The command for doing syntactical exact-match substitutions is subs, however, subs applies transformation rules throughout an expression only once. The documentation of eval claims that the (recursive) evaluation is repeated until either the result does not change, the documentation of applyrule claims that applyrule … applies the rules until no rule can be applied any more, and the documentation of MmaTranslator[Mma][ReplaceRepeated] claims that the single ReplaceRepeated command performs replacements until expression no longer changes.
So, if I comprehend correctly, 

restart;
x := [[[[]]]]: # Remove empty lists from x repeatedly.
(*⒈*) eval['recurse'](x, [[] = 'NULL']);
(*⒉*) applyrule([[] = 'NULL'], x);
(*⒊*) MmaTranslator:-Mma:-ReplaceRepeated(x, [[] = NULL])

should all return NULL, but in fact, 

eval['recurse'](x, [[] = 'NULL']);
 = 
                            [[[[]]]]

applyrule([[] = 'NULL'], x);
Error, (in PatternMatching:-AlgStruct:-TableLookup) invalid input: unknown uses a 1st argument, x, which is missing
MmaTranslator:-Mma:-ReplaceRepeated(x, [[] = NULL]);
 = 
                            () = ()

In other words, none of these replacements is feasible. 

Have I missed something? (It seems to me that an explicit procedural do...until loop can be actually avoidable here!) 

My main question is: How to change the font used in worksheet by Maple for 1D input from Courier to another font say times new roman? Is there a setting for this so it applies all the time?

ps. I found Can-I-Change-the-Default-Fonts-or-Style-for-Maple-Worksheets-and-Documents?language=en_US  (very hard to follow and confusing, but it seems that is only way to fix this problem now is to change the default font).

-----------------------------------------------------------------------------------------------------------------

I noticed strange font problem using Maple 2023 on windows 10. This problem does not show on Maple 2022.2 (at least I do not think I've seen it or noticed it before). 

Variables with _ between the names, will have the underscore not display sometimes as I move the cursor around (movie at end).

When scrolling back up, the underscores no longer become visible. 

But as I move the cursor over the variable name which containes the underscore, they will now show up.

I am sure this is a font issue. The zoom is set at 100%. I made no changes at all other than making the input 1D math as I normally do and set the default to worksheet. Some of my setting are below.

This could be a DPI issue settings of some sort. My monitor is standard monitor (not a 4K one) and again, I have not changed any settings on my PC after I installed Maple 2023 and did not change any hardware.

Here is some system information also

Here is the movie showing the problem

As I play more with it, I notice a common theme. This happens when I hit the UP ARROW to go to the line above. Then suddenly the underscroes no longer visible. Once I hit the LEFT arrow (now I am at the above line), they show up again.

Here is another movie which more clearly shows this.

This makes it very hard to work with the code in the worksheet. But I am sure this can be fixed as it looks like just a font configuration issue with Maple on windows. But I do not know what it is and how to fix it.

I found something new. When setting the ZOOM at 125% instead of 100% as above, I notice the underscores do not completely disappear but become THINNER but one can still see them. This affects only the underscores. When the ZOOM at 150%, they do not change at all.  Here is a movie. first part at 125%. Notice how they become little thinner when doing the same thing as above. But at 150% they remain visible because they do not change thinkness. When going back to 100% zoom, they  no longer show.

So the problem is that they are there all the time, but depending on the ZOOM level, they beome thinner and thinner until they become invisible to the eye.

I found some related issue on windows 10 with some application where this problem shows up.

some-characters-missing-or-cut-off-when-displayed-on-screen

 "When you view your document in Microsoft Word, some characters may be missing, or the top (or bottom) of some characters may be cut off.

This problem may affect the following types of characters:

Underscore"

The above is about WORD, but it could as well apply to Maple?

I also found  underscore not rendering with courier

"Underscore characters are not rendered in new Google Docs in the Courier
New 11pt or 12pt fonts."

My question is: How to change the font used in worksheet by Maple? Now it is using Courier. May be if I change the font, this problem will go away?

Update: Found a workaround!  It is the font used!  I changed from Courier to Times New Roman and now the underscore do not change thinkness!  I just need a way to make this permenant for all 1D Maple input.   Here is a new movie showing it is fixed. You can see the underscores remain visible, all at 100% ZOOM level. Once I change to Courier, the problem show up again. 

I am not sure if this is a Maple issue or windows.

Download easy_way.mw

The new command ArrayTools[GeneralOuterProduct] (introduced in Maple 2021) computes the generalized outer product of two rtables, and again, there exists a similar function Outer in Mma (cf. the end of this question). But in practice, it appears that this Maple command is not so fast as Mma's one. To begin with, we need to generate four lists: w, x, y, and z. Our goal is forming all possible combinations of the lowest‐level elements in a nested structure (rather than a flat structure). Now let us start the test.

In Mathematica (the real time is about ): 

And in Maple (the real time is about ): 
 

Download Outer.mw

As you can see, Maple and Mathematica returns identical results (∵p₁＝p₃); nevertheless, Maple consumes too much time: the ratio is 199.880/0.784176 ≈ 254.892. (What a wide gap between them!) 
So, is there any possibility of speeding up Maple's ArrayTools:-GeneralOuterProduct? Or any ideas of obtaining the same results in Maple efficiently?

Explanatory notes. Here is an illustrative animation: 

Let L be a list like

L:=[[3, 2], [2, 1], [1, 2], [1, 2], [2, 3], [2, 1], [1, 2], [1, 1], [2, 1], [1, 2], [1, 1], [2, 1], [1, 1], [1, 3], [1, 2], [2, 1], [1, 3], [1, 3], [1, 3], [1, 2], [2, 2], [2, 3]]

Now we consider [3,1] and [1,3] as same 

First we form a list gives us 

Lk:=[[[1,3],4],[[1.2],11],[[2,3],3],[[2,2],1],[[1,1],3]]

That is [1,3] appears 4 times in L

[1,2] appears 11 times in L

[2,3] appears 3 times in L

[1,1] appears.3 times in L

[2,2] appears 1 times in L

now we do addtion in [1,3] which is 1+3=4 therefore [[1,3],4] become [4,4]

[2,2] becomes 2+2=4 therefore [[2,2],1] is [4,1]

[[1,2],11] become [3,11]

[[2,3],3] becomes [5,3]

[[1,1],3] becomes [2,3]

So new list is [[4,4],[3,11],[5,3],[2,3],[4,1]]

so answer is from [4,4] we get 4 *4 , from [3,11] we get 3*11 , from [5,3] we get 5*3 and from [2,3] we get 2*3 from [4,1] we get 4*1

final required answer is (4*4)*(3*11)*(5*3)*(2*3)*(4*1)  =190080

Any list L like above if given kind help with a function which can do the above operation and give the final answer that is in above case 190080

Hi,

 Is it possible to write the Maple code to reach the partial differential equation from the following answer and reach the equation?

 Examples of it 

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

Could you help how to fix the code?

Download DEplot_v1.mw

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

Download Approfondimento_1_-_Calcolo_Sfera_2D.mw

I have JPG images and plots from a CAD code and from Matlab. I want to insert them into a Maple worksheet and do the following:

      1. Resize the images or plots while preserving aspect ratio

      2. Add a figure number and caption to the image or plot.

          I would prefer automatic numbering if that is available in Maple.

          I would also prefer to have the caption "linked" to the image or plot so that they can be moved together

I assumed that these kinds of tools were available in Maple, but I sure cannot find them. Any help will be greatly appreciated.

Thanks, Neill Smith

I just downloaded maple 2021 (I get i free from my school). I used maple for the last 4 years but, now when i opdatede to maple 2021 from version 2020, its just keep freezing i have try to uninstall 3 times by now and it still keep freezing.

Hi.

plot([cos(t), sin(t), t = 0 .. 2*Pi]) give a nice circle.

but

plot([cos(t), sin(t), t = 0 .. 2*Pi*10000])

have the whole circle filled.

Is this a bug or expected behavior?

Thanks.

Huajun

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.