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Re: Sundry Questions

  • To: mathgroup at
  • Subject: [mg61093] Re: Sundry Questions
  • From: "Jens-Peer Kuska" <kuska at>
  • Date: Mon, 10 Oct 2005 02:39:54 -0400 (EDT)
  • Organization: Uni Leipzig
  • References: <diabu7$ikb$>
  • Sender: owner-wri-mathgroup at


I would like to have a single question per 
posting, because it is also
more easy to you to follow the 1-20 soluions per 

a) Use Evaluate[] in ParametricPlot[]
p3 = ParametricPlot[
Evaluate[{x[t], y[t]} /. severalSols], {t, 0, 
Compiled -> False, DisplayFunction -> Identity];
Show[pvf, p3,
PlotRange -> {{-6, 6}, {-3, 3}}, AspectRatio -> 
DisplayFunction -> $DisplayFunction, Axes -> 
AxesLabel -> {"x", "y"}];

b) Function[] has a third argument for the 

Function[{z}, z ** z, {Listable}] [{a, b, c, d}]

c) I prefer the usage messages of the kernel and 
try to avoid the online-help notebooks.

d) here is why:


"SameTest is an option for functions like 
FixedPoint that specifies the \
comparison function to apply to pairs of results 
to determine whether they \
should be considered the same."

e) DSolve[x'''[t] == 0, x[t], t, 
GeneratedParameters -> (nonsense &)]
f) the question is total unclear, because
MatchQ[#, Subscript[_, _]] & /@

{x, x1, Subscript[x, 1], y, Subscript[y, 2], y2}

work as expected and you should say what

| solsList = {x1[t]->something,
| x2[t]->somethingElse} where the '1' and the '2' 
are actually
| subscripts"

mean because x1 is a symbol and has no subscript 
and I would like to know what
an "actualy subscript" is.

g-1) copy & paste from a ASCII file work for 
typesetted expressions only "cell wise",
   the FrontEnd will not see that
"bla bla bla

should be interpretet as "bla bla bla" and x^2
it will assume that you wish to copy the ASCII 
representation of it, and not the
interpreted mathematical expression for x^2 in the 
second line.
The FrontEnd will only do that, when the string 
start with "\!"
or if you use Edit| Copy as | ...

g-2) since the rule
rule = part_ :> (Null /; (Print["Trying :", 
InputForm[part]]; False))

should never match, the condition must be always 
False, otherwise the rule would match and the 
example can't show how the pattern matcher is 
applyed to the subexpressions. But Condition[] 
need to know whats to do when the test ist True, 
even when this can't happen in thist case. You can 
write anything instead of Null in the rule.



"Matt" <anonmous69 at> schrieb im 
Newsbeitrag news:diabu7$ikb$1 at
| Hello,
|  First off, what follows are multiple questions 
that I have
| accumulated from using Mathematica over the past 
couple of weeks.  I
| figured it would be less annoying to post in 
batches rather than a new
| question every day.  If I am incorrect in this, 
please let me know.
| Anyway, I appreciate any and all help to be 
offered.  Each new question
| will be delimited by 'Question:'.
| Question:  Problem producing output as shown in 
"Differential Equations
| with Mathematica" by Abell and Braselton on page 
| Before embarking on any of the following, I 
loaded the PlotField
| package via:
| <<Graphics`PlotField`
| What didn't work:
| pvf = PlotVectorField[{2 y, -1/4 x}, {x, -6, 6}, 
{y, -3, 3},
| DisplayFunction->Identity];
| severalSols = Map[DSolve[{x'[t]==2 
y[t],y'[t]==-1/4 x[t],
| (*
| I also tried Table instead of Map (which didn't 
work either) as
| follows:
| severalSols = Table[DSolve[{x'[t]==2 
y[t],y'[t]==-1/4 x[t],x[0]==2,
| y[0]==a},{x[t],y[t]},t], {a, 0.5, 2.5,0.5}];
| *)
| p3 = ParametricPlot[{x[t],y[t]}/.severalSols, 
| Compiled->False,DisplayFunction->Identity];
| Show[pvf,p3,
| The error I got was this:
| ParametricPlot::pptr: {x[t], y[t]} /. 
severalSols does not evaluate to
| a pair of real numbers at t = 
| Which, when I looked at what severalSols 
evaluates to by itself, made
| sense to me.
| What did work:
| pvf = PlotVectorField[{2 y, -1/4 x}, {x, -6, 6}, 
{y, -3, 3},
| DisplayFunction->Identity];
| severalSols = Table[DSolve[{x'[t]==2 
y[t],y'[t]==-1/4 x[t],x[0]==2,
| y[0]==a},{x[t],y[t]},t], {a, 0.5, 2.5,0.5}];
| parPlots  = Table[ParametricPlot[{x[t], y[t]} /. 
| {t,0,2Sqrt[2]Pi}, Compiled->False, 
| {a,1,5,1}];
| Show[pvf,parPlots,
| My question is this:
| How would I have made the failed attempt work 
without introducing the
| intermediate step of creating a new table of the 
graphics themselves?
| Question:  How do I set attributes for a pure 
function using the &
| approach as opposed to the Function[] approach?
| Question:  Selecting a word from the help, 
pressing F1, then navigating
| back to original page, starts you off back at 
the beginning, not where
| you were.  Is there a setting to change this 
behaviour to such that
| when you navigate back, your view of the 
previous page is where it was?
| (Much like a web page works for example).  Also, 
if I click on a
| function name, press F1, then navigate from the 
entry for Prepend by
| clicking on something like See Section 1.8.6, if 
I click the navigate
| backwards button twice, I do not go back to the 
original page that I
| started from.
| Question:  I saw 'SameTest' used in Mathematica 
Navigator 2, but I
| can't find it referenced in the help of 
Mathematica 5.1.  It does
| appear on the site under help 
for version 3.x.  Is
| SameTest deprecated?
| Question:  Is there a way to get 
GeneratedParameters to issue the same
| constant of integration instead of the form 
x0[1], x0[2], etc.?  (e.g.
| just plain x0 for each and every invocation 
where I specify
| GeneratedParameters)
| Question:  When dealing with subscripts, how do 
I do pattern matching?
| e.g. I have a list of rules such as solsList = 
| x2[t]->somethingElse} where the '1' and the '2' 
are actually
| subscripts, I can use x1[t] /. solsList to get 
back x1 or x2[t] /.
| solsList to get back x2 (where, again, '1' and 
'2' are subscripts).
| However, if I try to use Subscript[x,_] as the 
pattern, it never finds
| anything.
| Question:  On page 612 of Michael Trott's "The 
Mathematica Guidebook
| for Programming" he uses the following construct 
to demonstrate the
| order in which the various parts of an 
expression would be tried in a
| pattern matching and replacing process with the 
| rule = part_ \[RuleDelayed] (Null /; 
(Print["Trying :
| ",InputForm[part]]; False))
| \!\(expression\  = \ \((xu\^xu\  + \ 
yu\^yu)\)\^\(x0\^x0 + y0\^y0\) + \
| 1\)
| expression /. rule
| (I'm not sure why, but if I try to grab all 
three of the above lines
| and paste them into Mathematica, the middle line 
doesn't paste in
| properly.  If I past each line in separately, 
then it works.)
| His example works just fine.  Here is how I 
think it works:
| 'rule' contains a delayed rule with the 
following semantics:
| If the conditional evaluates to 'True', then 
'Null' would be applied to
| the matching subexpression, which I assume would 
do nothing (or would
| the matching subexpression be replaced by 
| The conditional to be evaluated is 
(Print["Trying : ",
| InputForm[part]]; False), which if I understand 
the use of the
| parentheses in this context, will always 
evaluate to 'False' because of
| the '; False)' at the end.  However, in the 
processing of the
| conditional, the Print statement will be 
executed with an argument of
| the string and the part that is currently being 
| Because of the way '/;' is defined ("a rule that 
applies only when a
| condition is satisfied"), I thought I'd 
investigate the behaviour of
| 'Print', i.e. what it returns.  I assumed, 
because of the added 'False'
| in the conditional, that somehow, 'Print' 
returns 'True'.  I'm not
| really sure how to evaluate what a function 
returns, but I figured I'd
| try something like this:
| True == Print["Trying : ", InputForm[x^2]]
| which returned
| True == Null
| I then assumed that Print returns Null, and 
decided to remove the
| 'False' part from the conditional, and it worked 
just as well as it did
| before:
| rule = part_ \[RuleDelayed] (Null /; 
(Print["Trying : ",
| InputForm[part]]))
| \!\(expression\  = \ \((xu\^xu\  + \ 
yu\^yu)\)\^\(x0\^x0 + y0\^y0\) + \
| 1\)
| expression /. rule
| So, my question is this:  What's the point of 
the 'False' in the
| conditional? and, on a minor note:  Because the 
conditional will always
| evaluate to 'False' (or 'Null' if the 'False' 
clause is eliminated),
| could the 'Null' of the beforehand part (Null /; 
etc.) be replaced by
| anything we wanted?
| Thanks very much,
| Matt

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