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19 years, 334 days
Ontario, Canada

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These are answers submitted by acer

another form...

acer 32373
August 09 2022
0 0

[note: I had this worksheet completed before I saw vv's Answer. I'm not really surprised how similar they are, taking natural approaches.]

The eq4 below (for c[2]) is not strictly necessary. It's just a rewriting of the eq1, by substituting the obtained solution for Z. I figured you might want two equations that did not have any c[2] or Z on their RHSs.

> 

restart
> 

kernelopts(version);

`Maple 17.02, X86 64 LINUX, Sep 5 2013, Build ID 872941`

 (1)
> 

eq1 := c[2] = Z^2/(2*(m+2));

c[2] = Z^2/(2*m+4)

 (2)
> 

eq2 := int((m*(c[2]-x^2/(2*(m+2))))^(1/m), x = 0 .. Z) = alpha

int((m*(c[2]-x^2/(2*m+4)))^(1/m), x = 0 .. Z) = alpha

 (3)
> 

assume(m >= 1);
> 

temp := IntegrationTools:-Change(eval(eq2, eq1), s = x/Z, s);

(1/2)*m^(1/m)*(m+2)^(-1/m)*Z*((1/2)*Z^2)^(1/m)*GAMMA(1/m+1)*Pi^(1/2)/GAMMA(1/m+3/2) = alpha

 (4)
> 

eq3 := `assuming`([isolate(combine(temp), Z)], [Z > 0]);

Z = (alpha*GAMMA((1/2)*(2+3*m)/m)/(2^(-(1+m)/m)*m^(1/m)*(m+2)^(-1/m)*Pi^(1/2)*GAMMA((1+m)/m)))^(m/(m+2))

  

c[2] = ((alpha*GAMMA((1/2)*(2+3*m)/m)/(2^(-(1+m)/m)*m^(1/m)*(m+2)^(-1/m)*Pi^(1/2)*GAMMA((1+m)/m)))^(m/(m+2)))^2/(2*m+4)

 (5)

 

 

> 

Now a simple sanity check (numeric, and exact).

evalf(eval(eval(subs(int = Int, eq2), [eq3, eq4]), [m = 2, alpha = 6]));

6.000000000 = 6.

 (6)
> 

simplify(eval([eq3, eq4], [m = 2, alpha = 6]));

[Z = 4*3^(1/2)/Pi^(1/2), c[2] = 6/Pi]

  

true

 (7)
> 

eval(eval(eq2, [eq3, eq4]), [m = 2, alpha = 6]);

6 = 6

 (8)

``

Download system_eqs_ac.mw

RootOf(0)...

acer 32373
August 05 2022
2 1

PDEtools:-Solve tries to simplify the RootOf that solve returns (when passed the numerator of the trig-expanded form of result), and generates RootOf(0).

Unfortunatelty,

result:=1/2*(Dirac(1,-t+4+k)+Dirac(1,t-4+k)-Dirac(1,-t+4+k)*cos(-t+4+k)
             +2*Dirac(-t+4+k)*sin(-t+4+k)+2*sin(t-4+k)*Dirac(t-4+k)
             -Dirac(1,t-4+k)*cos(t-4+k))/k:

result:=simplify(result):

denom(result);

             2 k

lprint(numer(result));
Dirac(1,-t+4+k)+Dirac(1,t-4+k)-Dirac(1,-t+4+k)*cos(-t+4+k)+2*Dirac(-t+4+k)*sin
(-t+4+k)+2*sin(t-4+k)*Dirac(t-4+k)-Dirac(1,t-4+k)*cos(t-4+k)

simplify(numer(result));

              0

statevariable...

acer 32373
August 04 2022
2 0

Avoiding a clash with the default value of statevariable,

> 

restart;
> 

kernelopts(version);

`Maple 2022.1, X86 64 LINUX, May 26 2022, Build ID 1619613`

> 

DynamicSystems:-SystemOptions('statevariable'=sv,
                              'continuoustimevar'=x):
> 

ode:=diff(y(x),x$2)+y(x) = 0;

diff(diff(y(x), x), x)+y(x) = 0

> 

DynamicSystems:-DiffEquation(ode,'outputvariable'=[y(x)]);

"module() ... end module"

Download DS_problem_ac.mw

Otherwise, this error message attains,

  restart;
  DynamicSystems:-SystemOptions('continuoustimevar'=x):
  Error, (in DynamicSystems:-SystemOptions) cannot assign x to
  continuoustimevar, already assigned to statevariable

idea...

acer 32373
August 01 2022
1 0

It's not difficult to make a prodecure that will color and join arbitrary v and k.

The results of printf are usually left-justified. Do you really need left-justified output? Left-justification is also possible. But I won't be around for the next 5 days.

> 

restart;
> 

F := proc(v,k,C) uses Typesetting;
      mrow(mn(sprintf("%s]",v),mathcolor=C),
           mn(sprintf(" is %g",k),mathcolor="Blue"));
end proc:
> 

F("1:1", 4, "Green");

"1:1] is 4"

> 

F("2:2", 1/3., "Red");

"2:2] is 0.333333"

Download color_string.mw

surfdata...

acer 32373
July 30 2022
0 0

If you use the command plots:-surfdata then you can easily add other (usual) plotting options.

For example, adding an option for orientation so that the X and Y values appear at the forefront.

> 

restart
> 

with(plots):
> 

X := `<,>`(1740, 2200, 2710, 3200, 3700, 4033):
> 

Y := `<,>`(0, 5, 10, 15, 20, 25, 30, 35, 40):
> 

F(X, 0), F(X, 5), F(X, 10), F(X, 15), F(X, 20), F(X, 25), F(X, 30), F(X, 35), F(X, 40) := Vector(6, {(1) = 1.342, (2) = 1.427, (3) = 1.397, (4) = 1.329, (5) = 1.329, (6) = 1.518}), Vector(6, {(1) = 1.449, (2) = 1.382, (3) = 1.303, (4) = 1.362, (5) = 1.379, (6) = 1.397}), Vector(6, {(1) = 1.341, (2) = 1.348, (3) = 1.339, (4) = 1.456, (5) = 1.388, (6) = 1.555}), Vector(6, {(1) = 1.419, (2) = 1.413, (3) = 1.325, (4) = 1.32, (5) = 1.362, (6) = 1.42}), Vector(6, {(1) = 1.486, (2) = 1.336, (3) = 1.449, (4) = 1.382, (5) = 1.534, (6) = 1.665}), Vector(6, {(1) = 1.395, (2) = 1.37, (3) = 1.38, (4) = 1.365, (5) = 1.345, (6) = 1.507}), Vector(6, {(1) = 1.399, (2) = 1.333, (3) = 1.365, (4) = 1.429, (5) = 1.418, (6) = 1.613}), Vector(6, {(1) = 1.343, (2) = 1.331, (3) = 1.306, (4) = 1.375, (5) = 1.63, (6) = 1.692}), Vector(6, {(1) = 1.422, (2) = 1.421, (3) = 1.323, (4) = 1.31, (5) = 1.508, (6) = 1.57})
> 

A := Array(1 .. numelems(X), 1 .. numelems(Y), 1 .. 3, proc (i, j, k) options operator, arrow; `if`(k = 1, X[i], `if`(k = 2, Y[j], F(X, Y[j])[i])) end proc, datatype = hfloat):
> 

surfdata(A, orientation = [-142, 72, 0]);

 

Download curve_three_d_ac.mw

If you use Carl's PLOT3D(MESH(...)) suggestion then you might wrap that result in a call to plots:-display, to add such other options. Eg,

    plot:-display(PLOT3D(MESH(A)), orientation = [-142, 72, 0])

Matrix indexing...

acer 32373
July 28 2022
2 6

You are not succeeding in constructing the two sets (of scalars or scalar equations) because your indexing into Matrices EQ and V is faulty.

You wrote, "I have a set of equations gathered in a vector." But that is not true. Your EQ is a 4x1 Matrix, and your V is a 1x4 Matrix.

> 

restart
> 

EQ := Matrix(4, 1, {(1, 1) = 32.1640740637930*Tau[1]-0.172224519601111e-4*Tau[2]-0.270626540730518e-3*Tau[3]+0.1570620334e-9*P[1]+0.3715450960e-14*sin(t), (2, 1) = -0.172224519601111e-4*Tau[1]+32.1667045885952*Tau[2]+0.587369829416537e-4*Tau[3]-0.1589565489e-8*P[1]+0.1004220091e-12*sin(t), (3, 1) = -0.270626540730518e-3*Tau[1]+0.587369829416537e-4*Tau[2]+32.1816411689934*Tau[3]-0.7419658527e-8*P[1]+0.5201228088e-12*sin(t), (4, 1) = 0.1570620334e-9*Tau[1]-0.1589565489e-8*Tau[2]-0.7419658527e-8*Tau[3]+601.876235436204*P[1]})
> 

V := Matrix(1, 4, {(1, 1) = Tau[1], (1, 2) = Tau[2], (1, 3) = Tau[3], (1, 4) = P[1]})
> 

q := 0:
> 

X := Matrix(4, 1, {(1, 1) = -0.1156532164e-15*sin(t), (2, 1) = -0.3121894613e-14*sin(t), (3, 1) = -0.1616209235e-13*sin(t), (4, 1) = -0.2074537757e-24*sin(t)})
> 

t := 1:
> 

Xf := fsolve({seq(EQ[r, 1], r = 1 .. 4)}, {seq(V[1, r] = q, r = 1 .. 4)});

{P[1] = -0.1745663328e-24, Tau[1] = -0.9731882592e-16, Tau[2] = -0.2626983734e-14, Tau[3] = -0.1359993176e-13}

> 

{seq(EQ[r, 1], r = 1 .. 4)}

{0.1570620334e-9*Tau[1]-0.1589565489e-8*Tau[2]-0.7419658527e-8*Tau[3]+601.876235436204*P[1], -0.270626540730518e-3*Tau[1]+0.587369829416537e-4*Tau[2]+32.1816411689934*Tau[3]-0.7419658527e-8*P[1]+0.5201228088e-12*sin(1), -0.172224519601111e-4*Tau[1]+32.1667045885952*Tau[2]+0.587369829416537e-4*Tau[3]-0.1589565489e-8*P[1]+0.1004220091e-12*sin(1), 32.1640740637930*Tau[1]-0.172224519601111e-4*Tau[2]-0.270626540730518e-3*Tau[3]+0.1570620334e-9*P[1]+0.3715450960e-14*sin(1)}

> 

{seq(V[1, r] = q, r = 1 .. 4)}

{P[1] = 0, Tau[1] = 0, Tau[2] = 0, Tau[3] = 0}

NULL

Download SoalNewton_ac.mw

comment...

acer 32373
July 27 2022
1 1
> 

restart;
> 

Frac_C:=proc(expr,a,x,alpha)
  local ig,m,tau;
  m:=ceil(alpha);
  ig := (x-tau)^(m-alpha-1)*diff(eval(expr,x=tau),tau$m);
  `assuming`([1/GAMMA(m-alpha)*int(ig,tau=a..x)],[x>a]);
end proc:
> 

Frac_C(x^(3.4),0,x,3/4);
evalf(%);

1.486084413*2^(1/2)*GAMMA(3/4)*x^(53/20)

2.575385653*x^(53/20)

> 

fracdiff((x)^(3.4),x,3/4);

2.575385654*x^(53/20)

> 

Frac_C(cos(x),0,x,1/2);

(cos(x)*FresnelS(x^(1/2)*2^(1/2)/Pi^(1/2))-sin(x)*FresnelC(x^(1/2)*2^(1/2)/Pi^(1/2)))*2^(1/2)

> 

fracdiff(cos(x),x,1/2);

(cos(x)*FresnelS(x^(1/2)*2^(1/2)/Pi^(1/2))-sin(x)*FresnelC(x^(1/2)*2^(1/2)/Pi^(1/2)))*2^(1/2)

Download Frac_C.mw

local gamma...

acer 32373
July 27 2022
1 1

You could declare gamma as local at the top-level, to avoid conflict with the predefined constant.

You could issue this command at the top of the worksheet.

_local(gamma)

sqrt(1+(cos(alpha(t))^2-1)*cos(gamma(t))^2)

(1+(cos(alpha(t))^2-1)*cos(gamma(t))^2)^(1/2)

simplify((1+(cos(alpha(t))^2-1)*cos(gamma(t))^2)^(1/2))

(cos(alpha(t))^2*cos(gamma(t))^2-cos(gamma(t))^2+1)^(1/2)

NULL

Download arg_removed_ac.mw

powers of sums...

acer 32373
July 26 2022
2 1

One objection that you might have to using normal here is that it will cause expansion of terms like (x+y)^3, etc, which can be unnecessarily expensive or even tricky to undo after the fact. (See first two examples below.) Using numer/denom has a similar issue.

It can be tricky to prevent this by using frontend. Instead, below I temporarily freeze the bases of exponentiated sums.

I do not claim that this will handle all kinds of example that you intend, since we have not been told the full class and the hardest kind of example you want handled.

> 

restart;
> 

F := e->thaw(normal(subsindets(e,'`^`'(`+`,anything),
                               u->`^`(freeze(op(1,u)),op(2,u))))):

 

> 

expr := (x+y)^5/(B*C^3)+C^2;

(x+y)^5/(B*C^3)+C^2

> 

normal(expr);

(B*C^5+x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5)/(B*C^3)

> 

F(expr);
simplify(%-expr);

((x+y)^5+C^5*B)/(B*C^3)

0

> 

expr2 := (x+y)^5/(B*(C+E)^3)+(C+E)^2;

(x+y)^5/(B*(C+E)^3)+(C+E)^2

> 

normal(expr2);

(B*C^5+5*B*C^4*E+10*B*C^3*E^2+10*B*C^2*E^3+5*B*C*E^4+B*E^5+x^5+5*x^4*y+10*x^3*y^2+10*x^2*y^3+5*x*y^4+y^5)/(B*(C+E)^3)

> 

F(expr2);
simplify(%-expr2);

((x+y)^5+(C+E)^5*B)/(B*(C+E)^3)

0

> 

F(A/B+C);

(B*C+A)/B

Download normal_ex.mw

integration...

acer 32373
July 25 2022
5 0

So, you want to compute antiderivatives, by integrating?

> 

restart;
> 

with(InertForm):
> 

A := ee -> subsindets(int(convert(ee(__t),diff),__t),
                      anyfunc(identical(__t)), u->op(0,u)):
> 

examp := D(y/x);
A(examp);
Display(%D(A(examp)), 'inert'=false);

D(y)/x-y*D(x)/x^2

y/x

0, "%1 is not a command in the %2 package", _Hold, Typesetting

> 

examp := D(x*y);
A(examp);
Display(%D(A(examp)), 'inert'=false);

D(x)*y+x*D(y)

x*y

0, "%1 is not a command in the %2 package", _Hold, Typesetting

> 

examp := D(x^2+y^2);
A(examp);
Display(%D(A(examp)), 'inert'=false);

2*D(x)*x+2*D(y)*y

x^2+y^2

0, "%1 is not a command in the %2 package", _Hold, Typesetting

Download umm.mw

The above applies the input expression to a dummy name, __t. (For some other, as yet unprovided examples it might serve better to initially substitute for application on that dummy.)

column Vectors...

acer 32373
July 24 2022
0 2

For some strange reason pointplot accepts a list of lists, or a list of column Vectors, but not a list of row Vectors.

I changed it below, to use column Vectors.

I used Maple 2021.2 for this.

> 

restart;
with(LinearAlgebra):
with(plots):
> 

EqBIS := proc(P, U, V) local a, eq1, M1, t, PU, PV, bissec1; a := (P - U)/LinearAlgebra:-Norm(P - U, 2) + (P - V)/LinearAlgebra:-Norm(P - V, 2); M1 := P + a*t; eq1 := op(eliminate({x = M1[1], y = M1[2]}, t)); return op(eq1[2]); end proc:
> 

A := <4, 8>;
B := <4, 2>;
C := <1, 4>;
EqBIS(A, B, C);

A := Vector(2, {(1) = 4, (2) = 8})

B := Vector(2, {(1) = 4, (2) = 2})

C := Vector(2, {(1) = 1, (2) = 4})

-5*y-20+15*x

> 

Cen := proc(M, N, R) local eq1, eq2, sol; eq1 := EqBIS(M, N, R) = 0; eq2 := EqBIS(N, M, R) = 0; sol := simplify(solve({eq1, eq2}, {x, y})); return [subs(sol, x), subs(sol, y)]; end proc:
Cen(A,B,C):

CircleParm := t -> [(-t^2 + 1)/(t^2 + 1), 2*t/(t^2 + 1)];

proc (t) options operator, arrow; [(-t^2+1)/(t^2+1), 2*t/(t^2+1)] end proc

> 

P1 := Vector(CircleParm(1/4));

P2 := Vector(CircleParm(5));
P3 := Vector(CircleParm(-1/10));
P4 := Vector(CircleParm(-3/2));

P1 := Vector(2, {(1) = 15/17, (2) = 8/17})

P2 := Vector(2, {(1) = -12/13, (2) = 5/13})

P3 := Vector(2, {(1) = 99/101, (2) = -20/101})

P4 := Vector(2, {(1) = -5/13, (2) = -12/13})

> 

C1 := Vector(Cen(P1, P2, P3));

C1 := Vector(2, {(1) = (1/44642)*(1066*17^(1/2)-255*26^(1/2))*101^(1/2)-(1/442)*26^(1/2)*17^(1/2), (2) = (1/44642)*(156*17^(1/2)-833*26^(1/2))*101^(1/2)+(21/442)*26^(1/2)*17^(1/2)})

> 

Pts := [P1, P2, P3, P4, C1];

Pts := [Vector(2, {(1) = 15/17, (2) = 8/17}), Vector(2, {(1) = -12/13, (2) = 5/13}), Vector(2, {(1) = 99/101, (2) = -20/101}), Vector(2, {(1) = -5/13, (2) = -12/13}), Vector(2, {(1) = (1/44642)*(1066*17^(1/2)-255*26^(1/2))*101^(1/2)-(1/442)*26^(1/2)*17^(1/2), (2) = (1/44642)*(156*17^(1/2)-833*26^(1/2))*101^(1/2)+(21/442)*26^(1/2)*17^(1/2)})]

> 

display(implicitplot([x^2 + y^2 - 1], x = -2 .. 2, y = -4 .. 2, colour = [blue], scaling = constrained), pointplot(Pts, symbolsize = 16));

> 

 

Download jamet_ac.mw

Relabel...

acer 32373
July 24 2022
1 1
> 

restart;
> 

Relabel := proc(g,s,k) uses GT=GraphTheory;
  GT:-RelabelVertices(g,subs(Equate(s,k),GT:-Vertices(g)));
end proc:

 

> 

with(GraphTheory):

 

> 

G := Graph({{1,2},{1,3},{1,4},{1,5},{3,4},{2,5}}):

 

> 

S := [1,3,5];

[1, 3, 5]

> 

K := [a,1,"[1,2,3,4]"];

[a, 1, "[1,2,3,4]"]

> 

H := Relabel(G,S,K):

 

> 

Vertices(G);

[1, 2, 3, 4, 5]

> 

Vertices(H);

[a, 2, 1, 4, "[1,2,3,4]"]

Download relabel.mw

examples...

acer 32373
July 22 2022
3 1
> 

restart;
> 

convert(U(xi)^2, list, `*`);

[U(xi)^2]

> 

convert(U(xi), list, `*`);

[U(xi)]

> 

convert(U(xi)^2*y(xi)^5, list, `*`);

[U(xi)^2, y(xi)^5]

> 

convert(U(xi)^2*y(xi)^5*p(xi), list, `*`);

[U(xi)^2, y(xi)^5, p(xi)]

> 

convert(U(xi)^2+y(xi)^5, list, `*`);

[U(xi)^2+y(xi)^5]

> 

convert(U(xi)^2+y(xi)^5, list, `+`);

[U(xi)^2, y(xi)^5]

Download convert_list.mw

three ways...

acer 32373
July 07 2022
2 1

Here are three ways, that show the numerals in upright Roman.

I don't care so much for solutions in which any numerals appear in italic, eg.
   caption=typeset("Or like this ",10^`8`)

note 1: I have utilized special display mechanisms because the input 10^8 becomes 100000000 due to automatic simplification by the kernel/engine. It cannot be prevented by delaying evalution, ie. unevaluation quotes (single right-ticks).

> 

restart;
> 

with(plots):
> 

logplot(10^(x),x=0..8,size=[300,300],legend=[y(x)=10^(x)],legendstyle=[location=top],
        caption=typeset("Like this ",InertForm:-Display(10%^8,inert=false)));

> 

logplot(10^(x),x=0..8,size=[300,300],legend=[y(x)=10^(x)],legendstyle=[location=top],
        caption=typeset("Or like this ",`#msup(mn(10),mn(8))`));

Download inert_exponent.mw

note 2: An alternative is to enter 10^8 in 2D Input mode, right-click and in the popup menu choose "2D Math"->"Convert To"->"Atomic Variable". That produces a pure name that conveniently happens to pretty-print just like the input, and which can be re-used in the caption. You could even do that directly in your plot call.

> 

restart
> 

with(plots)


Below, I selected the 10^8 bit of the 2D Input, then right-clicked and converted it to "Atomic Variable". Then I executed the statement.

> 

logplot(10^x, x = 0 .. 8, size = [300, 300], legend = [y(x) = 10^x], legendstyle = [location = top], caption = typeset("Or like this ", `#msup(mn("10"),mn("8"))`))

Download inert_atomic_variable.mw

Typesetting...

acer 32373
July 06 2022
1 0

The mechanism by which the GUI accomplishes the numeric formatting constructions is not generally documented. But quite a bit may be discovered through the debugger. (I used anames to figure out what to first start debugging...)

Below I use Maple 2022.1, with interface(typesetting) returning the default value extended, and interface(prettyprint) returning the default value 3.

Let's consider your image, showing "Scientific" with 2 "Decimal places" and 1 "Minimum Exponent Digits". I set that to be the numeric formatting for the input,
    5.123456789;
Something (perhaps originating in some streamcall from the GUI) makes the following Library call, which results in a bit of Typesetting function-call-structure which renders accordingly.

> 

Typesetting:-Typeset:-Kernel(5.123456789,
                             numericformatting = ["0.0{2}E-0{1}",
                             true, true, false, false]);

Parse:-ConvertTo1D, "invalid input %1", 5.123456789

> 

lprint(%);

Typesetting:-mcomplete(Typesetting:-mrow(Typesetting:-mn("5.12",family =
"Times New Roman",size = "12",bold = "false",italic = "false",underline =
"false",subscript = "false",superscript = "false",foreground = "[0,0,255]",
background = "[255,255,255]",opaque = "false",executable = "false",readonly =
"true",composed = "false",converted = "false",imselected = "false",placeholder
= "false",`selection-placeholder` = "false",font_style_name = "2D Output",
mathvariant = "normal"),Typesetting:-mo("&times;",family = "Times New Roman",
size = "12",bold = "false",italic = "false",underline = "false",subscript =
"false",superscript = "false",foreground = "[0,0,255]",background =
"[255,255,255]",opaque = "false",executable = "false",readonly = "true",
composed = "false",converted = "false",imselected = "false",placeholder =
"false",`selection-placeholder` = "false",font_style_name = "2D Output",
mathvariant = "normal",fence = "false",separator = "false",stretchy = "false",
symmetric = "false",largeop = "false",movablelimits = "false",accent = "false",
lspace = "0.2222222em",rspace = "0.2222222em"),Typesetting:-msup(Typesetting:-
mn("10",family = "Times New Roman",size = "12",bold = "false",italic = "false",
underline = "false",subscript = "false",superscript = "false",foreground =
"[0,0,255]",background = "[255,255,255]",opaque = "false",executable = "false",
readonly = "true",composed = "false",converted = "false",imselected = "false",
placeholder = "false",`selection-placeholder` = "false",font_style_name =
"2D Output",mathvariant = "normal"),Typesetting:-mn("0",family =
"Times New Roman",size = "12",bold = "false",italic = "false",underline =
"false",subscript = "false",superscript = "false",foreground = "[0,0,255]",
background = "[255,255,255]",opaque = "false",executable = "false",readonly =
"true",composed = "false",converted = "false",imselected = "false",placeholder
= "false",`selection-placeholder` = "false",font_style_name = "2D Output",
mathvariant = "normal"),superscriptshift = "0")),5.123456789)

Download numformatting_stuff.mw

So it looks as if the GUI may be forming that list as value for the numericformatting option, based on the stuff in the popup menu in your image. Figuring out all the rules it may use in doing so could be a chore.

I do not know what those four true/false arguments mean, and the names of the keyword options only help so much with my guessing:
    showstat(Typesetting:-Typeset:-Kernel);

So, I believe that this is how it works. But I don't think that it's intended for general user consumption.

And figuring it out completely might be time-consuming. I doubt many people would enjoy figuring these out:
  showstat(Typesetting:-Typeset:-Tdisplay);
  showstat((Typesetting::Typeset)::Tn);
 

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