I simplified my setup as much as possible. Please check lambdas.mw.

While I think I managed to obtain some analytical solutions, they look a bit strange for two reasons:

1) They do not depend on the exogenous parameters as I expected. In fact, mu_jk and mu_ki should only depend on q_0jk and q_0ki, while lambda_jk and lambda_ki should only depend on BigSigma_0jk, BigSigma_0ki, smallsigma_ujk and smallsigma_uki.

2) Strong dependence on q_0jk and q_0ki: if I were to setup these two parameters to zero or to the same value I can't obtain solutions anymore (especially for the lambdas). Does it mean that they are not really "free" parameters?

I noticed that if I combine the two equations from the FOCs of mu_jk and mu_ki into one system (is this even legit?), I get q_0jk = - q_0ki * (lambda_jk / lambda_ki). This is also easy to see if I apply the calibration at the beginning of the script (remove hashtags on all the params with the exception of q_0jk and q_0ki) and then divide lambda_jk by lambda_ki. Why?

I am quite sure that the computations are correct (I checked multiple times), but I am now questioning my setup. In which ways does my setup differ from the one below?

Essentially, I am trying to extend the following problem. As you see below, mu depends only on p_0 (the one-dimensional equivalent of my q_0jk and q_0ki) and lambda depends only on BigSigma_0 and smallsigma_u (the one-dimensional equivalents of my BigSigma_0jk, BigSigma_0ki, smallsigma_ujk and smallsigma_uki).

Thank you.

Hello!

I have changed the the global character size from 12 to 14 but it is not stable. Suddenly size 12 is coming up when a try to copy a row to a another row in the same worksheet.

It is very annoying!!

Any tips????

Regards

Kjell

Download 0_one.mw

Just experienced a strange response from Maple when I changed the Font anti-aliasing to enabled.

With Font anti-aliasing disabled I ran evalf(Pi,100) and Maple returned 100 digits - no problem.  I then did some other errands in other programs leaving Maple idle, when I came back I thought I would change anti-aliasing to enabled and see if maybe that's the reason why some users are experiencing icons disappearing etc..

Well I re entered and evalueated evalf(Pi,100) and Maple only output 10 digits.  Huh??? What!? Why?  changed font anti-aliasing back but no joy.  So I closed Maple and I got a pop up

Maybe it was hiding behind Maple I don't know but I don't think it was there until I closed Maple.  It seems this OpenJDK platform I believe is causing a lot of Maple issues.

Whoa!  That's really odd.  My restart was with Maple Font anti-aliasing enabled I performed a evalf(Pi,100) and no problem.  I changed to Font anti-aliasing disabled and evalf(Pi,100) presented me with 10 digits!

What the heck is going on.  This font anti-aliasing enabled caused my Maple to slow down as the screen filled up (as I recorded in a earlier post months ago) and now toggling anti-aliasing causes the outputs to not work as expected.  It's gotta be an open JDK issue. (FYI closing Maple did not produce the same pop-up as earlier - I expect idling maple for a while might)

Please check the following examples, first without using Units, and the second using it:

No Units:

With Units:

Why does the with(Units) doesn't compute the value? How can I make it work?

Thanks

in phase portrait 3d , i use 4 initial condition, How  can I draw each initial condition in diferent colour. it very helpfull so i can see the moving of each IC. Thank you

I'm learning about simplifications in Maple and I'm trying to make it simplify simple trigonometric expressions like sin(x) / cos(x) to tan(x), but it doesn't.

I tried the commands simplify(sin(x) / cos(x)), simplify(sin(x) / cos(x), trig) and nothing works. It still returns:

I managed to make it work using convert(sin(x)/cos(x), tan):

BUT it creates more problems than it solves, because if I have something like , I would like it to simplify as tan(x)*cos(x), but instead it converts everything to tan and I get a much more complicated expression:

Can someone help me please?

Hi,

Can anybody explain why

with(Units):
A := 1, 2, 3:
B := 4, 5, 6:
AB := B - A;

outputs 11, but the output is 3, 3, 3 without the Units package?

Best regards,

Mikkel

I have some c# function that i want to use in maple, and I doing all according to this arcticle : https://www.mapleprimes.com/posts/38019-Calling-Out-To-C-From-Maple
but i still get this: 
Any ideas what i should do?

Download easy_way.mw

Here are all non-isomorphic 3-regular vertex-transitive graphs with 62 vertices. I wanted to draw them all at once, but I found that tables cannot use the map function.

with(GraphTheory):
CubicVT[1] := Graph({{23,60}, {37,6}, {36,27}, {61,19}, {60,29}, {2,52},
{40,43}, {23,25}, {45,50}, {1,30}, {11,17}, {13,41}, {34,4}, {11,54}, {26,49}, 
{56,2}, {49,51}, {3,21}, {47,28}, {24,52}, {13,7}, {48,27}, {51,42}, {4,60}, 
{55,45}, {46,21}, {46,38}, {57,14}, {4,31}, {24,8}, {47,20}, {44,5}, {55,43}, 
{30,31}, {18,41}, {17,42}, {46,37}, {36,16}, {8,43}, {58,30}, {17,53}, {25,5}, 
{5,31}, {24,9}, {9,53}, {22,26}, {35,50}, {48,20}, {12,36}, {33,13}, {12,58}, 
{33,29}, {35,14}, {3,19}, {41,42}, {14,10}, {25,21}, {37,32}, {2,48}, {52,10}, 
{61,10}, {57,58}, {38,7}, {3,62}, {29,51}, {35,8}, {39,32}, {49,6}, {1,27}, 
{39,40}, {12,50}, {56,53}, {59,62}, {34,15}, {18,9}, {1,28}, {22,55}, {33,15}, 
{39,7}, {44,57}, {59,38}, {11,26}, {45,54}, {15,59}, {44,19}, {47,62}, {16,54}, {61,20}, {23,6}, {56,16}, {22,32}, {18,40}, {34,28}});

CubicVT[2] := Graph({{39,7}, {18,41}, {11,17}, {22,32}, {46,29}, {24,8},
{18,40}, {44,19}, {55,43}, {23,25}, {45,9}, {46,38}, {59,38}, {13,6}, {39,51}, 
{48,27}, {56,16}, {57,58}, {25,21}, {52,10}, {17,43}, {22,41}, {61,20}, {15,59},
{14,27}, {39,32}, {24,54}, {42,32}, {17,53}, {56,35}, {41,42}, {34,15}, {2,52}, 
{40,43}, {33,13}, {36,10}, {44,28}, {49,6}, {56,2}, {45,54}, {25,15}, {2,50}, 
{58,20}, {61,30}, {57,48}, {48,20}, {47,62}, {35,8}, {37,6}, {13,7}, {4,31}, 
{47,28}, {35,50}, {1,19}, {49,7}, {60,29}, {61,19}, {51,42}, {11,26}, {55,45}, 
{3,4}, {36,27}, {16,54}, {9,53}, {11,40}, {47,5}, {14,10}, {23,59}, {16,8}, 
{5,31}, {24,9}, {12,36}, {3,21}, {62,31}, {22,26}, {33,37}, {57,14}, {46,37}, 
{34,21}, {1,28}, {12,52}, {34,4}, {44,5}, {12,50}, {38,60}, {55,53}, {23,60}, 
{1,30}, {58,30}, {33,29}, {3,62}, {26,18}, {49,51}});

CubicVT[3] := Graph({{23,60}, {37,6}, {38,51}, {36,27}, {61,19}, 
{60,29}, {2,52}, {40,43}, {23,25}, {1,30}, {17,39}, {11,17}, {34,4}, {33,21}, 
{23,7}, {56,2}, {1,10}, {11,8}, {49,51}, {3,21}, {47,28}, {13,7}, {48,27}, 
{25,28}, {51,42}, {55,45}, {13,26}, {46,38}, {57,14}, {4,31}, {24,8}, {44,5}, 
{55,43}, {44,27}, {2,58}, {15,6}, {18,41}, {46,37}, {58,30}, {17,53}, {5,31}, 
{24,9}, {9,53}, {22,26}, {35,50}, {48,20}, {12,36}, {33,13}, {18,54}, {50,53}, 
{24,36}, {33,29}, {3,30}, {41,42}, {14,10}, {25,21}, {20,31}, {12,61}, {52,10}, 
{57,58}, {3,62}, {35,8}, {39,32}, {49,6}, {29,32}, {12,50}, {56,43}, {55,42}, 
{22,9}, {34,15}, {1,28}, {39,7}, {45,52}, {59,5}, {59,38}, {57,47}, {60,62}, 
{11,26}, {37,41}, {35,48}, {45,54}, {15,59}, {44,19}, {47,62}, {16,54}, {46,4}, 
{61,20}, {14,16}, {56,16}, {34,19}, {22,32}, {18,40}, {49,40}});

CubicVT[4] := Graph({{13,9}, {39,7}, {18,41}, {33,28}, {11,17}, {39,8}, 
{22,32}, {24,8}, {18,40}, {44,35}, {44,19}, {55,43}, {23,25}, {46,38}, {59,38}, 
{34,27}, {2,47}, {12,31}, {48,27}, {7,62}, {56,16}, {57,58}, {25,21}, {52,10}, 
{3,10}, {61,20}, {15,59}, {45,58}, {5,6}, {39,32}, {17,53}, {41,42}, {34,15}, 
{2,52}, {59,20}, {48,53}, {40,43}, {38,40}, {33,13}, {49,6}, {56,2}, {45,54}, 
{1,16}, {48,20}, {55,37}, {47,62}, {35,8}, {14,43}, {37,6}, {13,7}, {4,31}, 
{47,28}, {35,50}, {60,29}, {61,19}, {51,42}, {24,61}, {22,50}, {11,26}, {55,45},
{11,36}, {4,51}, {49,54}, {36,27}, {16,54}, {9,53}, {14,10}, {5,31}, {24,9}, 
{12,36}, {21,32}, {3,21}, {18,52}, {22,26}, {15,41}, {56,42}, {17,29}, {57,14}, 
{46,37}, {1,28}, {34,4}, {44,5}, {23,26}, {12,50}, {60,30}, {23,60}, {1,30}, 
{58,30}, {33,29}, {3,62}, {57,25}, {46,19}, {49,51}});

CubicVT[5] := Graph({{39,7}, {18,41}, {11,17}, {22,32}, {24,8}, {18,40},
{44,19}, {56,49}, {55,43}, {23,25}, {52,42}, {2,3}, {14,18}, {59,38}, {46,38}, 
{62,32}, {48,27}, {56,16}, {26,21}, {15,40}, {57,58}, {25,21}, {58,43}, {33,30},
{52,10}, {22,36}, {61,20}, {15,59}, {13,8}, {39,32}, {28,7}, {17,53}, {41,42}, 
{23,17}, {34,15}, {2,52}, {40,43}, {33,13}, {49,6}, {56,2}, {45,54}, {47,16}, 
{25,10}, {12,34}, {61,53}, {5,51}, {48,20}, {39,50}, {47,62}, {35,31}, {35,8}, 
{37,6}, {13,7}, {4,31}, {47,28}, {35,50}, {60,29}, {61,19}, {51,42}, {11,26}, 
{57,60}, {55,45}, {6,19}, {44,24}, {36,27}, {16,54}, {9,53}, {14,10}, {5,31}, 
{24,9}, {12,36}, {11,48}, {3,21}, {22,26}, {29,9}, {57,14}, {46,37}, {1,28}, 
{55,38}, {46,20}, {34,4}, {59,27}, {4,41}, {44,5}, {1,45}, {12,50}, {23,60}, 
{1,30}, {58,30}, {33,29}, {3,62}, {49,51}, {37,54}});

CubicVT[6] := Graph({{39,7}, {57,54}, {18,41}, {11,17}, {22,32}, {24,8},
{18,40}, {44,19}, {55,43}, {11,33}, {23,25}, {4,48}, {46,38}, {59,38}, {12,17}, 
{47,29}, {48,27}, {56,16}, {57,58}, {25,21}, {52,10}, {16,41}, {61,20}, {15,59},
{35,26}, {56,30}, {39,32}, {6,43}, {17,53}, {41,42}, {34,15}, {2,52}, {27,9}, 
{40,43}, {33,13}, {14,62}, {49,6}, {56,2}, {34,49}, {45,54}, {13,3}, {28,52}, 
{48,20}, {47,62}, {35,8}, {7,53}, {37,6}, {13,7}, {4,31}, {47,28}, {35,50}, 
{60,29}, {2,40}, {61,19}, {51,42}, {58,21}, {11,26}, {55,45}, {22,60}, {1,23}, 
{25,39}, {36,27}, {16,54}, {46,18}, {9,53}, {14,10}, {36,5}, {5,31}, {37,31}, 
{24,9}, {12,36}, {24,32}, {55,10}, {8,20}, {15,61}, {3,21}, {44,38}, {22,26}, 
{57,14}, {45,51}, {46,37}, {1,28}, {34,4}, {44,5}, {12,50}, {50,19}, {23,60}, 
{1,30}, {59,42}, {58,30}, {33,29}, {3,62}, {49,51}});

CubicVT[7] := Graph({{27,20}, {57,30}, {24,53}, {19,20}, {37,49}, 
{13,29}, {11,17}, {56,52}, {24,8}, {18,40}, {44,19}, {57,10}, {55,43}, {28,62}, 
{6,51}, {46,38}, {33,7}, {18,42}, {48,27}, {56,16}, {4,5}, {57,58}, {25,21}, 
{11,22}, {12,27}, {25,60}, {61,20}, {44,31}, {62,21}, {15,59}, {17,9}, {39,32}, 
{41,42}, {2,10}, {2,52}, {37,38}, {11,53}, {36,50}, {45,54}, {46,6}, {2,16}, 
{44,61}, {14,58}, {26,32}, {5,19}, {48,61}, {37,6}, {13,7}, {47,28}, {49,42}, 
{35,50}, {3,47}, {12,35}, {4,15}, {23,29}, {55,54}, {34,59}, {55,40}, {1,58}, 
{46,59}, {45,16}, {9,53}, {8,9}, {40,41}, {22,39}, {14,10}, {45,43}, {5,31}, 
{12,36}, {56,54}, {23,21}, {24,35}, {50,8}, {28,30}, {18,43}, {34,31}, {22,26}, 
{7,32}, {3,25}, {14,52}, {15,38}, {26,17}, {34,4}, {1,47}, {33,60}, {23,60}, 
{1,30}, {33,29}, {3,62}, {51,41}, {36,48}, {49,51}, {13,39}});

DrawGraph~(CubicVT)

Error, invalid input: GraphTheory:-DrawGraph expects its 1st argument, H, to be of type {GRAPHLN, list(GRAPHLN), set(GRAPHLN)}, but received Graph({{1, 30}, {1, 47}, {1, 58}, {2, 10}, {2, 16}, {2, 52}, {3, 25}, {3, 47}, {3, 62}, {4, 5}, {4, 15}, {4, 34}, {5, 19}, {5, 31}, {6, 37}, {6, 46}, {6, 51}, {7, 13}, {7, 32}, {7, 33}, {8, 9}, {8, 24}, {8, 50}, {9, 17}, {9, 53}, {10, 14}, {10, 57}, {11, 17}, {11, 22}, {11, 53}, {12, 27}, {12, 35}, {12, 36}, {13, 29}, {13, 39}, {14, 52}, {14, 58}, {15, 38}, {15, 59}, {16, 45}, {16, 56}, {17, 26}, {18, 40}, {18, 42}, {18, 43}, {19, 20}, {19, 44}, {20, 27}, {20, 61}, {21, 23}, {21, 25}, {21, 62}, {22, 26}...
Why can lists use the map function, but tables cannot?

DrawGraph~([seq(CubicVT[i],i=1..7)])

tablemap.mw

That is to say, a generalized map. 
E.g., here is a nested list: 

nl := [[[[s, t]], [u, [v, w]]], [[x, [y, z]]]]:

We can use map to apply the mapped function F to "each operand" (i.e., the first‐level parts) of : 

:-map(F, nl);
 = 
         [F([[[s, t]], [u, [v, w]]]), F([[x, [y, z]]])]

But in Mathematica, we can make further explorations: 

In[1]:= nl = {{{{s, t}}, {u, {v, w}}}, {{x, {y, z}}}}; 

In[2]:= Map[F, nl, {1}] (*Maple's result*)

Out[2]= {F[{{{s, t}}, {u, {v, w}}}], F[{{x, {y, z}}}]}

In[3]:= Map[F, nl, {2, -2}]

Out[3]= {{F[{F[{s, t}]}], F[{u, F[{v, w}]}]}, {F[{x, F[{y, z}]}]}}

In[4]:= Map[F, nl, {-3, 3}]

Out[4]= {{F[{F[{s, t}]}], F[{F[u], F[{v, w}]}]}, {F[{F[x], F[{y, z}]}]}}

In[5]:= Map[F, nl, {0, \[Infinity]}, Heads -> \[Not] True]

Out[5]= F[{F[{F[{F[{F[s], F[t]}]}], F[{F[u], F[{F[v], F[w]}]}]}], F[{F[{F[x], F[{F[y], F[z]}]}]}]}]

Note that the last case has been implemented in Maple as MmaTranslator[Mma][MapAll]:  

MmaTranslator:-Mma:-MapAll(F,nl);
 = 
   F([F([F([F([F(s), F(t)])]), F([F(u), F([F(v), F(w)])])]), 

     F([F([F(x), F([F(y), F(z)])])])])

Naturally, how to reproduce the other two results in Maple programmatically? (The output may not be easy to read or understand; I have added an addendum below.)

Addendum. It is also possible to display in "tree" structure (like dismantle) manually: 

`[]`
(
    `[]`
    (
        `[]`
        (
            `[]`
            (
                s
            ,
                t
            )
        )
    ,
        `[]`
        (
            u
        ,
            `[]`
            (
                v
            ,
                w
            )
        )
    )
,
    `[]`
    (
        `[]`
        (
            x
        ,
            `[]`
            (
                y
            ,
                z
            )
        )
    )
)

As you can see, the "depth" of  is five (0, 1, 2, 3, and 4), while the classical map just maps at the first "level". (Moreover, such descriptions may lead to a confusion.)

Supplement. Unfortunately, there remains a bug in the MmaTranslator[Mma][Level]. Compare: 

MmaTranslator:-Mma:-Level(nl, [4]); (*Maple*)
                             [v, w]

MmaTranslator:-Mma:-Level(nl, [-1]); (*Maple*)
          [s, t, u, v, w, x, y, z, -1, x, c, r, y, 2]

In[6]:= Level[nl, {4}] (*Mathematica*)

Out[6]= {s, t, v, w, y, z}

In[7]:= Level[nl, {-1}] (*Mathematica*)

Out[7]= {s, t, u, v, w, x, y, z}

Hey guys.

I want to replace _Z1, _Z2 and _B2 with n but it doesn't work. Can anyone help?

An example is attached.

Regards,

Oliveira

Example3.mw

I have noticed this before few times. I wonder if others have seen it.

When I have Maple open, (with may be few worksheets open) and not being used at all for anything and it is not running anything, after sometime (say 2-4 hrs or more), when I go back to using Maple, I find the GUI unresponsive. Nothing happens. Clicking on anything does nothing, It is frozen. Resizing the window, it become black and does not repaint.  

But If I wait about 5-10 minutes after doing this window resizing, it suddenly becomes responsive again and it become alive again.  This happened twice this week, where I was about to just kill Maple. Good thing I did not.

It feels like the Maple process/frontend went to sleep when not being used, and it takes few minutes to wake it up by shaking the window. I do not know what else could explain this.

This is windows 10. Latest updates and lots of RAM and nothing else is running on the PC at this time.

I go take a nap, come back and notice this. It does not happen all the time, but noticed it twice this week.

Any others seen this problem? Does Maple process go to sleep or hibernate when it detects it is not being used for sometime? Looking at task manager when this happens, I see no CPU activity at all and no memory changes at all in any of the servers.exe. So I think this might be a GUI issue, where Java go to sleep or something.   

Or it could be a windows 10 issue and not Maple. But I only noticed this with Maple where it seems to go to sleep when not used.

Hello there, 

Is there any chance to ask this one question?

The attached (following) worksheet shows the result of LieDerivative operation, which is not correct. 

The correct answer is given in the image in the middle of the worksheet. Is there any particular reason regarding Maple's way of conducting the operation in that way?

Download Q20230307.mw