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lcz

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6 years, 163 days
changsha, China
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Does function Solve have limitations b...

lcz 1039 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 1039
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 1039 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 1039 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.

 

Two colors dye the same Vertex of graph...

lcz 1039 Maple 2020
graphtheory color
September 17 2020
2 3

I'm thinking of better demonstrating the cartesian product of a graph.
With the help documentation, we can easily find the cartesian product of two graphs.

with(GraphTheory):
G := CycleGraph([v__1,v__2,v__3,v__4]);
H:=Graph({{u__1,u__2}}):
DrawGraph(G,size=[250,250],stylesheet=[vertexborder=false,vertexpadding=10,edgecolor = "Red",
vertexcolor="navy",edgethickness=3]);
DrawGraph(H,size=[250,250],stylesheet=[vertexborder=false,vertexpadding=10,edgecolor = "Blue",
vertexcolor="Gold",edgethickness=3]);


GH:=CartesianProduct(G,H)
DrawGraph(GH,style=spring)

 

 

 

When I saw Wikipedia's demo diagram, https://en.wikipedia.org/wiki/Cartesian_product_of_graphs

I was fascinated,and I also wanted to visually reflect the nature of Cartesian product by doing different staining of vertices.
It is easy for me to dye the vertices in one color, but it is difficult for two different colors .

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