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lcz

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6 years, 129 days
changsha, China
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Is parse in textplot not useful?...

lcz 994 Maple 2020
typesetting textplot plotting
December 27 2020
3 3

By the code

P := plot( [ sin(x)-x+(x^3)/3! ] ) :
L := plots[textplot]( [ 3 , 15 , sin(x)-x+(x^3)/3! ],  axes = none) :
plots[display]( P ,L, axes = normal )

I'd like to put the text sin(x)-x+(x^3)/3!  not  sin(x)-x+(x^3)/6   in the image.

I thought  that parse can do that

parse("sin(x)-x+(x^3)/3!")

But One use it in plots[textplot] , it is not useful!

P := plot( [ sin(x)-x+(x^3)/3! ] ) :
L := plots[textplot]( [ 3 , 15 , parse("sin(x)-x+(x^3)/3!") ],  axes = none) :
plots[display]( P ,L, axes = normal )

How to do? Thanks!

Does function Solve have limitations b...

lcz 994 Maple 2020
solve implicit rootof
December 26 2020
1 0

 The code

s:=solve(sin(x)=3*x/Pi,x)

gives us following output:

s := RootOf(-sin(_Z)*Pi + 3*_Z)

The allvalues command attempts to find symbolic representations of the roots using solve.
But  the code:

allvalues(s);
solve(sin(x)=3*x/Pi,x,AllSolutions)

gives us 

RootOf(-sin(_Z)*Pi + 3*_Z, 0.5235987756), RootOf(-sin(_Z)*Pi + 3*_Z, -0.5235987756), 0

RootOf(-sin(_Z)*Pi + 3*_Z)

To see the roots of sin(x)-3*x/Pi   we use plot

plot(sin(x)-3*x/Pi,x=-100..100)

 

plot(sin(x)-3*x/Pi,x=-Pi/4..Pi/4)

And we can also figure out  three roots of this function are 0 ,  Pi/6 and -Pi/6. 

High probability it has no other root.

seq(eval(sin(x)-3*x/Pi,x=i),i in [-Pi/6,0,Pi/6])

0, 0, 0

Why doesn't Maple do anything about it

 

 

 

How to split a list into two lists by ev...

lcz 994
list
December 19 2020
2 4

 I want to split a arbirtray list of elements by position into two new lists containing all the even and odd elements.

Example: With a list like this:

ls:=["a", "b", "c", "d", "e"]

how can I get two lists like this:

["a", "c", "e"], ["b", "d"]

How to do it in Maple ? Thanks！ 

Maybe selectremove is useful?

 

 

 

 

 

No solution or infinite solutions？...

lcz 994 Maple 2020
polynomial solve
December 09 2020
1 2

 

This is the last step of my calculation. I get  following system of equations：

s:={a__11 = -b__1^2 + 5/4, a__12 = -b__1*b__2 + 7/4, a__13 = -b__1*b__3 - 1/2, a__14 = -b__1*b__4 - 1/2, a__15 = -b__1*b__5 - 1/2, a__16 = -b__1*b__6 - 1/2, a__17 = -b__1*b__7 - 1/2, a__22 = -b__2^2 + 5/4, a__23 = -b__2*b__3 - 1/2, a__24 = -b__2*b__4 - 1/2, a__25 = -b__2*b__5 - 1/2, a__26 = -b__2*b__6 - 1/2, a__27 = -b__2*b__7 - 1/2, a__33 = -b__3^2 - 1, a__34 = -b__3*b__4 + 1, a__35 = -b__3*b__5, a__36 = -b__3*b__6, a__37 = -b__3*b__7 + 1, a__44 = -b__4^2 - 1, a__45 = -b__4*b__5 + 1, a__46 = -b__4*b__6, a__47 = -b__4*b__7, a__55 = -b__5^2 - 1, a__56 = -b__5*b__6 + 1, a__57 = -b__5*b__7, a__66 = -b__6^2 - 1, a__67 = -b__6*b__7 + 1, a__77 = -b__7^2 - 1, b__1 = b__1, b__2 = b__2, b__3 = b__3, b__4 = b__4, b__5 = b__5, b__6 = b__6, b__7 = b__7}

 

I want to solve this system of equations

solve(s,{a__11, a__12, a__13, a__14, a__15, a__16, a__17, a__22, a__23, a__24, a__25, a__26, a__27, a__33, a__34, a__35, a__36, a__37, a__44, a__45, a__46, a__47, a__55, a__56, a__57, a__66, a__67, a__77, b__1, b__2, b__3, b__4, b__5, b__6, b__7})

 

But I  didn't get any more valuable information 

Actually I'd like to  know if there is no  real solution.

If there is a real number solution,   one is enough for me.

Any help would be greatly appreciated

 

layouts about DrawGraph...

lcz 994 Maple 2020
graphtheory drawgraph
October 15 2020
0 3

I've been studying the  drawing  of graph lately .    One of the themes is  1-planar graph .

A 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point,  where it crosses a single additional edge. If a 1-planar graph, one of the most natural generalizations of planar graphs, is drawn that way, the drawing is called a 1-plane graph or 1-planar embedding of the graph.

 

 

 

 

 

I know it is NP hard to determine whether a graph is a 1-planar . My idea is to take advantage of some mathematical software to provide some roughly and  intuitive understanding before determining .

Now,  the layout of vertices or edges becomes important.  The drawing of a plane graph is a good example.

G1:=AddEdge( CycleGraph([v__1,v__2,v__3,v__4]),{{v__2,v__4},{v__1,v__3}}):
DrawGraph(G1)
DrawGraph(G1,style=planar)

K5 := CompleteGraph(5);
DrawGraph(K5);
vp:=[[-1,0],[1,0],[-0.2,0.5],[0.2,0.5],[0,1]];
SetVertexPositions(K5,vp);  #modified the vertex position
DrawGraph(K5);

My problem is that I see that  Maple2020 has updated a lot of layouts about DrawGraph  graph theory backpack , and I don’t know which ones are working towards the least possible number of crossing of  each edges of graph . 

Some links that may be useful:

https://de.maplesoft.com/products/maple/new_features/Maple2020/graphtheory.aspx

https://de.maplesoft.com/support/help/Maple/view.aspx?path=GraphTheory/SetVertexPositions

I think the software can improve some calculations related to topological graph theory, such as crossing number of graph, etc.

 

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