Maple 2021 Questions and Posts

These are Posts and Questions associated with the product, Maple 2021

Hi Everyone,

I intend to find the invariants of a 2nd-order Tensor using the representation of the rotational group as an Infinitesimal generator. However, maple does not seem to find the correct invariants $\tr \mathbf{a}$, $\tr \mathbf{a}^2$, $\tr \mathbf{a}^3$. Maple only returns an empty set. I can't seem to figure out why that is the case.

Here is my code

NULL

restart

with(PDETools)

assume(r >= 0)

interface(showassumed = 0)

X_z2 := (-a__21-a__12)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__11))+(a__11-a__22)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))-a__23*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))+(a__11-a__22)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+(a__12+a__21)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__22))+a__13*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))-a__32*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+a__31*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32)) = 0

(-a__21-a__12)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__11))+(a__11-a__22)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))-a__23*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))+(a__11-a__22)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+(a__12+a__21)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__22))+a__13*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))-a__32*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+a__31*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32)) = 0

(1)

X_y2 := (-a__31-a__13)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__11))-a__32*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))+(a__11-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))-a__23*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+a__21*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))+(a__11-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+a__12*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32))+(a__13+a__31)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__33)) = 0

(-a__31-a__13)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__11))-a__32*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))+(a__11-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))-a__23*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+a__21*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))+(a__11-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+a__12*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32))+(a__13+a__31)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__33)) = 0

(2)

X_x2 := -a__13*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))+a__12*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))-a__31*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+(-a__32-a__23)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__22))+(a__22-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))+a__21*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+(a__22-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32))+(a__23+a__32)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__33)) = 0

-a__13*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__12))+a__12*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__13))-a__31*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__21))+(-a__32-a__23)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__22))+(a__22-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__23))+a__21*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__31))+(a__22-a__33)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__32))+(a__23+a__32)*(diff(f_1(x, y, z, a__11, a__12, a__13, a__21, a__22, a__23, a__31, a__32, a__33), a__33)) = 0

(3)

sys := [X_z2, X_y2, X_x2]

sol := pdsolve(sys)

(4)

NULL

Download SO(3)_spherical_2.mw

Any input would be appreciated!

Hello;

Hope you are fine. I need to learn how can I call my code in the other file of maple, define new value for A and can get results. For this purpose, I just take an simple example as

questionmaple.mw

restart; A := 5; B := 10; AAA[0] := 10; for i from 0 while i <= A do AAA[i+1] := B*i*AAA[0] end do

5

 

10

 

10

 

0

 

100

 

200

 

300

 

400

 

500

(1)
 

``

Download questionmaple.mw

Good day,

I am looking for some guidance with the Syrup toolbox

I have a netlist that was generated with the Altium designer Spice simulator (XSpice based), I was able to import it into LTSpice and verrify the results.

I want to move it into maple to make use of the modellica code generation.

I then began modifying the netlist in order to meet the netlist syntax of Syrup. One of the most prominant change I needed to make was the arbitrary input nodes for my Voltage dependant Voltage sources. 

Therefore, for any line that implies arbitrary sources such as:

E_U8_E1 U8_N208620 LO
+ VALUE { IF(V(U8_N208706, 0) > 0.5, 5, -5) }

was changed to:

V1    16   17 1vdc

E_U8_E1 U8_N208620 LO 16 17
+ VALUE { IF(V(U8_N208706, 0) > 0.5, 5, -5) }

This, of course, is a non ideal workaround which brings me to question 1,

Is there a way to define a arbitrary source with the Spice parser in Syrup?

Once these changes were made, it seems the Solve function in Syrup can parse the netlist without issue, however when it gets to the Solve portion it throws the following error:

Solve("file://C:/Users/msavoy/Documents/Spice_cct/inverter_newfet_nonot.cir", 'tran');
Solve: Analyzing SPICE deck "The Apple" (ignoring this line)
Error, (in Syrup:-Solve) invalid input: rcopy uses a 1st argument, A (of type anything), which is missing

Attached is a copy of the netlist, inverter_newfet_nonot.txtI am honestly at a lost as to what could be throwing the rcopy error

Furthermore, I wanted to test out the Modellica code generation in Syurp, it appears that it does not like having subcircuits, as running the test:

V 1 0 1
L1 1 2 L
C1 2 0 C
L2 2 3 L
C2 3 0 C
L3 3 4 L
C3 4 0 C
Vshort 4 5 0
Rt 5 0 1
.SUBCKT TEST A B C Y
V1 14 15 1
EINT YINT 0 14 15
+ VALUE {IF(V(A) > 0.5 && V(B) > 0.5 && V(C) > 0.5, 1, 0)}
RINT YINT Y 1
CINT Y 0 1n
.ENDS TEST
.end

provides the error of:

test_c := ToModelica("file://C:/Users/msavoy/Documents/Spice_cct/test_cct_RCL.txt", 'probes' = ["Rt.v"], 'parameters' = {C = 2, L = 1});
Error, (in Syrup:-ToModelica) invalid input: nodeToModelica expects its 1st argument, node, to be of type nonnegint, but received Y

Is it possible to define a sub circuit in a netlist that is to be converted to Modellica, or do all subcircuits need to be defined in their own file?

Thank you

!Edits: I have found  a existing polynomial algorithm, but I still have difficulty implementing it. 2022/10/26

 

The edge connectivity of a connected graph G  is the minimum number of edges whose deletion from the graph G disconnects G. Below we are concerned with a particular kind of edge-cut.

  • For a connected graph G=(V ,E), an edge set S ⊂ E is a restricted-edge-cut, if G−S is disconnected and every connected component of  G−S has at least 2 vertices. 

Clearly, a restricted-edge-cut is an edge cut with a special requirement.

  • The restricted-edge-connectivity of G, denoted by κres(G), is defined as the cardinality of a minimum restricted-edge-cut.

For example, a graph g is as follows.

 

Clearly, its edge-connectivity is 1 since (0,3) or (0,4) is a edge cut of g. But we can find that  if we remove the edge (0,3), then "3" is a isolated vertex. Similarly, "4" is a isolated vertex if we remove  (0,4). It is not difficult to find g has exactly the two cut-edges (0,3) and (0,4).

 

Based on the definition of the restricted-edge-cuts, neither {(0,3)} nor  {(0,4)} are restricted-edge-cuts A minimum restricted-edge-cut is {(0,1),(0,2)} since every connected component of G-{(0,1),(0,2)} has  (at least) 2 vertices.

So  κres(g) is 2.  My problem is:

Given a graph G, how to calculate the restricted-edge-connectivity of  G?  Moreover, how to find a minimum restricted-edge-cut? 

A specific graph that I want to test is as follows. (it has 16 vertices and 56 edges.) I would like to calculate its restricted-edge-connectivity and find a minimum restricted-edge-cut. 

g:=ConvertGraph("O~tIID@wL~j`PbOqgLJ@p");
DrawGraph(g, stylesheet=[vertexborder=false,vertexpadding=15,edgecolor = "Black",
     vertexcolor="Black",edgethickness=2])

EdgeConnectivity(g) 

6

One option I came up with is to find all 6-edge subsets first. Test if they satisfy  the restricted condition (one by one). Then continue to increase to 7 or more. But this violent calculation may get stuck in the first step. That is, test all the minimum edge cut sets (Note that we will consider 32468436 edge-subsets!) I was referring to the efficiency aspect.  

with(Iterator):
C:=Combination(58,6):
K:=Edges(g):
#sub:=seq( K[[seq(c[]+1)]], c=C); # do not run this code since it has 32468436 members.

 

Any language is acceptable.( C or C++, Python. )

PS: Some time ago, I also asked a related question (but with some differences) on mathematica stack (Find all the minimum edge cuts of a graph). Although Bob Hanlon  gave a reply, the actual result is not good.

 

Edits: The following literature gives a polynomial algorithm for computing the restricted-edge-connectivity of a given  graph. The heart of it is to computing the least cardinality of some  edge-pairs's edge separator. I'm stuck here.

  • Esfahanian A H, Hakimi S L. On computing a conditional edge-connectivity of a graph[J]. Information processing letters, 1988, 27(4): 195-199.

How to implement this algorithm is my current concern.

polysols(diff(u(x), x) = u(x)^2 - 1) produces no results, while it can be verified by direct observation that u(x) = 1 is a polynomial solution.

I have maplesim installed and I get the error "Error, `MapleSim` does not evaluate to a module" when I run A:=MapleSim:-LinkModel(); in a Maple worksheet.

Does anyone know how to solve this error?

Hello everybody.

I wrote the attached code. this code gives a good result when "H" parameter is equal to 0.5. Even in this condition if I change other parameters, I can get a true result as well. But when I change "H" parameter to 0.6,0.7,0.8 or 0.9 the code can't be executed anymore and I can't get a result.

based on the paper, for H=0.6,0.7,0.8 or 0.9. we have a result.

what's the problem?

can anyone please help me to solve this problem?

thank you for your help in advance.

1.mw

Maple 2021.
I expect after exporting to pdf view of page with plot like on fig. 1.

It means with font=[TIMES, ROMAN, 12] as in maine text.
But I obtaned this view of page on pdf (fig. 2) with smaller font-size.

In previouse versions there are no the problem like this.
Dear community, how to fix this annoying inconvenience?

 fig. 1.  fig. 2.

Hi.  I am using the linux version of Maple.  I seem to experience more bombs in Maple/Linux vs MathCad/Windows.  The program just froze as I was entering text.  Just text.  It is not a disaster since I make very frequent saves.  But it is very annoying.  I was a heavy user of MathCad from about 2005 to 2019.  In the early days, it bombed a lot.  But I do not recall that it ever bombed when I was entering text.  Any suggestions?  Would there be a limition on the number of text characters?  Is it Linux?  Other than this problem, it is a great program.

Anyone experience a delay in typing as the screen fills with text/math etc.?

I'm using Maple 2021 and as the space is filled typing slows. I can finish typing and watch the last 4 keys enter on the screen.

I have a student who then she uses tools/assistent/import data and then the file then Maple claims the Excel file is empty? She uses Maple 2021.2. File works on other my and other student computers. 

primes_integrale_exp.mwThe integral in x of 

exp(-sqrt(x^2 + c))

was done by Maple 11 but return unevaluated in Maple 2021,

see attached worksheet 

I run Maple 2021 under Ubuntu 20.04 on a new Lenovo laptop with 32Gb of Ram. Every time I start Maple, it runs for a few minutes and then loses the "kernel connection". I have to save the worksheet and re-start Maple. In dmesg, I find:

[ 1436.724570] oom-kill:constraint=CONSTRAINT_NONE,nodemask=(null),cpuset=/,mems_allowed=0,global_oom,task_memcg=/user.slice/user-1000.slice/user@1000.service,task=mserver,pid=8037,uid=1000
[ 1436.724589] Out of memory: Killed process 8037 (mserver) total-vm:31723552kB, anon-rss:31289772kB, file-rss:60kB, shmem-rss:0kB, UID:1000 pgtables:61656kB oom_score_adj:0
[ 1437.151441] oom_reaper: reaped process 8037 (mserver), now anon-rss:0kB, file-rss:0kB, shmem-rss:0kB

indicating that Maple's virtual memory exceeded 30 Gb! This happens even if the only command I execute is, for instance, "resrart" or "A:=1" and nothing else. It also happens when no other applications are running and the "top" command indicates that around 30Gb of RAM is available.

In this state, Maple is utterly useless to me. This was a new install of Maple and a fresh install of Ubuntu on a new laptop, surely I am not the only one seeing this?

I have tried setting a 30Gb limit in "kerneloptions" for "stacklimit" but that di not make a difference.

If you have seen any behaviour like this, please respond. Is there some bug in Maple that leads to oncontrolled and unprovoked memory grabbing?

ImportGraph reads one or more graphs from a file. For a file containing multiple graphs, the supported formats are digraph6, graph6, and sparse6. I notice that one option is "output = graph or list, or iterator". However, in my programming with Maple, I was reminded several times that list is only good for a small amount of data.  

Although I can convert the list to an array using the convert function, the time spent in the conversion process needs to be considered.

restart: 
with(GraphTheory):
L:=ImportGraph("C:/Users/eul10c.g6", graph6, output=list):#31026 connected eulerian graphs on 10 vertices graphs and Change to your path here.
convert(L,Array) 

So does it make more sense to provide an "output=Array" as an output option?

eul10c.txt

macOS 12.3 + Maple 2021.2

* select a region on a document
* context click
* --> Copy as image

Copy as image does not put an image on the clipboard.

What is solution?

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