Advanced Search

MaplePrimes Questions

adomian polynomial for nolinear function...

Asked by: usmanjutt 15
differentiation summation duplicate-question
October 15 2020
1  1

i have two nonlinear functions from which one is exicuted properly but 2nd funnction not risponde properly. i can not understan how to overcome it
 

> 

restart
> 

with(LinearAlgebra):
> 

> 

F := proc (x) options operator, arrow; x^2 end proc:
> 

F(u(t));

u(t)^2

 (1)
> 

G := proc (w) options operator, arrow; w*dw/dt end proc:
> 

G(h(t));

h(t)*dw/dt

 (2)
> 

for n from 0 while n <= 6 do V[n] := (diff(F(sum(t^i*u[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n); U[n] := (diff(G(sum(t^i*h[i], i = 0 .. n)), [`$`(t, n)]))/factorial(n) end do:
> 

t := 0;

0

 (3)
> 

for i from 0 while i <= n-1 do A[i] := V[i]; B[i] := U[i] end do;

u[0]^2

  

h[0]*dw/dt

  

2*u[0]*u[1]

  

h[1]*dw/dt

  

2*u[0]*u[2]+u[1]^2

  

h[2]*dw/dt

  

2*u[0]*u[3]+2*u[1]*u[2]

  

h[3]*dw/dt

  

2*u[0]*u[4]+2*u[1]*u[3]+u[2]^2

  

h[4]*dw/dt

  

2*u[0]*u[5]+2*u[1]*u[4]+2*u[2]*u[3]

  

h[5]*dw/dt

  

2*u[0]*u[6]+2*u[1]*u[5]+2*u[2]*u[4]+u[3]^2

  

h[6]*dw/dt

 (4)
> 

for j from 0 while j <= n-1 do u[0] := 1; u[j+1] := int(x*B[j], x)+int(A[j], x) end do;

1

  

(1/2)*x^2*h[0]*dw/dt+x

  

1

  

(1/2)*x^2*h[1]*dw/dt+(1/3)*x^3*h[0]*dw/dt+x^2

  

1

  

(1/2)*x^2*h[2]*dw/dt+(1/3)*x^3*h[1]*dw/dt+(5/12)*x^4*h[0]*dw/dt+x^3+(1/20)*h[0]^2*dw^2*x^5/dt^2

  

1

  

(1/2)*x^2*h[3]*dw/dt+(1/3)*x^3*h[2]*dw/dt+(1/6)*x^4*h[1]*dw/dt+(1/6)*x^5*h[0]*dw/dt+(1/2)*x^4+(13/180)*h[0]^2*dw^2*x^6/dt^2+(2/5)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^5+(1/2)*((1/2)*h[1]*dw/dt+1)*x^4

  

1

  

(1/2)*x^2*h[4]*dw/dt+(1/3)*x^3*h[3]*dw/dt+(5/12)*x^4*h[2]*dw/dt+(1/15)*x^5*h[1]*dw/dt+(1/18)*x^6*h[0]*dw/dt+(1/5)*x^5+(139/1260)*h[0]^2*dw^2*x^7/dt^2+(2/15)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*x^5+(1/160)*h[0]^3*dw^3*x^8/dt^3+(1/3)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^6+(2/5)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^5+(1/9)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^6/dt+(1/5)*((1/2)*h[1]*dw/dt+1)^2*x^5

  

1

  

(1/2)*x^2*h[5]*dw/dt+(1/3)*x^3*h[4]*dw/dt+(5/12)*x^4*h[3]*dw/dt+(1/6)*x^5*h[2]*dw/dt+(1/45)*x^6*h[1]*dw/dt+(1/63)*x^7*h[0]*dw/dt+(139/5040)*h[0]^2*dw^2*x^8/dt^2+(17/1296)*h[0]^3*dw^3*x^9/dt^3+(1/15)*x^6+(4/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^7+(1/15)*((1/2)*h[1]*dw/dt+1)*x^6+(2/21)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(2/15)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/15)*((1/2)*h[1]*dw/dt+1)^2*x^6+(1/4)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^8+(2/7)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(2/5)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^5+(1/4)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^8+(2/7)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^5/dt+(2/63)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^7/dt

  

1

  

(1/20)*h[2]^2*dw^2*x^5/dt^2+(1/3)*x^3*h[5]*dw/dt+(5/12)*x^4*h[4]*dw/dt+(1/6)*x^5*h[3]*dw/dt+(1/18)*x^6*h[2]*dw/dt+(2/315)*x^7*h[1]*dw/dt+(1/252)*x^8*h[0]*dw/dt+(139/22680)*h[0]^2*dw^2*x^9/dt^2+(2167/90720)*h[0]^3*dw^3*x^10/dt^3+(7/8800)*h[0]^4*dw^4*x^11/dt^4+(1/2)*x^2*h[6]*dw/dt+(2/105)*x^7+(2/9)*((13/180)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(1/3)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/4)*(((1/2)*h[1]*dw/dt+1)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)+(1/3)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^8+(2/7)*(((1/2)*h[1]*dw/dt+1)*((5/12)*h[1]*dw/dt+1)+(1/9)*h[0]*dw^2*h[2]/dt^2)*x^7+(1/3)*((1/3)*((1/2)*h[1]*dw/dt+1)*h[2]*dw/dt+(1/6)*h[0]*dw^2*h[3]/dt^2)*x^6+(1/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^8+(2/105)*((1/2)*h[1]*dw/dt+1)*x^7+(1/42)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(4/105)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^7+(2/105)*((1/2)*h[1]*dw/dt+1)^2*x^7+(1/18)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/14)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^8+(2/21)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^7+(2/15)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^6+(1/18)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^9+(1/14)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(2/21)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^7+(1/9)*((1/10)*((1/3)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(25/144)*h[0]^2*dw^2/dt^2)*x^9+(1/8)*((1/20)*h[2]*dw^3*h[0]^2/dt^3+(5/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^8+(1/7)*((5/12)*h[0]*dw^2*h[2]/dt^2+((1/3)*h[1]*dw/dt+1)^2)*x^7+(2/9)*((139/1260)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((43/180)*h[0]*dw/dt+(8/45)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)/dt)*x^9+(1/4)*((43/180)*h[0]*dw/dt+(8/45)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/6)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((3/10)*h[1]*dw/dt+4/5+(1/10)*h[0]*dw^2*h[2]/dt^2+(1/5)*((1/2)*h[1]*dw/dt+1)^2)/dt)*x^8+(2/7)*((3/10)*h[1]*dw/dt+4/5+(37/120)*h[0]*dw^2*h[2]/dt^2+(1/5)*((1/2)*h[1]*dw/dt+1)^2)*x^7+(1/3)*((5/12)*h[2]*dw/dt+(1/6)*h[0]*dw^2*h[3]/dt^2)*x^6+(2/5)*((1/3)*h[3]*dw/dt+(1/4)*h[0]*dw^2*h[4]/dt^2)*x^5+(1/5)*((1/2)*h[1]*dw/dt+1)*h[3]*dw*x^5/dt+(1/15)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^6/dt+(1/126)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^8/dt+(1/6)*h[2]*dw*((1/3)*h[1]*dw/dt+1)*x^6/dt

 (5)
> 

y := sum(u[l], l = 0 .. n-1);

1+(1/2)*x^4+(1/5)*x^5+(1/2)*x^2*h[0]*dw/dt+(1/2)*x^2*h[1]*dw/dt+(1/3)*x^3*h[0]*dw/dt+(1/2)*x^2*h[2]*dw/dt+(1/3)*x^3*h[1]*dw/dt+(5/12)*x^4*h[0]*dw/dt+(1/20)*h[0]^2*dw^2*x^5/dt^2+(1/2)*x^2*h[3]*dw/dt+(1/3)*x^3*h[2]*dw/dt+(1/6)*x^4*h[1]*dw/dt+(1/6)*x^5*h[0]*dw/dt+(13/180)*h[0]^2*dw^2*x^6/dt^2+(1/2)*x^2*h[4]*dw/dt+(1/3)*x^3*h[3]*dw/dt+(5/12)*x^4*h[2]*dw/dt+(1/15)*x^5*h[1]*dw/dt+(1/18)*x^6*h[0]*dw/dt+(139/1260)*h[0]^2*dw^2*x^7/dt^2+(1/160)*h[0]^3*dw^3*x^8/dt^3+(1/2)*x^2*h[5]*dw/dt+(1/3)*x^3*h[4]*dw/dt+(5/12)*x^4*h[3]*dw/dt+(1/6)*x^5*h[2]*dw/dt+(1/45)*x^6*h[1]*dw/dt+(1/63)*x^7*h[0]*dw/dt+(139/5040)*h[0]^2*dw^2*x^8/dt^2+(17/1296)*h[0]^3*dw^3*x^9/dt^3+x+(1/15)*x^6+x^3+(2/15)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^6+(1/15)*((1/2)*h[1]*dw/dt+1)^2*x^6+(1/4)*((13/180)*h[0]^2*dw^2/dt^2+(1/2)*h[0]*dw*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)/dt)*x^8+(2/7)*((3/10)*h[0]*dw/dt+(1/5)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/2)*h[0]*dw*((5/12)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*((5/12)*h[1]*dw/dt+1+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(2/5)*((1/3)*h[2]*dw/dt+(1/4)*h[0]*dw^2*h[3]/dt^2)*x^5+(1/4)*((1/20)*((1/2)*h[1]*dw/dt+1)*h[0]^2*dw^2/dt^2+(5/36)*h[0]^2*dw^2/dt^2)*x^8+(2/7)*((5/12)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt+(1/3)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(1/3)*(((1/2)*h[1]*dw/dt+1)*((1/3)*h[1]*dw/dt+1)+(1/6)*h[0]*dw^2*h[2]/dt^2)*x^6+(4/105)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^7+(1/15)*((1/2)*h[1]*dw/dt+1)*x^6+(2/21)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^7+(2/15)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^6+(1/5)*((1/2)*h[1]*dw/dt+1)*x^5+(1/3)*((5/12)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/3)*h[1]*dw/dt+1)/dt)*x^6+(2/5)*((1/3)*h[1]*dw/dt+1+(1/4)*h[0]*dw^2*h[2]/dt^2)*x^5+(1/5)*((1/2)*h[1]*dw/dt+1)^2*x^5+(2/5)*((1/3)*h[0]*dw/dt+(1/2)*h[0]*dw*((1/2)*h[1]*dw/dt+1)/dt)*x^5+(1/2)*((1/2)*h[1]*dw/dt+1)*x^4+(1/5)*((1/2)*h[1]*dw/dt+1)*h[2]*dw*x^5/dt+(2/63)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^7/dt+(1/9)*h[0]*dw*((1/2)*h[1]*dw/dt+1)*x^6/dt+x^2

 (6)
> 

``
> 

NULL


 

Download incomplete_example.mw

Help!. Transition probability matrix plot for firs...

Asked by: ogunmiloro 120
statistics probability plotting
October 15 2020
0  15


 

> 

P = (Matrix(5, 5, {(1, 1) = .6199, (1, 2) = .1450, (1, 3) = 0.636e-1, (1, 4) = .1549, (1, 5) = 0.166e-1, (2, 1) = .6550, (2, 2) = 0.2e-3, (2, 3) = 0.870e-1, (2, 4) = .1827, (2, 5) = 0.751e-1, (3, 1) = .2990, (3, 2) = .1294, (3, 3) = 0.10e-2, (3, 4) = .4925, (3, 5) = 0.781e-1, (4, 1) = .2773, (4, 2) = .7184, (4, 3) = 0.43e-2, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0.9e-3, (5, 2) = .6229, (5, 3) = .3762, (5, 4) = 0, (5, 5) = 0}))

P = (Matrix(5, 5, {(1, 1) = .6199, (1, 2) = .1450, (1, 3) = 0.636e-1, (1, 4) = .1549, (1, 5) = 0.166e-1, (2, 1) = .6550, (2, 2) = 0.2e-3, (2, 3) = 0.870e-1, (2, 4) = .1827, (2, 5) = 0.751e-1, (3, 1) = .2990, (3, 2) = .1294, (3, 3) = 0.10e-2, (3, 4) = .4925, (3, 5) = 0.781e-1, (4, 1) = .2773, (4, 2) = .7184, (4, 3) = 0.43e-2, (4, 4) = 0, (4, 5) = 0, (5, 1) = 0.9e-3, (5, 2) = .6229, (5, 3) = .3762, (5, 4) = 0, (5, 5) = 0}))

 (1)
> 


 

Download Transition_Probaility_Markov_chain.mw

layouts about DrawGraph...

Asked by: lcz 994
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.

 

Why won't this code display an ellipse?...

Asked by: Earl 930
polar conic plotting
October 15 2020
0  4

The uploaded worksheet plots conics in polar coordinates.

A circle, parabola and hyperbola all plot correctly, but the plot command for the ellipse displays a shifted circle. What's wrong?

Conic_quandry.mw

How to find sgn on maple?...

Asked by: Ahmed111 130
signum
October 15 2020
0  0

How to find sgn on maple?

signum.mw

How to generate all non-isomorphic graphs of a cer...

Asked by: DJJerome1976 535
graphtheory order select
October 14 2020
1  4

I am trying to generate all non-isomorphic graphs of a certain order and size that have the same degree sequence (not necessarily regular). I assume I would have to use the select option in GraphTheory[NonIsomorphicGraphs] command, however, there are no examples (that I could find) of how to use the option. Any idea how this could be done?

How to duplicate rows/columns in a matrix?...

Asked by: DJJerome1976 535
matrix row
October 14 2020
0  2

I have an n x n matrix. I am trying to write a procedure that will randomly choose a row (column) in the matrix, and replace another row (column) with the entries of the chosen row (column). So, the end result will be another n x n matrix that has two identical rows (columns). How could one do this?

RE: Substitution...

Asked by: pik1432 245
simplification
October 14 2020
0  2

Hello there, 

Would you please tell me how to get the 'Desired' expression from the 'Sec_Z2prim' expression?

My 'Attempt' did not work. 


 

> 

restart;
> 

TR_turns_ratio := N = n2 / n1;

N = n2/n1

 (1)
> 

Sec_Z2prim := Z1 = Z2*n1^2/n2^2;

Z1 = Z2*n1^2/n2^2

 (2)
> 

Attempt := subs(TR_turns_ratio, Sec_Z2prim) assuming (n1 > 0, n2 > 0);

Z1 = Z2*n1^2/n2^2

 (3)
> 

Desired := Z1 = Z2*(1/N)^2;

Z1 = Z2/N^2

 (4)
> 

 

 

Thank you, 
 

Download Q20201014.mw

Exporting  a piecewise functions in Maple to Matla...

Asked by: Maple_lover1 125
October 14 2020
1  14

I usually piecewise functions in my maple codes. I want to export  the my maple code to a Matlab code in order to utilize advantages of plots of Matlab.

What methods would you recommend me?

 

For example:

Suppose that I have a piecewise u function.

restart:
u:=1/(1. + exp(x))^2 + 1/(1. + exp(-5.*t))^2 - 0.2500000000 + x*(1/(1. + exp(1 - 5*t))^2 - 1./((1. + exp(-5*t))^2) + 0.1776705118 + 0.0415431679756514*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + 0.00922094377856479*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + 0.0603742508215732*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) - 0.00399645630498528*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.)) + (-0.00243051684581302*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000809061198761621*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0152377552205917*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00195593427342862*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 1.732050808, 0.) + (-0.000433590063316381*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000146112803263678*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.00319022339097685*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.000477063086307787*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0. <= t and t <= 0.5000000000, 30.98386677*t - 7.745966692, 0.) + (-0.00276114805649180*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) - 0.000933166016624500*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) - 0.0207984584912892*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) - 0.00314360556336114*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 1.732050808, 0.) + (0.000172746997599710*piecewise(0. <= x and x <= 0.5000000000, 1.732050808, 0.) + 0.0000586775450031145*piecewise(0. <= x and x <= 0.5000000000, 30.98386677*x - 7.745966692, 0.) + 0.00136190009033518*piecewise(0.5000000000 <= x and x <= 1., 1.732050808, 0.) + 0.000211410172315387*piecewise(0.5000000000 <= x and x <= 1., 30.98386677*x - 23.23790008, 0.))*piecewise(0.5000000000 <= t and t <= 1., 30.98386677*t - 23.23790008, 0.);

 

 

I use the following code to transform a Matlab code, but the output is not working in Matlab.

 

with(CodeGeneration):
 	
Matlab(u,resultname="w");

 

how to obtain all solutions with multiplicity from...

Asked by: nm 8552
polynomial solve pdetools
October 14 2020
2  8

Using solve on this example:

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);

gives solution x=1, with multiplicty 3

              1, 1, 1

When using PDEtools:-Solve

restart;
eq:=x^3 - 3*x^2 + 3*x - 1=0;
solve(eq,x);
PDEtools:-Solve(eq,x);

it gives

         x = 1

How can one make it show x=1, x=1, x=1 ?

Found that only when using PDEtools:-Solve(eq,x,numeric) it gives 

           x = 1., x = 1., x = 1.

How to make it do the same without using numeric?

Maple 2020.1.1

 

why error takes argument without ()?...

Asked by: nm 8552
programming error
October 13 2020
0  3

What is the reason that error accepts its arguments without being inside paranthesis? This is different from all other Maple functions I've seen. For example, both these below work the same

f := proc (x) 
     if x<0 then 
        error "invalid x: %1", x; 
     else 
        x^(1/2); 
     end if 
end proc:

And

g := proc (x) 
     if x<0 then 
        error("invalid x: %1", x); 
     else 
        x^(1/2)
     end if 
end proc:

One can't do for other Maple functions. For example sin x  gives an error. It must be sin(x)

Looked at help page for error and did not see something about this difference.

ConvertingCartesian to Polar Plots...

Asked by: anthonyfl 65
coordinates polar inequal
October 13 2020
0  3

I have been having difficulty with plotting these graphs from Cartesian to Polar. I know that with double integrals there is an inclusion of r when you go from Cartesian to Polar. I think my graph of the function being integrated is correct. I am having difficulty with the command for the shaded region. I know with Cartesian, I can use inequal command to get the right shaded area. Will this command work with polar coordinates? 

I attached the Maple worksheet.

Thank you all for help in advance!

Is sorting here backwards?...

Asked by: Joe Riel 9530
sort
October 12 2020
1  0

When I select "oldest first", the first post shown is the newest.  Vice-versa when selecting "newest first".  Am I misunderstanding the meaning of the term?  I suppose it doesn't matter as both options are available but it's weird.

How to correct this error ?...

Asked by: JAMET 375
ellipse
October 12 2020
1  1
eqell := expand((x+(1/2)*R1-(1/2)*R)^2/a^2+y^2/b^2-1); geometry:-ellipse(ell, eqell, [x, y]); detail(ell); ellipse: hint: unable to determine if 1/(1/2*R+1/2*R1)^2*(1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R^2+2/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1*R+1/(-8*R^3*R1+14*R^2*R1^2-3*R*R1^3)*R1^2) is zero Error, (in geometry:-ellipse) the given polynomial/equation is not an algebraic representation of a ellipse. How to manage this error ? Thank you.

Question about compound / structured types...

Asked by: greatpet 130
type
October 12 2020
1  4

The expressions f(1), f(1,2,3), or f with any number of arguments, all match the type specfunc(f), while the expression f(g(1), 2 ,3) matches the type f(g(anything), anything, anything). However, is there a type which is matched by expressions like f(g(1), 2, 3 ...), with an arbitrary number of arguments after g(something)?

 

First 369 370 371 372 373 374 375 Last Page 371 of 2308