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radhika

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why infinity comes in integral sign?...

radhika 30 Maple
infinity integration differentialgeometry
August 05 2018
0 0

After calculations the integral contains infinity. what it resembles? Is it correct  answer?  Please check the file maple
 

> 

restart
> 

with(DifferentialGeometry):with(JetCalculus):NULL``
> 

DGsetup([x, t], [u], E, 1):

``

 

 
E > 

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))/((u[1]-u[2])^3*(u[1]+u[2])^3)

(1.1)
E > 

``

E > 

A := evalDG((-3*t*u[1]^2*u[2]-t*u[2]^3+x*u[1]^3+3*x*u[1]*u[2]^2)*((-2*u[]^2+1)*(-u[1, 1]+u[2, 2])+2*u[]*(-u[1]^2+u[2]^2))*`&w`(Dx, Dt)/((u[1]-u[2])^3*(u[1]+u[2])^3))

_DG([["biform", E, [2, 0]], [[[1, 2], -(3*t*u[1]^2*u[2]+t*u[2]^3-x*u[1]^3-3*x*u[1]*u[2]^2)*(2*u[]^2*u[1, 1]-2*u[]^2*u[2, 2]-2*u[]*u[1]^2+2*u[]*u[2]^2-u[1, 1]+u[2, 2])/((u[1]-u[2])^3*(u[1]+u[2])^3)]]])

 (1.2)
E > 

simplify(HorizontalHomotopy(A))

_DG([["biform", E, [1, 0]], [[[1], -t*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((t*u[2]^6+(-3*x*u[1]-u[])*u[2]^5+(2*t*u[1]^2+3*u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4+(2*x*u[1]^3-2*u[]*u[1]^2-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1])*u[2]^3+18*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[1]^2*u[2]^2+(x*u[1]^5+3*u[]*u[1]^4-12*u[]*(t*u[1, 2]+x*u[1, 1])*u[1]^3)*u[2]+3*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity], [[2], x*(int(-infinity*(u[1]+u[2])*(1+(u[2, 2]+u[1, 1, 2]+u[1, 2, 2]+u[2]+u[1, 2])*_z1)*_z1*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*t*u[2]^6+(-3*_z1*x*u[1]-u[])*u[2]^5+3*_z1*((2/3)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^4-12*(-(1/6)*_z1*x*u[1]^2+(1/6)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[1]*u[2]^3+18*_z1*u[1]^2*(-(1/6)*t*u[1]^2+u[]*(t*u[1, 1]+x*u[1, 2]))*u[2]^2-12*u[1]^3*(-(1/12)*_z1*x*u[1]^2-(1/4)*u[]*u[1]+_z1*u[]*(t*u[1, 2]+x*u[1, 1]))*u[2]+3*_z1*u[]*u[1]^4*(t*u[1, 1]+x*u[1, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+infinity*(u[1]+u[2])*_z1*(1+(u[1, 1, 2]+u[1, 2, 2]+u[1]+u[1, 1]+u[1, 2])*_z1)*(u[1]-u[2])*(u[1]^4+u[2]^4)*signum(1, (_z1*x*u[1]^6+(-3*_z1*t*u[2]-u[])*u[1]^5+3*_z1*((2/3)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4-12*u[2]*(-(1/6)*t*_z1*u[2]^2+(1/6)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[1]^3+18*_z1*u[2]^2*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^2-12*(-(1/12)*t*_z1*u[2]^2-(1/4)*u[]*u[2]+_z1*u[]*(t*u[2, 2]+x*u[1, 2]))*u[2]^3*u[1]+3*_z1*u[]*u[2]^4*(t*u[1, 2]+x*u[2, 2]))/(_z1^2*(u[1]-u[2])^4*(u[1]+u[2])^4))+6*(u[]*(u[1]^2-u[2]^2+u[]*(-u[1, 1]+u[2, 2]))*_z1^2-(1/2)*u[2, 2]+(1/2)*u[1, 1])*(t*u[1]^2*u[2]+(1/3)*t*u[2]^3-(1/3)*x*u[1]^3-x*u[1]*u[2]^2), _z1 = 0 .. 1))/((u[1]-u[2])^3*(u[1]+u[2])^3)-signum((x*u[1]^6+(-3*t*u[2]-u[])*u[1]^5+(2*x*u[2]^2+3*u[]*(t*u[1, 2]+x*u[2, 2]))*u[1]^4+(2*t*u[2]^3-2*u[]*u[2]^2-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2])*u[1]^3+18*(-(1/6)*x*u[2]^2+u[]*(t*u[1, 2]+x*u[2, 2]))*u[2]^2*u[1]^2+(t*u[2]^5+3*u[]*u[2]^4-12*u[]*(t*u[2, 2]+x*u[1, 2])*u[2]^3)*u[1]+3*u[]*(t*u[1, 2]+x*u[2, 2])*u[2]^4)/((u[1]-u[2])^4*(u[1]+u[2])^4))*infinity]]])

 (1.3)
E > 

``

> 

``
E > 

``
E > 

``


 

Download maple1.mw

1.mw maple1.pdf

Can we use this euler lagrange command f...

radhika 30 Maple 2016
differential-equation euler lagrange
May 15 2018
0 0

Can we use this euler lagrange command for the system of pde's?

If we have a system without lagrangian then euler opertor is applied corresponding to three dependent variables.

so we have three equations but in this euler lagrange command no dependent variable is mentioned.   

Why maple does not respond to the comman...

radhika 30 Maple 13
differentialgeometry
May 02 2018
0 1

I was calculating the total derivative of a function but maple does not respond to the commands like alias,diff,totaldiff etc.

please see the attached pdf.multiplier.pdfmultiplier.pdf

How to convert maple file into pdf file?...

radhika 30 Maple 18
pdf export
March 15 2018
0 1

How to convert maple file into the pdf file?For example the attacahed file is maple file.I want to convert this to a pdf file.

conservation_of_wave_eq.mw

GeM package ( add-on )...

radhika 30 Maple
package
March 13 2018
0 0

How can I install GeM software from the link http://cpc.cs.qub.ac.uk/?

I have tried many times but I didn't get.

 

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