MaplePrimes - Maple 2015 Posts and Questions

How to force particular units?

Mac Dude — Wed, 08 Jul 2026 15:51:43 Z

I am adding 'specificheat' as a property to the Element database in Maple.

In my .mapleinit I have added the property so it is permanent

I have a Package that loads the values in from a table using

ScientificConstants:-ModifyElement(parse(elemt),specificheat=[value=data[i,4]*1000,units='J/kg/K']);

which runs in a loop for all elements I have values for. This all works.

My issue: GetUnit() returns a unit of m^2/(s^2*K). While this is not wrong, I want it to stay J/(kg*K), which is much more suitable for my work (and, besides, is the SI unit for specific heat). I can use convert to fix it on a case-by-case basis, but that is decidedly clumsy.

Is there a way to do that?

This is in Maple 2015. I have access to Maple 2023 as well, but not where I am right now. I really need this to work on all of them.

TIA,

M.D.

Removing spaces in plots:-sparsematrixplot

sand15 — Thu, 21 May 2026 09:43:24 Z

M being some sparse matrix, plots:-sparsematrixplot(M) displays a patchwork of squares with two different colors: one for elements of M different 0 and the other for elements of M equal to 0.
The squares are separated by what visually appears like blank lines (in fact tere are no such lines, just gaps between the different squares making them not adjacent).

So my question: Is it possible, without resorting to any workaround based upon PLOT(POLYGONS(..)) or plottools functions (I know how to write such workarounds and I'm not interested in that) to suppress these "white lines", or otherwise said to make the squares adjacent?
I thought that maybe some (hidden?) option acting like style=patchnogrid could exist, or to an undocumented feaure...

Thanks for your reply.

PDF of functions of univariate random variables

sand15 — Tue, 03 Mar 2026 09:04:46 Z

Although the worksheets provided here have been developed under Maple 2015, they should work correctly with newer versions, except perhaps for commands that use the 'op' function ('piecewise' mainly).

In the sequel the acronym 'pdf' stands for 'probability density function'.

CONTEXT

This post originates from a recent question by @JoyDivisionMan and the ensuing discussion.

In a few words, the OP noticed Maple 2025 failed to return a result and asked why. In his reply, @acer identified a code regression somewhere in between Maple 2023 and Maple 2025.
Like Maple 2023 "my" Maple 2015 does not fail but provide... a wrong answer: Do versions in between 2015 and 2024 return wrong results too?

In this post I explain how we can calculate the result by hand (only elementary maths required), why Maple 2015 (and likely newer versions) returns an incorrect result, why Maple generally fails in returning a result, and finally provide several examples to illustrate that even mathematically simple.
The various test cases I present are all equally simple for a skilled human agent, but conversely all beyond the reach of Statistics:-PDF.
This raises the question: Can a robust algorithm for calculating this PDF be developed without resorting to an expert system (I don't like the term AI) that mimics human reasoning?

THE MAIN OBSERVATION

Let X some continuous univariate random variable (CURV) and a real valued function from defined over the support of . Let Y the random variable defined by Y = (X).

The main observation about Statistics:-PDF is that unless very specific situations, this procedure does not build the correct expression of pdf(Y) as soon as is not a strictly monotone function

Here are a fex exceptions to this claim:

X any CURV , : x ⟼ xⁿ , n positive integer (correct solution even if is not monotone)

X ~ Uniform(-1, 1) , : x ⟼ arctanh(x) (no result returned even if is strictly monotone).

It is worth saying that, only by chance, Statistics:-PDF may sometimes return the correct result even if is a non monotone function.
For instance, in @JoyDivisionMan's question, the procedure was indeed capable to provide a correct result for the case X ~ Uniform(0, 2) , : x ⟼ arctanh(x) but this was only because two errors balanced each other out. Replace X ~ Uniform(0, 2) by X ~ Uniform(a, a+2) and Maple is wrong (notice that the pdf of (X) remains unchanged whatever the value of a).

A GOOD DRAWING WORTH A THOUSAND WORDS

Here is a picture to help understand how to get the pdf of Y = (X) for a non monotone function (the case of a monotone function directly comes from this latter).

In this illustration X ~ Uniform(0, 2) , : x ⟼ sine(x).
To ease the explanation, I write X as a mixture of three uniform random variables X₁, X₂, X₃, whose supports are the intervals of the three branches of . More formally, X = (1/4)∙X₁ + (1/2)∙X₂ + (1/4)∙X₃.
The restrictions of to these three branches are denoted ₁, ₂, ₃.

The large rectangles below the horizontal axis represent the pdf of X₁, X₂, X₃  and the blue curve the function.
The image of the interval [y-dy, y+dy] by the inverse functions ₁^(-1) and ₂^(-1) of ₁ and ₂ are represented by the vertical rectangles [x₁-dy, x₁+dy] and [x₂-dy, x₂+dy] .
These two intervals bring a contribution to the pdf of Y (light gray blue on the right) represented by the horizontal violet rectangle on the right side of the picture.

The probability Prob(Y ∊ [y-dy, y+dy]) that Y belongs to the interval [y-dy, y+dy]) is simply the sum
Prob(Y ∊ [y-dy, y+dy]) = Prob(X₁ ∊ ₁^(-1)([y-dy, y+dy])) + Prob(X₂ ∊ ₂^(-1)([y-dy, y+dy]))

Let '_b^(-1)(y) denote the derivative of _b^(-1)(y).
Making dy tends to 0 gives
pdf(Y = y) =  pdf(X₁ = ₁^(-1)(y)) ×  | '₁^(-1)(y) | + pdf(X₂ = ₂^(-1)(y)) ×  | _'2^(-1)(y) |

As I said before there is truly no big math behind this, Except maybe those absolute values?
To understand where they come from zoom in on the rectangle = [x₁-dx, x₁+dx] ╳ [y-dy, y+dy] and denote X and Y the restrictions of X₁ and Y to .
Locally Y is proportional to A+B∙Xwhere constant B = '(x₁) and the value of constant A does not matter here.
So the pdf of Y is (a classical result)  pdf(Y = y) = pdf(X = (y-A)/C) / |C|.
Few details can be found Here.

MAPLE FAILURES AND WEAKNESSES

So why did Maple, at last some versions, produce a wrong result and why some versions are not even capable to return one?
The reason is that there is no big math only at first sight...because determining the inverse function of  can be quite tricky as soon as is not one-to-one map, for instance when is not strictly monotone.
When it is so ^(-1) must be defined for all the branches whose definition intervals intersect the support of X.

I spent a lot of time debugging the procedure Statistics:-PDF to understand why it either fails or produces incorrec results.
The sine_debug_nodebugoutput.mw worksheet presents the "X ~ Uniform(0, 2) , : x ⟼ sine(x)" case (as Mapleprimes stubbornly refuses to upload the worksheet containing the debugger trace, I convert it to sine_debug.pdf to help you see this trace).
To orient the core development team correcting this procedure (assumming they care), the critical procedures are

Statistics:-RandomVariables:-PDF:-Univariate:-GetValueTab[anything]
and Statistics:-RandomVariables:-GetInverse

At the very end it is this second procedure which is truly responsible of Maple failing to provide a result or returning an incorrect on, because it does not correctly build the inverse functions _b^(-1) for all the branches b which matter.

I wrote above that "it is only by chance that Maple provided the correct result for the non monotone function = cosine". Indeed Statistics:-PDF returns a wrong result when X ~ Uniform(z, z+2) and z is not a multiple of /2 (see cosine.mw).

Other important situations where Maple fails returning a result are those where is a polynomial function with different zeros located in the support of X.
I did not trace them but it seems that Statistics:-PDF does not know how to build the _b^(-1) in this case (even though it is quite simple, see "Polynomial" examples below).

A SELECTION OF EXAMPLES

Here is a selection of examples to demonstrate that even in rather complex cases the pdfs of (X) can be constructed quite easily (note that Maple either fails to compute them or to provide a correct result):

Three examples where X is a uniform random variable and the restriction of to the support of X is a non monotone polynomial function of increasing degree (the number of branches to consider is equal to the degree of ):
Polynomial_function_of_a_random_variable_1.mw,
Polynomial_function_of_a_random_variable_2.mw,
Polynomial_function_of_a_random_variable_3.mw
Two examples where the support o X is unbounded examples and = sine. Here an infinity number of branches must be accounted for, one of these two examples (X ~ Exponential) can be treated in a comple analytic way while the other (X ~ Normal) cannot thus leading to a truncated approximation of (X) pdf.
Infinte_support_sine.mw

OPEN QUESTION

Tracing Statistics:-PDF reveals an already complex algorithm designed to handle a broad variety of "canonical" situations. Even this the algorithm fails in almost all non-toy-problem such as this compilation proves Maple_failures.mw.
At first sight, there seems to be a contradiction between the (apparent?) simplicity with which one can obtain, by hand in sometimes in an ad hoc way, the expression of pdf((X)), whether it is exact or truncated, and the complexity of the Statistics:-PDF algorithm, which results in failure in all non trivial cases.

This observation leads to the important question "Is it possible to rewrite Statistics:-PDF in order to enlarge its domain of success?".
I have the feeling that this means designing an algorithm which focuses more on mimicing the human reasoning than identifying "canonical" situations (as it is done today).
An AI-driven algorithm maybe?

I repeat here that the maths are very simple, and all the more simple if you represent the random variable X as a mixture of components X₁, ... X_B, both having the same (truncated) distribution than X, and whose supports identify to the intervals of definition of the B branches of over the whole support of X.
The only difficulty lies in the identification of these branches and in the construction of the functions _b^(-1) over the supports of each X_b.

I have no answer to this question.

A Maple 2015 bug

sand15 — Mon, 22 Dec 2025 16:37:35 Z

This is a report of a Maple_2015's bug, apparently fixed in more recent versions, but which may have persisted for a few versions beyond 2015.
I don't think it's necessary to fill out an RCS form.

All started with an error in my code which was balanced by a maple 2015 bug. So I didn't see any error until I sent my code to @C_R who uses a newer Maple version.
More precisely, in my Maple 2015 code I defined a NxN matrix B, a vector A of length N, that I mistakenly defined as a vector column, and finally computed the quantity R = A . B . A⁺.
Of course Maple should have fire an error.

The bug is that Maple 2015 doesn't fire an error if A is a float vector and B a float matrix.

restart

>	kernelopts(version)

(1)

>	A := Vector(2, symbol=a): B := Matrix(2$2, symbol=b): R := A.B.A^+

Error, (in LinearAlgebra:-Multiply) cannot multiply a column Vector and a Matrix

>	A := Vector(2, i -> i): B := Matrix(2$2, (i, j) -> i+j): R := A.B.A^+

Error, (in LinearAlgebra:-Multiply) cannot multiply a column Vector and a Matrix

>	A := evalf(Vector(2, i -> i)): B := evalf(Matrix(2$2, (i, j) -> i+j)): R := A.B.A^+

(2)

>	R := A^+.B.A

(3)

Download Maple_2015_Bug.mw

A solve/parametric example, with assumptions

sand15 — Mon, 20 Oct 2025 19:53:07 Z

At the beginning was this problem asked to 11th-12th Grade students:

Let C a vertical cylinder of radius R_C = 10, and S a steel sphere of radius R = 4.
We place S into C and fill it with water up to the moment the water reaches the top of S.
Let V the volume of the water we used.
We then remove S and replaces it by another steel sphere S' with radius R' <> 4. Could it be that the free surface of the water reaches exactly the top of S'?
If it is so what is then the value of R'?

Mathematically does the equation (R_C²)⨯ (2R) - (4 R_S³/3) = (R_C²)⨯ (2R') - (4/3 R^'3), where R_C = 10 and R = 4, have other strictly positive solutions than the trivial one R' = R?

The answer here is yes: R' = 552^1/2 -2 ≅ 9.7473.. .

When I read this problem, I immediately asked myself the following question "Does a second sphere S' always exists whatever the values R_C > 0 and R ∊ (0, R_C]?".

In the attached worksheet I used two different Maple tools to answer this question:

firstly solve+assumptions plus plots:-inequal to visualize the (R_C, R) domain where S' exists,
next solve/parametric to present another way to get the characterization of this same domain.

The problem is that solve+assumptions and plots:-inequal both give the same correct result but solve/parametric does not.
PlotsInequal_vs_SolveParametric.mw

For this specific problem solve/parametric fails finding the correct result.
Is that a bug or did I misuse it?

Thanks in advance

modified Bessel function of the third kind with index 1

sand15 — Sun, 05 Oct 2025 16:58:09 Z

I'm not sure of the Maple function I have to use to represent the modified Bessel function of the third kind with index 1.

The Bessel function of the third kind is also named the Hankel function.

I mistakenly started to use HankelH1 or HankelH2 but quickly realized they are both complex-valued functions while the paper I'm working on uses a real-valued modified Bessel function of the third kind: finally, does this latter exist in Maple 2015?

Thanks in advance