Thomas Richard

Mr. Thomas Richard

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14 years, 24 days
Maplesoft Europe GmbH
Technical professional in industry or government
Aachen, North Rhine-Westphalia, Germany

MaplePrimes Activity


These are answers submitted by Thomas Richard

From the View menu, select Markers. A column will be inserted to the left of the worksheet. Scroll down until you see two document block markers with a thin red line. On both of these, right-click to open the context menu, then select Document Block > Show Command. The Typesetting:-RuleAssistant() lines will become visible then. Delete both and save your worksheet.

These products do not come bundled, so they have to be purchased separately.

Also take a look at the disjoint sets of platform support: Maple Calculator is available for Android and iOS; Maple on Windows, Linux, and macOS.

On Windows and macOS, I'm not getting any KCL either. However, value(u) returns this integral unevaluated.

We can convert the sines to exponentials, and then simplify (I haven't tried much here):

c:=convert(u,exp);
s:=simplify(c);
v:=value(s);
simplify(%);

A result in terms of Lommel functions.

What OS are you running Maple on?

In case of Windows, this FAQ page should help. Another customer confirmed this to me just a few days ago.

P.S. I suppose you mean the font size, as opposed to the font as such...

Maple does not convert that cosine value to an algebraic number by default, so we need to insert one step (or two if wanted):

rt := cos(2*Pi/7);
ro := convert(rt,RootOf);
evala(Minpoly(ro,x));
# if you want to see an explicit representation of the root:
ra := convert(ro,radical);
evala(Minpoly(ra,x));

 

No, a KCL error is not expected, of course. Supplying a method option helps, though:

int(integrand,x,method=MeijerG);
int(integrand,x,method=Risch);

Here's an approach using conversion to complex exponentials and then evalc'ing.

Probably not the most efficient, but easy to write down...

sineExpr-evalc.mw
 

restart:

 

sineExpr := (m::posint) -> local t, j; add(mul(ifelse(j <> t, sin(a[j] - b[t])/sin(b[j] - b[t]), sin(a[t] - b[t])), j = 1 .. m), t = 1 .. m);

proc (m::posint) local t, j; options operator, arrow; add(mul(ifelse(j <> t, sin(a[j]-b[t])/sin(b[j]-b[t]), sin(a[t]-b[t])), j = 1 .. m), t = 1 .. m) end proc

(1)

sineExpr(1);

sin(a[1]-b[1])

(2)

combine(evalc(normal(convert(sineExpr(1),exp),expanded)));

sin(a[1]-b[1])

(3)

combine(evalc(normal(convert(sineExpr(2),exp),expanded)));

sin(a[2]+a[1]-b[1]-b[2])

(4)

combine(evalc(normal(convert(sineExpr(3),exp),expanded)));

sin(a[3]+a[2]+a[1]-b[2]-b[3]-b[1])

(5)

combine(evalc(normal(convert(sineExpr(3),exp),expanded)));

sin(a[3]+a[2]+a[1]-b[2]-b[3]-b[1])

(6)

combine(evalc(normal(convert(sineExpr(4),exp),expanded)));

sin(a[4]+a[3]+a[2]+a[1]-b[3]-b[2]-b[4]-b[1])

(7)

combine(evalc(normal(convert(sineExpr(5),exp),expanded)));

sin(a[4]+a[3]+a[2]+a[1]+a[5]-b[2]-b[3]-b[1]-b[5]-b[4])

(8)

 


 

Download sineExpr-evalc.mw

 

The r.h.s. of your solution (multiplied by a constant factor) can be obtained via

simplify(sol,symbolic);

which is also confirmed by odetest.

Your initial example cannot be correct; please plot the hypergeom and the elementary representations. Maybe some typo or copy&paste error (which I often make...)?

Three of the four in your list are covered by

convert(%,StandardFunctions);

 

The recommended tool for evaluating algebraic numbers is evala. However, some preprocessing is needed for this expression:

evala(factor(expr));

In theory, factoring should not be necessary. So that's a weakness, I'd say.

In the definition of C2, you need to remove all the spaces so that it's recognized as a floating-point number, just like the other parameters. Otherwise it will be interpreted as an expression involving the unbound symbol e, which is syntactically valid - thus no error message appears.

The solve call will provide the approximate roots then, without resorting to RootOf representations. And no need to call allvalues.

You almost had it correct; essentially only the curly braces around Cond had to be removed. Some more cleanup was done in the attached file.

exact_solution_error_TR.mw

Edit: two errors of mine fixed

You could strip off the first column by appending [..,2..] to the definition of TR. However, that is ignored by the summarize=embed option. To work around, omit the option and do the embedding in a separate step:

TR := FrequencyTable(Obs, weights = Eff, headers, tableweights = [4, 2, 2, 2, 2])[..,2..]:
DocumentTools:-Tabulate(TR):

By the way, some previous steps can be shortened considerably, e.g.

Obs := lhs~(L):
Eff := rhs~(L):

If we supply one more item in the first list, it will work right away.

And for the second list, did you mean to start with 0, or perhaps 2? If I choose the latter, a simple result is found:

restart:
with(gfun):
List1 := [0,4,16,36,64,100,144]:
List2 := [2,3,6,11,18,27,38]:

R1 := listtorec(List1,f1(n));
rsol1 := rsolve(op(1,R1),f1(n));
simplify(rsol1);

R2 := listtorec(List2,f2(n));
rsol2 := rsolve(op(1,R2),f2(n));
simplify(rsol2);

 

Try this function definition instead:

phi := (x, y) -> Transpose(Multiply(Miv,<x,y,1>));

 

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