Hi, I am looking to color the area between the square and the circle (similar to the shadebetween command) and, in general, to color the area between two geometric shapes. Any suggestions? Thank you.

Couronne.mw

Just wonder if someone has any hints about correct code debugging.

Especially I'd like to know how often certain subroutines are called, and where from.

Dear Maple community,

I am facing a little problem verifying a power series solution obtained with Maple since the direct substitution back into the PDEs does not seem to be conclusive because the residual contains the powers of independent variables to almost any order.

Please see the enclosed Maple file with a minimal working example:

Download MinWorkingExa.mw

Thanks a lot in advance for any help or suggestions.

Kind regards,

DDe

Suppose I have an expression like the following:

h(t, x) :=  (m*t^2 + 6*t - 2*x)^2/(36*g*t^2)

I want to calculate multiple values of t in a single expression. Say, for t:= 1,5,10,15,20. I want to evaluate h(t,x) in vector form. so that I can extract for each t. How to write it?

I do not know if this caused by same crash in Reproducible--Server-Crash-Kernel-Connection-Has-Been-Lost  or not.

Could someone be able to find out? It happens each time the code is run on windows 10. 

Download another_server_crash_on_int_maple_2024_april_4_2024.mw

ps. reported to Maplesoft.

The above is new crash in Maple 2024. Below shows no crash in Maple 2023:

Download int_on_maple_2023.mw

Update:

Here is a movie showing the crash. It also happens from the command line. All on windows 10.

My ini file has  nothing in it, other than one command which prints the process ID which I had there for over a year now.  This is after restarting Maple fresh and nothing else running other than this one worksheet.

Here is movie showing the crash from command line also. On windows 10 pro.

Absolute beginner here - please bear with me.

I would like to generate an 81 rows x 24 columns table from three nested "for" loops. I would like each entry of this table to be a list of 4 numbers. My code (which does not work) is as follows:

local M, templist;
for i to 81 do
    for j to 24 do
        for k to 4 do
        M[i][j]:=[op(templist[k]), indice(C[i][1][k],rorder(orders[j],Sets[k]));];
        end do;
    end do;
end do;

In the above "indice" is a procedure that works fine and returns a number, and it works fine.

I would like the 4 numbers that are generated by the k loop to be stringed together into a list, so i thought I could use the temporary list "templist" to append to it the 4 numbers, which would then become the entry in row i and column j of matrix M, but it does not work, and instead I get a table of 81 tables. So for instance the first of these 81 tables is:

1 = table([1 = [4, 1], 2 = [4, 1], 3 = [4, 2], 4 = [4, 3], 5 = [4, 2], 6 = [4, 3], 7 = [4, 1], 9 = [4, 1], 8 = [4, 1], 11 = [4, 1], 10 = [4, 1], 13 = [4, 2], 12 = [4, 1], 15 = [4, 2], 14 = [4, 3], 18 = [4, 3], 19 = [4, 2], 16 = [4, 2], 17 = [4, 3], 22 = [4, 2], 23 = [4, 3], 20 = [4, 3], 21 = [4, 2], 24 = [4, 3]])

and I only have 2 values in each list, rather then the 4 I am after.

If I declare M as a 81x24 matrix, I get retunred a matrix of zeroes. Where am I going wrong?

If anyone could lend a hand, I'd be forever grateful. Thank you!

I just discoverd today the step solutions for series in Student package 

Now i try to solve this with my own steps here ..

Note: was not capable to get a closed form?

Download Het_Basel_Probleem_van_Euler.mw

1.mw.....can anyone hlep to sovle this equation...for omega(t)...
(-limit((1 - omega)^(k + 2), omega = 1, left) + 1)/(k + 2) = C*int((1 - `σ_a`*sin(2*pi*N))^k, N = 0 .. N)...in solution..integral didn't get rid

This is for my understanding (and the proper use of Maple terms)

?simplify refers to them (sqrt in this case) as procedures

simplify[sqrt](16^(3/2));
                               64

`simplify/sqrt`(16^(3/2));
                               64

simplify(16^(3/2), sqrt);
                               64

?combine calls them (this time exp and trig) names of options

combine(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)),[trig,exp]);#why the list?
                        exp(sin(a + b))

combine(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)),trig,exp);#no list
                        exp(sin(a + b))

combine[trig](exp(sin(a)*cos(b))*exp(cos(a)*sin(b)));#no exp required?!?
                        exp(sin(a + b))

(`combine/exp`@`combine/trig`)(exp(sin(a)*cos(b))*exp(cos(a)*sin(b)));
                        exp(sin(a + b))

If the terms command options and command procedures can be used interchangeably, how does evalf[4](...) fit into this scheme? 

Is there a special Maple term for the construct "proc[n]" where proc is a procedure/command name and n is not a name but of type numeric?

This Maplesoft guest blog post is from Prof. Dr. Johannes Blümlein from Deutsches Elektronen-Synchrotron (DESY), one of the world’s leading particle accelerator centres used by thousands of researchers from around the world to advance our knowledge of the microcosm. Prof. Dr. Blümlein is a senior researcher in the Theory Group at DESY, where he and his team make significant use of Maple in their investigations of high energy physics, as do other groups working in Quantum Field Theory. In addition, he has been involved in EU programs that give PhD students opportunities to develop their Maple programming skills to support their own research and even expand Maple’s support for theoretical physics.

The use of Maple in solving frontier problems in theoretical high energy physics

For several decades, progress in theoretical high energy physics relies on the use of efficient computer-algebra calculations. This applies both to so-called perturbative calculations, but also to non-perturbative computations in lattice field theory. In the former case, large classes of Feynman diagrams are calculated analytically and are represented in terms of classes of special functions. In early approaches started during the 1960s, packages like Reduce [1] and Schoonship [2] were used. In the late 1980s FORM [3] followed and later on more general packages like Maple and Mathematica became more and more important in the solution of these problems. Various of these problems are related to data amounts in computer-algebra of O(Tbyte) and computation times of several CPU years currently, cf. [4].

Initially one has to deal with huge amounts of integrals. An overwhelming part of them is related by Gauss’ divergence theorem up to a much smaller set of the so-called master integrals (MIs). One performs first the reduction to the MIs which are special multiple integrals. No general analytic integration procedures for these integrals exist. There are, however, several specific function spaces, which span these integrals. These are harmonic polylogarithms, generalized harmonic polylogarithms, root-valued iterated integrals and others. For physics problems having solutions in these function spaces codes were designed to compute the corresponding integrals. For generalized harmonic polylogarithms there is a Maple code HyperInt [5] and other codes [6], which have been applied in the solution of several large problems requiring storage of up to 30 Gbyte and running times of several days. In the systematic calculation of special numbers occurring in quantum field theory such as the so-called β-functions and anomalous dimensions to higher loop order, e.g. 7–loop order in Φ⁴ theory, the Maple package HyperLogProcedures [7] has been designed. Here the largest problems solved require storage of O(1 Tbyte) and run times of up to 8 months. Both these packages are available in Maple only.

A very central method to evaluate master integrals is the method of ordinary differential equations. In the case of first-order differential operators leading up to root-valued iterative integrals their solution is implemented in Maple in [8] taking advantage of the very efficient differential equation solvers provided by Maple. Furthermore, the Maple methods to deal with generating functions as e.g. gfun, has been most useful here. For non-first order factorizing differential equation systems one first would like to factorize the corresponding differential operators [9]. Here the most efficient algorithms are implemented in Maple only. A rather wide class of solutions is related to 2^nd order differential equations with more than three singularities. Also here Maple is the only software package which provides to compute the so-called ₂F₁ solutions, cf. [10], which play a central role in many massive 3-loop calculations

The Maple-package is intensely used also in other branches of particle physics, such as in the computation of next-to-next-to leading order jet cross sections at the Large Hadron Collider (LHC) with the package NNLOJET and double-parton distribution functions. NNLOJET uses Maple extensively to build the numerical code. There are several routines to first build the driver with automatic links to the matrix elements and subtraction terms, generating all of the partonic subprocesses with the correct factors. To build the antenna subtraction terms, a meta-language has been developed that is read by Maple and converted into calls to numerical routines for the momentum mappings, calls to antenna and to routines with experimental cuts and plotting routines, cf. [11].

In lattice gauge calculations there is a wide use of Maple too. An important example concerns the perturbative predictions in the renormalization of different quantities. Within different European training networks, PhD students out of theoretical high energy physics and mathematics took the opportunity to take internships at Maplesoft for several months to work on parts of the Maple package and to improve their programming skills. In some cases also new software solutions could be obtained. Here Maplesoft acted as industrial partner in these academic networks.

References

[1] A.C. Hearn, Applications of Symbol Manipulation in Theoretical Physics, Commun. ACM 14 No. 8, 1971.

[2] M. Veltman, Schoonship (1963), a program for symbolic handling, documentation, 1991, edited by D.N. Williams.

[3] J.A.M. Vermaseren, New features of FORM, math-ph/0010025.

[4] J. Blümlein and C. Schneider, Analytic computing methods for precision calculations in quantum field theory, Int. J. Mod. Phys. A 33 (2018) no.17, 1830015 [arXiv:1809.02889 [hep-ph]].

[5] E. Panzer, Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals, Comput. Phys. Commun. 188 (2015) 148–166 [arXiv:1403.3385 [hep-th]].

[6] J. Ablinger, J. Blümlein, C .Raab, C. Schneider and F. Wissbrock, Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms, Nucl. Phys. 885 (2014) 409-447 [arXiv:1403.1137 [hep-ph]].

[7] O. Schnetz, φ⁴ theory at seven loops, Phys. Rev. D 107 (2023) no.3, 036002 [arXiv: 2212.03663 [hep-th]].

[8] J. Ablinger, J. Blümlein, C. G. Raab and C. Schneider, Iterated Binomial Sums and their Associated Iterated Integrals, J. Math. Phys. 55 (2014) 112301 [arXiv:1407.1822 [hep-th]].

[9] M. van Hoeij, Factorization of Differential Operators with Rational Functions Coefficients, Journal of Symbolic Computation, 24 (1997) 537–561.

[10] J. Ablinger, J. Blümlein, A. De Freitas, M. van Hoeij, E. Imamoglu, C. G. Raab, C. S. Radu and C. Schneider, Iterated Elliptic and Hypergeometric Integrals for Feynman Diagrams, J. Math. Phys. 59 (2018) no.6, 062305 [arXiv:1706.01299 [hep-th]].

[11] A. Gehrmann-De Ridder, T. Gehrmann, E.W.N. Glover, A. Huss and T.A. Morgan, Precise QCD predictions for the production of a Z boson in association with a hadronic jet, Phys. Rev. Lett. 117 (2016) no.2, 022001 [arXiv:1507.02850 [hep-ph]].

@ecterrab

Fetching package "Physics Updates" from MapleCloud...

ID: 5137472255164416
Version: 1713
URL: https://maple.cloud

An error occurred, the package was not installed:
Could not open workbook: /tmp/cloudDownload3108059082303936092/Physics Updates_1712064079729.maple

Same problem on Maple 2024 for Windows and Linux!!!

Hi,

I am trying to generate a plot using a procedure. A dummy code is as follows:

***

fun := piecewise(x+y > 1, (x+y)^2, x-y);

temp_proc := proc(x, y)
local out, ind:

ind := 9:

if x > y then ind := 1 else ind := 0 end if; 

if ind = 1 then out := eval(5*fun, {:-x=x, :-y=y}) else out := eval(-5*fun, {:-x=x, :-y=y}) end if:

return(out);
end proc:

xt := 5: yt := 2:
out1_fin := temp_proc(xt, yt);

plot(out1_fin, z=-2..3);
 

***

The issue is as follows:

1. I am getting an error message for the code above: "Error, (in temp_proc) cannot determine if this expression is true or false: 2 < z".

2. The entire procedure and the plot command work well for a fixed "z". However, it is not useful for me as I am looking for a plot for various values of z. 

3. I hope I don't have to run the procedure by manually creating a list of z and then plotting the lists of z and out1_fin. 

4. I am using the "ind" variable because it simplifies my actual code, which involves multiple conditions defining the function "fun" that I need to plot. 

I would appreciate your input on how to resolve the issue. 

Regards,

Omkar

I am unable to change the font on the Palette menus or the pop up context boxes.

It is very frustrating, as I can hardly read them.

I am not sure if it is a computer setting or a Maple setting.

Any help would be appreciated

The following is a simple example of what I would like to do: 

M := Array(1 .. 10, 1 .. 2);

for i to 10 do
    M[i, 1] := i;
    M[i, 2] := 3*i;
end do;

Mt := Interpolation:-LinearInterpolation(M);
E := t -> Mt(t);
diffeq := D(C)(t) = E(t);
dsolve({diffeq, C(0) = 0}, {C(t)}, numeric);
Error, (in dsolve/numeric/process_input) unknown Interpolation:-LinearInterpolation([Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Vector(10, [1.,2.,3.,4.,5.,6.,7.,8.,9.,10.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]))])],Vector(10, [3.,6.,9.,12.,15.,18.,21.,24.,27.,30.], datatype = float[8], attributes = [source_rtable = (Array(1..10, 1..2, [[1.,3.],[2.,6.],[3.,9.],[4.,12.],[5.,15.],[6.,18.],[7.,21.],[8.,24.],[9.,27.],[10.,30.]], datatype = float[8]))]),uniform = true,verify = false) present in ODE system is not a specified dependent variable or evaluatable procedure