MaplePrimes - Maple Posts and Questions

How to tweak a procedure, for use with Grid?

emendes — Fri, 22 May 2026 17:09:55 Z

Hi,

I need to run the following procedure a couple of million times. Although it works, Maple sometimes chokes for no apparent reason (if there is a reason, please let me know). I was wondering whether an expert could help me tweak the procedure (or possibly rewrite it) to achieve the best possible performance. I am planning to use Grid:-Map or, if possible, Threads:-Map.

generateNonlinearModelsPlus := proc(model::list,fullmodel::list,vars::list:=[x,y,z])
description "This function generates a list of all models with one more monomial from the full model":
local tab::table(),n:=nops(model),i,j,k:=1,ans,terms,aaa,allmoncoefThreads:
# local procedure
allmoncoefThreads := proc(f::list,vars::list)
description "This function finds the monomials multipled by their coefficients for each expression (equation) of a list.":
local n:=numelems(f),i,mon:=[seq](0,i=1..n),M,cc:=[seq](0,i=1..n),ans:
for i from 1 to n do
  cc[i]:=[coeffs](expand(f[i]),vars, 'M'):
  mon[i]:=[M]:
end do:
ans:=[seq](zip((ww,vv)->ww*vv,cc[i],mon[i]),i=1..n):
return(ans)
end proc:
# main part
ans:=zip((w,v)->expand(simplify(v-w)),model,fullmodel): # Find the monomials that are not in model
terms:=allmoncoefThreads(ans,vars): # Separate the monomials
#
for i from 1 to n do
   aaa:=model:
   for j from 1 to nops(terms[i]) do
       aaa[i]:=model[i]+terms[i,j]:
       tab[k]:=aaa:
       k:=k+1:
   end do:
end do:
tab:=convert(tab,list):
return(tab):
end proc:

Here is an example of how I run it:

model:=[y*alpha[1, 2], z*alpha[2, 3], x^3*alpha[3, 10] + x*alpha[3, 1] + alpha[3, 0]]:

fullmodel:=[x^3*alpha[1, 10] + x^2*y*alpha[1, 11] + x^2*z*alpha[1, 12] + x*y^2*alpha[1, 13] + x*y*z*alpha[1, 14] + x*z^2*alpha[1, 15] + y^3*alpha[1, 16] + y^2*z*alpha[1, 17] + y*z^2*alpha[1, 18] + z^3*alpha[1, 19] + x^2*alpha[1, 4] + x*y*alpha[1, 5] + x*z*alpha[1, 6] + y^2*alpha[1, 7] + y*z*alpha[1, 8] + z^2*alpha[1, 9] + x*alpha[1, 1] + y*alpha[1, 2] + z*alpha[1, 3] + alpha[1, 0], x^3*alpha[2, 10] + x^2*y*alpha[2, 11] + x^2*z*alpha[2, 12] + x*y^2*alpha[2, 13] + x*y*z*alpha[2, 14] + x*z^2*alpha[2, 15] + y^3*alpha[2, 16] + y^2*z*alpha[2, 17] + y*z^2*alpha[2, 18] + z^3*alpha[2, 19] + x^2*alpha[2, 4] + x*y*alpha[2, 5] + x*z*alpha[2, 6] + y^2*alpha[2, 7] + y*z*alpha[2, 8] + z^2*alpha[2, 9] + x*alpha[2, 1] + y*alpha[2, 2] + z*alpha[2, 3] + alpha[2, 0], x^3*alpha[3, 10] + x^2*y*alpha[3, 11] + x^2*z*alpha[3, 12] + x*y^2*alpha[3, 13] + x*y*z*alpha[3, 14] + x*z^2*alpha[3, 15] + y^3*alpha[3, 16] + y^2*z*alpha[3, 17] + y*z^2*alpha[3, 18] + z^3*alpha[3, 19] + x^2*alpha[3, 4] + x*y*alpha[3, 5] + x*z*alpha[3, 6] + y^2*alpha[3, 7] + y*z*alpha[3, 8] + z^2*alpha[3, 9] + x*alpha[3, 1] + y*alpha[3, 2] + z*alpha[3, 3] + alpha[3, 0]]:

vars:=[x,y,z]:

ans:=generateNonlinearModelsPlus(model,fullmodel,vars)

Many thanks.

System of nonlinear Diophantine equations

Alfred_F — Thu, 21 May 2026 15:05:28 Z

For quite some time, I have wanted to solve the system attached in "test" using Maple. The smallest solution in natural numbers x, y, and z test.mw

Download test.mw

is known, and all these numbers are less than 4 × 10¹². Is this possible in Maple?

(x=1633780814400; y=252782198228; z=3474741058973)

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.

3-D histograms?

Mac Dude — Tue, 19 May 2026 20:42:00 Z

The title is the question. I am fairly certain that Maple in itself (up to 2023) does not have this. There is of course Statistics:-Histogram, but that is a 1-D histogram only.

Given 2 Vectors of floats, say, xvec[n] and yvec[n]. The idea would be to divide up a 2-D grid into "pixels" that accumulate a count when (xvec[i],yvec[i]) falls into the range for a pixel (xrange,yrange). Plotting each of these pixels as rectangular column creates the histogram.

I could of course program one myself, but as I am lazy and this seems like a common kind of plot (at least in statistics and in physics), someone may well have done such a thing. DDG search did not find anything, at least not wrt. Maple.

Here is an example plot close to what I am thinking of (random plot pulled off the web). The color scheme of the plot is not what I am after (although it does look nice).

Thanks in advance,

Mac Dude

Tribonacci numbers

Mister_Matthew_abc — Tue, 19 May 2026 20:35:22 Z

Hi MaplePrimes, and all,

Here is a new, to me, set of numbers
defined by ,
the first three numbers are {1,2,3}
and then,
the next number is the sum of the three
previous numbers,
so,
{1,2,3,6,11,20, ... }
but can only calculate a finite number of numbers
the, so called, Tribonacci numbers
could start with {0,1,0}
see online
https://oeis.org/A001590

and
triple_recursive_sequence_simple_first.mw

triple_recursive_sequence_simple_first.pdf

regards,
Matt

why the error message?

awass — Tue, 19 May 2026 15:32:21 Z

Here is a snippet of code that returns an error message. The details of the h procedure should be irrelevant.

h:=proc(k,x)
local z,w;
nans(parameters=[k,x]);
z:=nans(0.98);
w:=rhs(z[2]),rhs(z[3])
end proc;
h := proc (k, x) local z, w; nans(parameters = [k, x]); z :=

nans(.98); w := rhs(z[2]), rhs(z[3]) end proc;

h(7.7,0.3);
0.310903619302454933005944397083, 0.731944275983583692659532399302

plot([h(7.7,x),x=0..30]);
Error, (in dsolve/numeric/process_parameters) 'parameters' must be specified as a list of numeric values

Note that the line h(7.7,0.3); is just there to show that h functions well. It accepts 2 numerical inputs and spits out a pair of numerical values.

Why is plot not plotting? Why is plot asking about inner workings of h?

If I try

f:=proc(x,y)

cos(x),sin(x*y)
end proc;
plot([f(x,7.7),x=0..3]);
that woks fine. Plot does not inquire about f.