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"My friend George Mallory… once did an inexplicable climb on Snowdon. He had left his pipe on a ledge, half-way down one of the Liwedd precipices, and scrambled back by a short cut to retrieve it, then up again by the same route. No one saw what route he took, but when they came to examine it the next day for official record, they found an overhang nearly all the way. By a rule of the Climbers' Club, climbs are never named in honour of their inventors, but only describe natural features. An exception was made here. The climb was recorded as follows: 'Mallory's Pipe, a variation on route 2; see adjoining map. This climb is totally impossible. It has been performed once, in failing light, by Mr G. H. L. Mallory.'." -- "Goodbye to All That", Robert Graves

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These are replies submitted by acer

@lima_daniel 

Yes, hopefully it would behave itself, if you added more names to the list L.

Here is a variant that also includes a forced display of the terms in each product. (This is for visual display only; the result ans1 is an expression which can be used mathematically. But not this handling of raw2 below, which is designed just to print specially.)

Without too much effort you could put the various steps into a couple of re-usable procedures: to construct ans1 and to construct and specially print raw2.

restart

c := -(lambda*`θf`+lambda*`θi`+2*wf-2*wi)/lambda^3

d := (lambda*`θf`+2*lambda*`θi`+3*wf-3*wi)/lambda^2:

g := 6*c*x+2*d:

h := delta*g:

expr := expand(g*h)

4*delta*`θf`^2/lambda^2+16*delta*`θi`^2/lambda^2+36*delta*wi^2/lambda^4+36*delta*wf^2/lambda^4+72*delta*x^2*`θf`*`θi`/lambda^4+144*delta*x^2*`θf`*wf/lambda^5-144*delta*x^2*`θf`*wi/lambda^5-72*delta*x*`θf`*`θi`/lambda^3-120*delta*x*`θf`*wf/lambda^4+120*delta*x*`θf`*wi/lambda^4+144*delta*x^2*`θi`*wf/lambda^5-144*delta*x^2*`θi`*wi/lambda^5-168*delta*x*`θi`*wf/lambda^4+168*delta*x*`θi`*wi/lambda^4-288*delta*x^2*wf*wi/lambda^6+288*delta*x*wf*wi/lambda^5+36*delta*x^2*`θf`^2/lambda^4+144*delta*x^2*wi^2/lambda^6+24*delta*`θf`*wf/lambda^3-72*delta*wf*wi/lambda^4-144*delta*x*wi^2/lambda^5+16*delta*`θf`*`θi`/lambda^2-24*delta*x*`θf`^2/lambda^3-48*delta*x*`θi`^2/lambda^3+144*delta*x^2*wf^2/lambda^6+48*delta*`θi`*wf/lambda^3-48*delta*`θi`*wi/lambda^3+36*delta*x^2*`θi`^2/lambda^4-144*delta*x*wf^2/lambda^5-24*delta*`θf`*wi/lambda^3

L := [wi, wf, `θf`, `θi`];

[wi, wf, `θf`, `θi`]

CC := map(proc (p) options operator, arrow; delta*(`*`(op(p))) end proc, C):

ee := expand(expr):

ans1 := thaw(collect(ee, map(rhs, CCC), simplify));

36*delta*wi^2*(lambda^2-4*lambda*x+4*x^2)/lambda^6-72*(lambda^2-4*lambda*x+4*x^2)*delta*wf*wi/lambda^6-24*(lambda^2-5*lambda*x+6*x^2)*delta*`θf`*wi/lambda^5-24*`θi`*(2*lambda^2-7*lambda*x+6*x^2)*wi*delta/lambda^5+36*(lambda^2-4*lambda*x+4*x^2)*wf^2*delta/lambda^6+24*(lambda^2-5*lambda*x+6*x^2)*delta*`θf`*wf/lambda^5+24*`θi`*(2*lambda^2-7*lambda*x+6*x^2)*wf*delta/lambda^5+4*(lambda^2-6*lambda*x+9*x^2)*`θf`^2*delta/lambda^4+8*`θi`*(2*lambda^2-9*lambda*x+9*x^2)*`θf`*delta/lambda^4+4*(4*lambda^2-12*lambda*x+9*x^2)*`θi`^2*delta/lambda^4

simplify(expr-ans1);

0

CCCC := map(proc (p) options operator, arrow; delta*(`*`(op(p))) = freeze(`%*`(p[1], delta, p[2])) end proc, C):

raw2 := thaw(collect(ff, map(rhs, CCCC), proc (p) options operator, arrow; _K(simplify(p)) end proc)):

subsindets(raw2,specfunc(anything,`%*`),
           proc(p)
             local i;
             uses Typesetting;
             mrow(seq([eval('Typeset'(op(i,p))),mo("⋅")][],
                      i=1..nops(p)-1),
                  eval('Typeset'(op(nops(p),p))));
           end proc);

Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("wi"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wi")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("36"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("6")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("wf"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wi")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("72"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("6"))))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θf`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wi")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("24"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("5"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("6"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("5"))))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θi`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wi")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;"), Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("24"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2"))), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("7"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("6"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("5"))))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("wf"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wf")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("36"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("6")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θf`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wf")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("24"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("5"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("6"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("5")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θi`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("wf")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("24"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2"))), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("7"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("6"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("5")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θf`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("`θf`")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2")), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("6"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("9"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("4")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θi`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("`θf`")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("8"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("2"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2"))), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("9"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("9"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("4")))))+Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mi("`θi`"), Typesetting:-mo("⋅"), Typesetting:-mi("δ"), Typesetting:-mo("⋅"), Typesetting:-mi("`θi`")), Typesetting:-mo("⋅"), Typesetting:-mfenced(Typesetting:-mfrac(Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mrow(Typesetting:-mn("4"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("2"))), Typesetting:-mo("−"), Typesetting:-mrow(Typesetting:-mn("12"), Typesetting:-mo("⁢"), Typesetting:-mi("λ"), Typesetting:-mo("⁢"), Typesetting:-mi("x")), Typesetting:-mo("+"), Typesetting:-mrow(Typesetting:-mn("9"), Typesetting:-mo("⁢"), Typesetting:-msup(Typesetting:-mi("x"), Typesetting:-mn("2")))))), Typesetting:-msup(Typesetting:-mi("λ"), Typesetting:-mn("4")))))

 

Download Final_objective_orig_ac2.mw

@Carl Love The iterative formula x[i+1] = x[i] - 2*f(x[i])/D(f)(x[i]) is sometimes known as the double-step Newton method.

Part of its motivation arises from a desire to mitigate initially slow improvement in the case of an unfortunate choice of starting point.

IIRC there are some theorems -- for polynomials with only real roots -- that reveal that an overshoot can be dealt with handily (potentially starting a normal N.M. sequence aiming for the next greatest root), without having to repeat all earlier evaluations and while retaining monotonic convergence.

I do not recall seeing any modification of that approach in the case of multiple roots. [edit. However, see reference 1.]

My memory is not what it used to be. Google may help.

I could also add (and I suspect that this is more widely known, and I apologize if you already know it) that an iterative formula x[i+1] = x[i] - m*f(x[i])/D(f)(x[i]) is sometimes used to help with the handling of a root known to have multiplicity m (which might also be estimated).

I don't know if the OP is mixing up two concepts on purpose, or by accident, or something else. I don't find the OP's descriptions to be very clear.

[edit] Some references for double-step N.M. via Google, 1, 2, 3

[further edit] The first citation above has subsequently led me to look in Stoer & Bulirsch (my edition: 1980, esp. section 5.5 and theorem 5.5.9 and pp.274-278), where focus is on special case of a univariate polynomial with only real roots. I suppose this was what I was vaguely remembering earlier...

@Carl Love You can find it online, eg. Wikipedia or here.

A partial phrase from that cited Wikipedia page, "...it is actually the three-channel RGB color model supplemented with a 4th alpha channel. Alpha indicates how opaque each pixel is...".

Maple's ImageTools package has support for RGBA, (where the "A" standa for alpha). But its plot drivers do not.

So, for example a COLOR plotting substructure can contain the keyword RGB alongside a mxnx3 float[8] Array, but cannot contain RGBA as a keyword alongside a mxnx4 float[8] Array.

Hence my Answer below, where each point is used to form a separate plotting structure containing its own TRANSPARENCY substructure (all of which can then be displayed together).

@tomleslie By coincidence, I was already editing that sentence, while you were posting your comment. Thanks.

The central point is that the right command here is Search, not Has.

Could you provide a fully explicit example of the kind of data that you wanted plotted, and specify the kind of plot?

How exactly do you want something like an alpha channel to modify the shading? Do you want each plotted point to be affected separately? As a function of x values, or y values, or other?

Would you be satisfied with a gradation of intensity (and/or saturation), rather than directly as an alpha channel? (I realize that this is not the same thing. But it's unclear what precise visual effect you're string for. It's unclear whether you want to overlay the point symbols on top of another plotting artefact.)

It looks like you are trying to get the GUI to display a PLOT structure that contains an unsupported RGBA specification within a COLOR substructure.

How was it created?

@vv Perhaps, at least at some point in time. Some of the LinearAlgebra help pages on performance and efficiency have been revised, however.

But the behavior has been like this for something like the past 19 years. Examination of the code in the LinearAlgebra commands shows a degree of consistency of behavior in this regard, which (IMO) demonstrates a deliberate design decision.

There is an even stronger consequence of the behavior, which is that the ensuing float[8] datatype acts in practice as a gate-keeper against subsequent assignment of values not of numeric type. I find it significant that I cannot recall any complaint about that stronger (but surmountable) consequence. The behaviour might be sumarized as something roughly like this: if the data is all of type numeric and a float is present then the result for rtable arithmetic has datatype float[8] or sfloat.

@tomleslie Somebody from Maplesoft's QA (Quality Assurance) department is making test posts.

Some have already been deleted.

Perhaps they are testing 2dmath as rendered by the Maplenet backend if this site. Perhaps they are testing the Matlab link. Surely the details are not relevant to most of us.

The help page for topic VectorCalculus,Curvature does not state that it computes the signed curvature in the special cases of a plane curve. What that command computes is a magnitude.

The help page for topic Definition,curvature gives two definitions. Only the first is a definition for signed curvature for a plane curve.

@Jonas F As far as I know there is no special setting of the Maple 2019.1 GUI which reverts its behavior in this regard. Explicit action (ie. Shift-F5) may be required.

Asking about it again is unlikely to alter that.

This kind of thing has been reported before, I believe.

Another workaround is to convert the Heaviside to piecewise, before integrating.

I'll note that the issue can also arise for an exact value for the variance, in your example. It therefore seems reasonable (to me) that a workaround other than recourse to up-front numeric quadrature may sometimes be useful or desirable.

restart

with(Statistics)

X := RandomVariable(Normal(1, sqrt(2.25)))

int(PDF(X, x)*convert(Heaviside(x^7-5*x^4-3*x+1), piecewise), x = -infinity .. infinity)

.5275852105

 

Having a brief look at how it may go wrong, we might compare these:

 

X := RandomVariable(Normal(1, sqrt(225*(1/100))))

`assuming`([int(PDF(X, x)*Heaviside(x^7-5*x^4-3*x+1), x = -a .. a)], [a > 10]); limit(%, a = infinity); evalf(%)

-1/2+(1/2)*erf(-(1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, -.8961211535)+(1/3)*2^(1/2))-(1/2)*erf(-(1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, .3166780086)+(1/3)*2^(1/2))+(1/2)*erf((1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, 1.759427884)-(1/3)*2^(1/2))

-0.850712015e-1

`assuming`([int(PDF(X, x)*convert(Heaviside(x^7-5*x^4-3*x+1), piecewise), x = -a .. a)], [a > 10]); limit(%, a = infinity); evalf(%)

(1/2)*erf(-(1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, index = 5)+(1/3)*2^(1/2))-(1/2)*erf(-(1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, index = 1)+(1/3)*2^(1/2))-(1/2)*erf((1/3)*2^(1/2)*RootOf(_Z^7-5*_Z^4-3*_Z+1, index = 2)-(1/3)*2^(1/2))+1/2

.5275852105

 

Download Bug_HS_PDF.mw

@Mohamed19 Yes, your earlier claim was wrong.

Your latest claim is also wrong.

@Christian Wolinski Your first suggestion is correct.

output=':-Q'

@Stretto I realize that this is going to sound crazy, but... there are actually two different kinds of file that Maple uses on MS-Windows, both of which are named maple.ini .

One of these contains saved preferences for the Java GUI. That's the one you've described. That's not the one that you need here.

What you want is a file that contains only plaintext Maple commands (or is empty). The online help for that is indeed topic worksheet/reference/initialization, as you found. You can create this file in one of the locations listed on that help page.

I suggest that you go with choice 3). I suggest that you do not mess around with maplejava.i4j.ini and try and change any location setting. You just need a file maple.ini in the folder that Maple thinks is your "home directory". It'll be a location similar to C:\\Users\userid\maple.ini but of course userid will be different.

You can even issue the Maple command  kernelopts(homedir)  to discover what Maple thinks is your home directory.

 

 

The simplest example I have so far is:

restart;

expr := (7 + a/b)/(1 + c/d):

latex( expr );
{1 \left( 7+{\frac {a}{b}} \right)  \left( 1+{\frac {c}{d}} \right) ^{
-1}}

The problem seems to be due to weak coding in procedure `latex/latex/*`.

Specifically, line 43 is a general else fallback, without any consideration for the special case that local numShort could be equal to 1.

showstat(`latex/latex/*`,42..43);

`latex/latex/*` := proc(e)
local subexp, den, ee, ff, subee, i, k, num, texlist, `\\,`, `\\frac `, `\\sqrt `, 
  `{`, `}`, ccnt, keepcnt, ll, nlist, numTall, numShort, denTall, denShort;
global _LatexSmallFractionConstant;
       ...
  42           texlist := '`{`', '`(`', `latex/print`(numShort), '`)`', 
                 texlist, '`}`'
           else
  43           texlist := '`{`', `latex/print`(numShort), texlist, '`}`'
       ...
end proc

If I replace that else with elif numShort<>1 then the errant 1 is not present in the generated LaTeX. I will test some more examples, and try and form a FromInert/ToInert hotfix.

This would not address my other concern, that the denominator renders like (den)^(-1) instead of within \frac{...}{den} . That'd likely require a deeper rewrite of this routine.

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