acer

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These are replies submitted by acer

You've forgotten to provide any details of your problem.

@Carl Love And the More...Delete menu item is also missing here now.

The other posting also remains.

I had passed along the details to those in charge. (The poisoning might be be tricky; I don't know.)

@mmcdara No worries!

The int result improved in Maple 2019. The factoring of the quartic by simplify came in Maple 2016.

@mmcdara That appears to be related to your version.

restart

kernelopts(version)

`Maple 2025.1, X86 64 LINUX, Jun 12 2025, Build ID 1932578`

f := 2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= sqrt(2), -(sqrt(t^2-1)*t^2+2*sqrt(t^2-1)*arcsin((t^2-2)/t^2)-4*t^2+2*sqrt(t^2-1)+4)/sqrt(t^2-1), sqrt(2) < t, 0)

myM := int(f, t = 0 .. x):

myM assuming x>0, x<1; # see version

(1/2)*x^4+Pi*x^2-(8/3)*x^3

int(f, t = 0 .. x) assuming x > 0, x < 1;

(1/2)*x^4+Pi*x^2-(8/3)*x^3

simplify(%); # see version

 

(1/6)*x^2*(3*x^2+6*Pi-16*x)

Download myM_ac.mw

@Carl Love Yes, and the Flag button as well. I noticed this on a pair of postings from a few days ago.

I was planning on reporting it.

@mmcdara Fwiw the symbolic median (your Exact) can be further simplified.

In trig representation, there is no small imaginary component/artefact, when evalf'd.

restart

kernelopts(version)

`Maple 2025.1, X86 64 LINUX, Jun 12 2025, Build ID 1932578`

f := 2*t*piecewise(t <= 0, 0, t <= 1, t^2+Pi-4*t, t <= sqrt(2), -(sqrt(t^2-1)*t^2+2*sqrt(t^2-1)*arcsin((t^2-2)/t^2)-4*t^2+2*sqrt(t^2-1)+4)/sqrt(t^2-1), sqrt(2) < t, 0)

myM := int(f, t = 0 .. x):

# omitting the rationale
myM=1/2 assuming x>0, x<1;

(1/2)*x^4+Pi*x^2-(8/3)*x^3 = 1/2

G := solve({myM=1/2, x>0, x<1},x,explicit) assuming x>0, x<1:

simplify((evalc(simplify(G)))):
evalf(%);
lprint(%%);

{x = .5120032673}

{x = 1/3*(4*(Pi^2-3)^(1/4)*(16-3*Pi+3*(Pi^2-3)^(1/2)*cos(1/3*arctan((-27*Pi^4+
96*Pi^3-54*Pi^2+864*Pi-2331)^(1/2)/(Pi^3+9*Pi-48))))^(1/4)-(16-3*Pi+3*(Pi^2-3)^
(1/2)*cos(1/3*arctan((-27*Pi^4+96*Pi^3-54*Pi^2+864*Pi-2331)^(1/2)/(Pi^3+9*Pi-48
))))^(3/4)*(Pi^2-3)^(1/4)+((-3*Pi^2*cos(1/3*arctan((-27*Pi^4+96*Pi^3-54*Pi^2+
864*Pi-2331)^(1/2)/(Pi^3+9*Pi-48)))-6*Pi*(Pi^2-3)^(1/2)+32*(Pi^2-3)^(1/2)+9*cos
(1/3*arctan((-27*Pi^4+96*Pi^3-54*Pi^2+864*Pi-2331)^(1/2)/(Pi^3+9*Pi-48))))*(16-\
3*Pi+3*(Pi^2-3)^(1/2)*cos(1/3*arctan((-27*Pi^4+96*Pi^3-54*Pi^2+864*Pi-2331)^(1/
2)/(Pi^3+9*Pi-48))))^(1/2)+(36*Pi-128)*(Pi^2-3)^(1/2))^(1/2))/(Pi^2-3)^(1/4)/(
16-3*Pi+3*(Pi^2-3)^(1/2)*cos(1/3*arctan((-27*Pi^4+96*Pi^3-54*Pi^2+864*Pi-2331)^
(1/2)/(Pi^3+9*Pi-48))))^(1/4)}

Download Median_acc.mw

@jalal That's does not explicitly show us what you did in your original attachment in this thread's Question.

Why can't you show us the explicit code that constructs your Tables, in your newer approach?

Is your modified (inspired) approach still using some procedure F similar (even if without piecewise...) to that in your older worksheet's approach?

@mmcdara It seems possible to replace (by a1..a8) all the names in ra[1] except eta, gamma, and phi (noting that phi does not even appear in the rhs's of the equations).

The result is somewhat unwieldy, though.

How are those Tables of outputs constructed? Are they inserted Tasks? Could you provide a version of your worksheet in which the underlying Task(s) or construction mechanism is shown?

The OP's followup example showed that he didn't want  1/`%+`(k,7)  which is the inert form for k+7.  Carl's already pointed out that OP's inconsistency in requests.

So I've redone my followup Replies to show either a fully active expression, or one where the user can utilize either a partially or fully inert/active form.

Now also for Product.

And for an infinite bound.

Hopefully without too many mistakes.

restart

Parse:-ConvertTo1D, "`%1` is not a module or member", InertForm

 

trieq(Sum(1/(k+7), k = -2 .. 3))

Sum(1/(k+7), k = -2 .. 3) = `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = 2131/2520

trieq(Sum(1/(k+7), k = -2 .. 3))

Sum(1/(k+7), k = -2 .. 3) = `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = 2131/2520

trieq(Sum(1/`%+`(k, 7), k = -2 .. 3))

Sum(1/`%+`(k, 7), k = -2 .. 3) = `%+`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) and `%+`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) = 2131/2520

trieq(Sum(i^2, i = 1 .. 5))

Sum(i^2, i = 1 .. 5) = `%+`(1, 4, 9, 16, 25) and `%+`(1, 4, 9, 16, 25) = 55

trieq(Sum(`%^`(i, 2), i = 1 .. 5))

Sum(`%^`(i, 2), i = 1 .. 5) = `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) and `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) = 55

trieq(Product(i^2, i = 1 .. 5))

Product(i^2, i = 1 .. 5) = `%*`(1, 4, 9, 16, 25) and `%*`(1, 4, 9, 16, 25) = 14400

 

trieq(Product(`%^`(i, 2), i = 1 .. 5))

Product(`%^`(i, 2), i = 1 .. 5) = `%*`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) and `%*`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) = 14400

trieq(Product(i^2, i = 1 .. 5))

Product(i^2, i = 1 .. 5) = `%*`(1, 4, 9, 16, 25) and `%*`(1, 4, 9, 16, 25) = 14400

trieq(Product(1/(k+7), k = -2 .. 3))

Product(1/(k+7), k = -2 .. 3) = `%*`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%*`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = 1/151200

trieq(Product(1/`%+`(k, 7), k = -2 .. 3))

Product(1/`%+`(k, 7), k = -2 .. 3) = `%*`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) and `%*`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) = 1/151200


And now, for fun, also with symbolic summation...

Parse:-ConvertTo1D, "`%1` is not a module or member", InertForm

multi_eq_symb(Sum(i^2, i = 1 .. 5))

Sum(i^2, i = 1 .. 5) = `%+`(1, 4, 9, 16, 25) and `%+`(1, 4, 9, 16, 25) = `%/`(`%*`(5, `%+`(5, 1), `%+`(`%*`(2, 5), 1)), 6) and `%/`(`%*`(5, `%+`(5, 1), `%+`(`%*`(2, 5), 1)), 6) = 55

multi_eq_symb(Sum(`%^`(i, 2), i = 1 .. 5))

Sum(`%^`(i, 2), i = 1 .. 5) = `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) and `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) = `%/`(`%*`(5, `%+`(5, 1), `%+`(`%*`(2, 5), 1)), 6) and `%/`(`%*`(5, `%+`(5, 1), `%+`(`%*`(2, 5), 1)), 6) = 55

multi_eq_symb(Sum(1/(k+7), k = -2 .. 3))

Sum(1/(k+7), k = -2 .. 3) = `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = `%+`(%Psi(`%+`(3, 8)), `%*`(-1, %Psi(`%+`(-2, 7)))) and `%+`(%Psi(`%+`(3, 8)), `%*`(-1, %Psi(`%+`(-2, 7)))) = 2131/2520

multi_eq_symb(Sum(i, i = -10 .. -2))

Sum(i, i = -10 .. -2) = `%+`(-10, -9, -8, -7, -6, -5, -4, -3, -2) and `%+`(-10, -9, -8, -7, -6, -5, -4, -3, -2) = `%+`(`%/`(`%*`(-2, `%+`(-2, 1)), 2), `%*`(`%/`(-1, 2), -10, `%+`(-10, -1))) and `%+`(`%/`(`%*`(-2, `%+`(-2, 1)), 2), `%*`(`%/`(-1, 2), -10, `%+`(-10, -1))) = -54

multi_eq_symb(Product(1/(k+7), k = -2 .. 3))

Product(1/(k+7), k = -2 .. 3) = `%*`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%*`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = `%/`(%GAMMA(`%+`(-2, 7)), %GAMMA(`%+`(3, 8))) and `%/`(%GAMMA(`%+`(-2, 7)), %GAMMA(`%+`(3, 8))) = 1/151200

multi_eq_symb(Product(i, i = 1 .. 20))

Product(i, i = 1 .. 20) = `%*`(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) and `%*`(1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20) = %GAMMA(`%+`(20, 1)) and %GAMMA(`%+`(20, 1)) = 2432902008176640000

multi_eq_symb(Sum(1/`%^`(2, i), i = 3 .. 10))

Sum(1/`%^`(2, i), i = 3 .. 10) = `%+`(1/`%^`(2, 3), 1/`%^`(2, 4), 1/`%^`(2, 5), 1/`%^`(2, 6), 1/`%^`(2, 7), 1/`%^`(2, 8), 1/`%^`(2, 9), 1/`%^`(2, 10)) and `%+`(1/`%^`(2, 3), 1/`%^`(2, 4), 1/`%^`(2, 5), 1/`%^`(2, 6), 1/`%^`(2, 7), 1/`%^`(2, 8), 1/`%^`(2, 9), 1/`%^`(2, 10)) = `%+`(`%*`(-1, `%^`(2, `%*`(-1, 10))), `%^`(2, `%+`(1, `%*`(-1, 3)))) and `%+`(`%*`(-1, `%^`(2, `%*`(-1, 10))), `%^`(2, `%+`(1, `%*`(-1, 3)))) = 255/1024

multi_eq_symb(Sum(2^(-i), i = 7 .. infinity))

Sum(2^(-i), i = 7 .. infinity) = `%^`(2, `%+`(1, `%*`(-1, 7))) and `%^`(2, `%+`(1, `%*`(-1, 7))) = 1/64

multi_eq_symb(Product(4*i^2/(4*i^2-1), i = 1 .. 3))

Product(4*i^2/(4*i^2-1), i = 1 .. 3) = `%*`(4/3, 16/15, 36/35) and `%*`(4/3, 16/15, 36/35) = `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2))), `%^`(4, `%+`(3, 1)), `%^`(%GAMMA(`%+`(3, 1)), 2)), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2), `%^`(`%^`(2, `%+`(3, 1)), 2), %GAMMA(`%+`(3, `%/`(1, 2))), %GAMMA(`%+`(3, `%/`(3, 2))))) and `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2))), `%^`(4, `%+`(3, 1)), `%^`(%GAMMA(`%+`(3, 1)), 2)), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2), `%^`(`%^`(2, `%+`(3, 1)), 2), %GAMMA(`%+`(3, `%/`(1, 2))), %GAMMA(`%+`(3, `%/`(3, 2))))) = 256/175

multi_eq_symb(Product(4*`%^`(i, 2)/(4*`%^`(i, 2)-1), i = 1 .. 3))

Product(4*`%^`(i, 2)/(4*`%^`(i, 2)-1), i = 1 .. 3) = `%*`(4*`%^`(1, 2)/(4*`%^`(1, 2)-1), 4*`%^`(2, 2)/(4*`%^`(2, 2)-1), 4*`%^`(3, 2)/(4*`%^`(3, 2)-1)) and `%*`(4*`%^`(1, 2)/(4*`%^`(1, 2)-1), 4*`%^`(2, 2)/(4*`%^`(2, 2)-1), 4*`%^`(3, 2)/(4*`%^`(3, 2)-1)) = `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2))), `%^`(4, `%+`(3, 1)), `%^`(%GAMMA(`%+`(3, 1)), 2)), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2), `%^`(`%^`(2, `%+`(3, 1)), 2), %GAMMA(`%+`(3, `%/`(1, 2))), %GAMMA(`%+`(3, `%/`(3, 2))))) and `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2))), `%^`(4, `%+`(3, 1)), `%^`(%GAMMA(`%+`(3, 1)), 2)), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2), `%^`(`%^`(2, `%+`(3, 1)), 2), %GAMMA(`%+`(3, `%/`(1, 2))), %GAMMA(`%+`(3, `%/`(3, 2))))) = 256/175

multi_eq_symb(Product(4*i^2/(4*i^2-1), i = 1 .. infinity))

Product(4*i^2/(4*i^2-1), i = 1 .. infinity) = `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2)))), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2))) and `%/`(`%*`(`%^`(`%^`(2, 1), 2), %GAMMA(`%+`(1, `%/`(-1, 2))), %GAMMA(`%+`(1, `%/`(1, 2)))), `%*`(`%^`(4, 1), `%^`(%GAMMA(1), 2))) = (1/2)*Pi

NULL

Download ts_multi_sum_5.mw

@Carl Love Some months ago, the order of Answers-with-equal-votes changed from the historically longstanding oldest on top to (ugh) newest on top.

Christopher might not have noticed that change in behavior. When you originally answered, after me, your Answer was on top of mine.

My requests to get this new and confusing behavior reverted have not had success.

And now using `%+` instead of replacing Sum by sum, because I just realized that it would allow be to enter the expression without inert operators.

After writing this, I see that it's getting close to Carl's approach. (I hadn't noticed his use of `%+` for inertly adding the terms. I confess that I didn't read it carefully enough, sorry, even though I saw that he'd mentioned not needing the expression entered by the user with inert operators. I guess I missed the point.)

This is a pretty simple procedure, but can handle several kinds of example and is flexible because the particular aspects/level of inertness can be specified in the input.

restart

Parse:-ConvertTo1D, "`%1` is not a module or member", InertForm

 

trieq(Sum(1/(k+7), k = -2 .. 3))

Sum(1/(k+7), k = -2 .. 3) = `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = 2131/2520

trieq(Sum(1/`%+`(k, 7), k = -2 .. 3))

Sum(1/`%+`(k, 7), k = -2 .. 3) = `%+`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) and `%+`(1/`%+`(-2, 7), 1/`%+`(-1, 7), 1/`%+`(0, 7), 1/`%+`(1, 7), 1/`%+`(2, 7), 1/`%+`(3, 7)) = 2131/2520

trieq(Sum(1/(k+7), k = -2 .. 3))

Sum(1/(k+7), k = -2 .. 3) = `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) and `%+`(1/5, 1/6, 1/7, 1/8, 1/9, 1/10) = 2131/2520

trieq(Sum(i^2, i = 1 .. 5))

Sum(i^2, i = 1 .. 5) = `%+`(1, 4, 9, 16, 25) and `%+`(1, 4, 9, 16, 25) = 55

trieq(Sum(`%^`(i, 2), i = 1 .. 5))

Sum(`%^`(i, 2), i = 1 .. 5) = `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) and `%+`(`%^`(1, 2), `%^`(2, 2), `%^`(3, 2), `%^`(4, 2), `%^`(5, 2)) = 55

NULL

Download ts_multi_sum_4.mw

The OP's second (followup) example, using my second approach in my Answer:

I did command-completion on Sum, to get it as the 2D Input with inert gray Sigma. But you could also just type the argument in text code, eg. Sum(`%/`(1,k+7),k=-2..3)

restart

Parse:-ConvertTo1D, "`%1` is not a module or member", InertForm

 

trieq(Sum(`%/`(1, k+7), k = -2 .. 3))

Sum(`%/`(1, k+7), k = -2 .. 3) = `%/`(1, 5)+`%/`(1, 6)+`%/`(1, 7)+`%/`(1, 8)+`%/`(1, 9)+`%/`(1, 10) and `%/`(1, 5)+`%/`(1, 6)+`%/`(1, 7)+`%/`(1, 8)+`%/`(1, 9)+`%/`(1, 10) = 2131/2520

trieq(Sum(1/`%+`(k, 7), k = -2 .. 3))

Sum(1/`%+`(k, 7), k = -2 .. 3) = 1/`%+`(-2, 7)+1/`%+`(-1, 7)+1/`%+`(0, 7)+1/`%+`(1, 7)+1/`%+`(2, 7)+1/`%+`(3, 7) and 1/`%+`(-2, 7)+1/`%+`(-1, 7)+1/`%+`(0, 7)+1/`%+`(1, 7)+1/`%+`(2, 7)+1/`%+`(3, 7) = 2131/2520

trieq(Sum(`%/`(1, k+7), k = -2 .. 3))

Sum(`%/`(1, k+7), k = -2 .. 3) = `%/`(1, 5)+`%/`(1, 6)+`%/`(1, 7)+`%/`(1, 8)+`%/`(1, 9)+`%/`(1, 10) and `%/`(1, 5)+`%/`(1, 6)+`%/`(1, 7)+`%/`(1, 8)+`%/`(1, 9)+`%/`(1, 10) = 2131/2520

trieq(Sum(1/`%+`(k, 7), k = -2 .. 3))

Sum(1/`%+`(k, 7), k = -2 .. 3) = 1/`%+`(-2, 7)+1/`%+`(-1, 7)+1/`%+`(0, 7)+1/`%+`(1, 7)+1/`%+`(2, 7)+1/`%+`(3, 7) and 1/`%+`(-2, 7)+1/`%+`(-1, 7)+1/`%+`(0, 7)+1/`%+`(1, 7)+1/`%+`(2, 7)+1/`%+`(3, 7) = 2131/2520

trieq(Sum(`%^`(i, 2), i = 1 .. 5))

Sum(`%^`(i, 2), i = 1 .. 5) = `%^`(1, 2)+`%^`(2, 2)+`%^`(3, 2)+`%^`(4, 2)+`%^`(5, 2) and `%^`(1, 2)+`%^`(2, 2)+`%^`(3, 2)+`%^`(4, 2)+`%^`(5, 2) = 55

trieq(Sum(`%^`(i, 2), i = 1 .. 5))

Sum(`%^`(i, 2), i = 1 .. 5) = `%^`(1, 2)+`%^`(2, 2)+`%^`(3, 2)+`%^`(4, 2)+`%^`(5, 2) and `%^`(1, 2)+`%^`(2, 2)+`%^`(3, 2)+`%^`(4, 2)+`%^`(5, 2) = 55

NULL

Download ts_multi_sum_3.mw

ps. It's more useful to tell us what other kinds of example you want handled, and exactly how, up front.

The GUI adds extra space so that you can rotate the cube without parts of it going out-of-view (ie. beyond the inlined plotting window).

You can manually right-click on the plot and zoom into it a little, to make the cube occupy more of the inlined plotting window. (You can also get such a effect programatically, with a bit of effort. But I'm not sure how that survives exporting to animated .gif file, if that's an end-goal).

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