Ronan

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12 years, 135 days
East Grinstead, United Kingdom

MaplePrimes Activity


These are replies submitted by Ronan

@vv Thank you. worled well!

@Markiyan Hirnyk What I mean't was e.g (form one of the answers supplied) 

I wish to see what the Basis equations contain in terms of the produsts of the variables.

 

@nutnutman Firstly "vv 575" substitution method is really excellent. I decided to try a bit more complex too. Higher order derivatives and mixed derivatives. I looked at the link you provided, I didn't have a clue either. Have not used the substitution method here but it could be applied.

restart

The Next 2 lines are just testing

``

sum(a^i, i = 1 .. 6)+sum(a^i, i = 8 .. 3)+sum(a^i, i = 5 .. 10)+a^7+a^4

a^10+a^9+a^8+a^7+a^6+a^5+a^4+a^3+a^2+a

(1)

sum(a^i, i = 1 .. l-1)+sum(a^i, i = l+1 .. p-1)+sum(a^i, i = p+1 .. 10)+a^l+a^p

a^l/(a-1)-a/(a-1)+a^p/(a-1)-a^(l+1)/(a-1)+a^11/(a-1)-a^(p+1)/(a-1)+a^l+a^p

(2)

s := sum((sum(f[t](x[i, k], a[k]), k = 1 .. l-1)+sum(f[t](x[i, k], a[k]), k = l+1 .. p-1)+sum(f[t](x[i, k], a[k]), k = p+1 .. n)+f[t](x[i, l], a[l])+f[t](x[i, p], a[p]))^2, i = 1 .. m)

sum((sum(f[t](x[i, k], a[k]), k = 1 .. l-1)+sum(f[t](x[i, k], a[k]), k = l+1 .. p-1)+sum(f[t](x[i, k], a[k]), k = p+1 .. n)+f[t](x[i, l], a[l])+f[t](x[i, p], a[p]))^2, i = 1 .. m)

(3)

dsa[l] := diff(s, a[l])

sum(2*(sum(f[t](x[i, k], a[k]), k = 1 .. l-1)+sum(f[t](x[i, k], a[k]), k = l+1 .. p-1)+sum(f[t](x[i, k], a[k]), k = p+1 .. n)+f[t](x[i, l], a[l])+f[t](x[i, p], a[p]))*(diff(f[t](x[i, l], a[l]), a[l])), i = 1 .. m)

(4)

d2sa[l] := diff(s, a[l], a[l])

sum(2*(diff(f[t](x[i, l], a[l]), a[l]))^2+2*(sum(f[t](x[i, k], a[k]), k = 1 .. l-1)+sum(f[t](x[i, k], a[k]), k = l+1 .. p-1)+sum(f[t](x[i, k], a[k]), k = p+1 .. n)+f[t](x[i, l], a[l])+f[t](x[i, p], a[p]))*(diff(diff(f[t](x[i, l], a[l]), a[l]), a[l])), i = 1 .. m)

(5)

dsa[p] := diff(s, a[p])

sum(2*(sum(f[t](x[i, k], a[k]), k = 1 .. l-1)+sum(f[t](x[i, k], a[k]), k = l+1 .. p-1)+sum(f[t](x[i, k], a[k]), k = p+1 .. n)+f[t](x[i, l], a[l])+f[t](x[i, p], a[p]))*(diff(f[t](x[i, p], a[p]), a[p])), i = 1 .. m)

(6)

``

d3 := diff(s, a[l], a[p])

sum(2*(diff(f[t](x[i, p], a[p]), a[p]))*(diff(f[t](x[i, l], a[l]), a[l])), i = 1 .. m)

(7)

d4 := diff(s, a[l], a[p], a[p])

sum(2*(diff(diff(f[t](x[i, p], a[p]), a[p]), a[p]))*(diff(f[t](x[i, l], a[l]), a[l])), i = 1 .. m)

(8)

``


Download diff_sum_2.mw

 

 

@vv Never thought of "subs" and being able to add them that way.

@Carl Love That is a point I wasn't sure about myself.

@nutnutman 

What I posted was just an idea. Don't really know what you are doing. Post a work sheet (as I did) with a more complex example. That might encourage others to look at the problem. Nobody wants to retype complex formulas.

I am using Maple 18. Documentation says Solidworks 2013 required. I am on SW 2015. Connection won't open. Have you access to SW 2013?

@Kitonum That works quitew well.

@Thomas Richard  Thank You

Well I can't see a way. I was oringinaly asking hopeing maple could automatically reduce the answer. The original problem was to do with a problem in Rational Trigonometry. I wandered off into the weeds working it out (with the help of Maple) as my answer shows. Here is a link to how the solution is arrived at http://www.youtube.com/watch?v=FsQb0_Lgphc&list=PL3C58498718451C47 . I guess one would need to evaluate/ relate both solutions and see how one  relates to the other. I don't have a tidy worksheet that is worth posting. I could do one though.

Well I can't see a way. I was oringinaly asking hopeing maple could automatically reduce the answer. The original problem was to do with a problem in Rational Trigonometry. I wandered off into the weeds working it out (with the help of Maple) as my answer shows. Here is a link to how the solution is arrived at http://www.youtube.com/watch?v=FsQb0_Lgphc&list=PL3C58498718451C47 . I guess one would need to evaluate/ relate both solutions and see how one  relates to the other. I don't have a tidy worksheet that is worth posting. I could do one though.


rationalize(expand(41/sqrt(2141+936*sqrt(5)-4*sqrt(488725+218558*sqrt(5)))))

-(1/68921)*(2141+936*5^(1/2)-4*(488725+218558*5^(1/2))^(1/2))^(1/2)*(2141+936*5^(1/2)+4*(488725+218558*5^(1/2))^(1/2))*(-681+304*5^(1/2))

(1)

``

``

(->)

2.4530850560107217717909335149612374992321847859381

(2)

``

``

2*sqrt(5-2*sqrt(5))+1

2*(5-2*5^(1/2))^(1/2)+1

(3)

(->)

2.4530850560107217717909335149612374992321847859305

(4)

``


Download Rationalize_ans.mw


Look like worksheet didn't attach. "nd try

In the definition of spherical coords the order is r, theta , phi

SetCoordinates('spherical'[r, theta, phi]),

in the definition of the Vector field the order is r, phi ,theta

A := VectorField(`<,>`(A_r(r, phi, theta), `A_θ`(r, phi, theta), `A_φ`(r, phi, theta)))

Why is this?

In the definition of spherical coords the order is r, theta , phi

SetCoordinates('spherical'[r, theta, phi]),

in the definition of the Vector field the order is r, phi ,theta

A := VectorField(`<,>`(A_r(r, phi, theta), `A_θ`(r, phi, theta), `A_φ`(r, phi, theta)))

Why is this?

Thank you. That is a great help. Got something to work with now.

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