqrt(2).n(digits=40) 1.414213562373095048801688724209698078570 Sage is missing the errror forwarding of Mathematica. Yes, Sage does not have a numerical type that does Mathematica's significance arithmetic. An interesting thread about the merits and demerits of significance arithmetic is http://sci.tech-archive.net/Archive/sci.math.symbolic/2008-03/msg00014.html . One could do a little work to get Sage's interval arithmetic to do something similar. --Mike -- 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 unsubscribe, reply using remove me as the subject.
