Axel Vogt

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20 years, 252 days
Munich, Bavaria, Germany

MaplePrimes Activity


These are replies submitted by Axel Vogt

Sometimes the following works: Convert MeijerG to a Sum, the 0 term formally divides by 0 giving some troubles for Maple. So split in 2 parts and treat the 0 term as limit. For the example that recipe does it:
  MeijerG([[1,1],[2]],[[1,1/2,1/2],[]],x);
  convert(%,Sum): subs(_k1=k,%);
  theSum:=select(has,%,Sum);

# thus: that MeijerG writes as 4*Pi*x + theSum, 
# so show that theSum is 0 for x=1

  summand(theSum):
  a:=unapply(%,k,x);

# term k=0
  'limit(a(k,1),k=0)': '%'=simplify(%);
  ``=evalf(rhs(%));

                 lim    a(k, 1) = 4 (-1 + 2 ln(2)) Pi
                k -> 0
                           = 4.8543181080696

# remaining tail
  'Sum(a(k,1),k=1..infinity)': '%'= value(%);
  ``=evalf(rhs(%));

               infinity
                -----
                 \
                  )     a(k, 1) = -4 (-1 + 2 ln(2)) Pi
                 /
                -----
                k = 1
                           = -4.8543181080696

Adding both expressions gives theSum, so it is 0.

I think one learns that stuff at school (construction with ruler and circle, Pythagoras or so) and I am almost sure it is needed for some stuff in Physics at school to. It is more that one forgets it. If the exercise would have been like " ... with ruler and circle and then do with Maple ... " it would be clear, how to proceed. I had only few Profs towards that direction (or variants) and that's one reason, why I think giving the direct solution is not the best way to 'teach' how to apply learned stuff (if it is done with care through some studies).
Even so I understand that students are an important target group it is quite questionable to solve obvious homework before delivery date. Certainly I got 'nice' help through my studies as well (like many others) but this is not a good idea in general. However one thing is serious: s/he talks of the circle as a line. While I doubt the exercise is formulated like that, it shows a fundamental miss- understanding in nomenclature, indicating a lack of basic Math. This is no sin, one can learn that - but students will not realize it, if being provided by solutions - and their tutors will neither. My answer would have been: the hint reminds you, that the radius _is_ perpendicular to a circle, so find _the_ line through the center and your point. Just my personal opinion & knowing about my own imperfectness :-) BTW: It is not uncommon to declare oneself female through an appropriate user name to receive help - I always have some doubts on that - and using 85 exclamation marks does not sound like that ...
plots[implicitplot](x^2+y^2=25,x=-5..0,y=-5..0) and for an answer search for the homework forum
One can pack A into the M's, so setting A=2 it becomes more simple, but equivalent and playing with codegen/simplify I get the following as a valid solution TOL := [Z = Z, Y = (((-M2*M3+M1*M3)*X2+(M2*M3-M1*M2)*X3)*X1-(M3-M2) *M1*X3*X2-I*((M3-M2)*(X3-X2)*(M2*M3+(-M3-M2+M1)*M1)*(X2*X3+(-X3+X1-X2) *X1))^(1/2))*Z/((-(M3-M2)*M1*Z-(-M2*M3+M1*M3)*X2-(M2*M3-M1*M2)*X3)*X1+ ((M3-M2)*M1*X3+(M2*M3-M1*M2)*Z)*X2+(-M2*M3+M1*M3)*Z*X3), V = ((M3-M2)* (X3-X2)*(M2*M3+(-M3-M2+M1)*M1)*(X2*X3+(-X3+X1-X2)*X1))^(1/2)*Z/((-(M3- M2)*M1*Z-(-M2*M3+M1*M3)*X2-(M2*M3-M1*M2)*X3)*X1+((M3-M2)*M1*X3+(M2*M3- M1*M2)*Z)*X2+(-M2*M3+M1*M3)*Z*X3)*I, G = (((M2-M1)*X2+(M1-M3)*X3)*X1+(M3 -M2)*X2*X3+(-(M3-M2)*X1-(M1-M3)*X2-(M2-M1)*X3-I*((M3-M2)*(X3-X2)*(M2*M3+ (-M3-M2+M1)*M1)*(X2*X3+(-X3+X1-X2)*X1))^(1/2))*Z)/((-(M3-M2)*M1*Z-(- M2*M3+M1*M3)*X2-(M2*M3-M1*M2)*X3)*X1+((M3-M2)*M1*X3+(M2*M3-M1*M2)*Z)*X2+ (-M2*M3+M1*M3)*Z*X3)] The complex 'I' is a bit artificial (through the square roots) May be an appropriate way would be to use the Groebner package.
The determinant is a polynom in the variables of the matrix and thus in your parameters, the degree increases with the dimension. So it is not unlikely that Maple first needs time to compute the polynom (I forgot the complexity) and then can not explicitly solve it, but returns 'RootOf'. A variant to Jacques' suggestion would be to study the structure of your matrix first (may be already some transforms give you a decomposition, it need not be LU). BTW det = 0 is the same as 'not full rank' which often is simplier (and faster to compute - sometimes, but not in general ...).
For me it is not clear what you would consider as a solution. Usually one solves for (one or more) indeterminate, you do not say something towards that. The equation stands for a surface in 3-space (over the reals or over integers) with coordinates x,y and z. What are you looking for, what should Maple reply?
Thanks for your encouraging reply Jacques :-) Ok, there is still the 'oldish' way of studying posted examples of educated users ...
This kind of (functional - is it the correct word?) programming is (at least) very hard to read for me. Are there some examples to get more used to it (more or less: step by step) ? I mean whithout 'abstract' background first ... PS: the posted sheet in 'mw' format is an example, where saving in classical format is not directly possible due to label references ... what a shame for Maple.
hm ... earlier had problems, but with Firefox it is ok (even id I do not like the box width). Anyway: usually I write my text separately in a file (at least at home) ... not only because of formating ... it helps me to write not too much in a Germish style ...
and if you delete the output before copying or saving? may be not what you want, but sometimes a work around is not that bad ...
Thank you for the quick reply!
Thank you for the quick reply!
actually I only bookmarked that as recent posts [since switching to other views is quite slow since the page seems to load quite a lot (even if just using the 'back' button to load pages already viewed)], 'recent' should be at the menu bar
for me the suggestion (avoiding type checking and using a 'cascade' of if's) works down to Maple 9.5
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