I don't have an answer to Brandon's remark, but John, should this be in Trac?
On Jan 6, 2008 8:59 PM, [EMAIL PROTECTED] <[EMAIL PROTECTED]> wrote: > > I realize this is a bit naive (and not completely related to the OP) > but as it currently stands the CC used in sage is essentially a > subfield of QQ(i). It may be better to implement RR and CC using > exact precision (though admittedly this will come at a cost in > performance) and allow the real field elements to be coerced to > approximations using mpfr when the user wishes. Doing so would also > allow for more straightforward interaction with maxima's solver (the > default solver in sage), or anything else using > sage.calculus.calculus.SymbolicArithmetic. > > Or is there another reason that the default RR and CC do not use exact > precision, other than very slight performance issues? I suspect the > current reason is that Singular is not equipped to deal with exact > precision RR and CC. I'm just curious if this would be a good thing > in the long run. > > > > On Jan 6, 11:57 am, "John Cremona" <[EMAIL PROTECTED]> wrote: > > You are right about the correct inner product definition for complex > > vectors. In your first example Sage seems not to be doing any > > conjugation. > > > > RR is real numbers (to some precision) while QQ is rational numbers > > (which are exact). If you want complex numbers with real and > > imaginary parts in QQ that qould be anumber field QQ(i). But I would > > not expect Sage to automatically see how to take an inner product of > > vectors whose entries are in number fields (for which there is no easy > > answer since number fields in general have both real and complex > > embeddings). I doubt if that is what you mean, so that leaves you > > working with CC which will definitely be approximate (even with exact > > input). > > > > Now the fact that Sage does not (apparently) recognise complex vectors > > and use an appropriate definition for inner_product() is surely a bug. > > It should be easy to fix if the parent field is CC (or is coerciable > > to CC?). > > > > John > > > > On 06/01/2008, Fabio Tonti <[EMAIL PROTECTED]> wrote: > > > > > > > > > sage: u=vector([2+3*I,5+2*I,-3+I]) > > > sage: v=vector([1+2*I,-4+5*I,0+5*I]) > > > sage: p1=u*v;p1.expand() > > > 9*I - 39 > > > sage: p2=u.inner_product(v);p2.expand() > > > > > 9*I - 39 > > > sage: p3=u.dot_product(v);p3.expand() > > > 9*I - 39 > > > sage: p4=u.inner_product(vector([i.conjugate() for i in > v]));p4.expand() > > > 3 - 19*I > > > > > Am I right in the assumption that for the inner product of two complex > > > vectors, the result should be the sum of the element wise > multiplication of > > > the element of the first vector times the complex conjugate of the > element > > > of the second vector? I had to do this by hand, as you can see for p4. > I had > > > a look at Mathematica, and it seems like they don't do it either. So I > might > > > be wrong. > > > > > Another thing: > > > sage: parent(p1) > > > Symbolic Ring > > > sage: parent(u) > > > Vector space of dimension 3 over Symbolic Ring > > > is it meant to be over symbolic Ring? > > > > > and one more: > > > sage: k=vector([complex(1,2),complex(3,4),complex(25,15)]) > > > Traceback (most recent call last): > > > ... > > > TypeError: unable to find a common ring for all elements > > > > > seriously? why that? > > > sage: > > > u=vector(CC,[complex(1,2),complex(3,4),complex(25,15)]);u > > > (1.00000000000000 + 2.00000000000000*I, 3.00000000000000 + > > > 4.00000000000000*I > > > , 25.0000000000000 + 15.0000000000000*I) > > > And now I've got creepy precision stuff in there. And the inner > product > > > still doesn't do what I'd like it to. > > > > > Does a complex number from CC constructed by complex(<re>,<im>) have > as > > > resulting real and imaginary part have elements from RR? What's the > > > difference between RR and QQ anyway? QQ is arbitrary precision, does > RR use > > > machine precision maybe? > > > > > Now maybe I've asked too many questions, but I've had no luck with the > > > reference manual so far (maybe I just don't get the explanations in > > > there...). > > > I know that today there's the big AMS meeting (good luck for that), so > no > > > need to hurry in order to reply for anyone. And excuse my English, > there > > > maybe some mistakes since I'm in a rush... > > > > > Thanks a lot, Fabio > > > > -- > > John Cremona > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
