kill(all)$load(sqdnst)$((sqrt(2)+1)*(sqrt(2)-1)^3)^(1/2)$ratsimp(%^2);
sqrt(%);
sqrtdenest(%); (%05)sqrt(2)-1
But I can not transform following formula. Give up.Please tell me how to transform this. kill(all)$load(sqdnst)$((sqrt(a)+1)*(sqrt(a)-1)^3)^(1/2)$ratsimp(%^2);
sqrt(%);
sqrtdenest(%); (%05)sqrt(a^2+(2-2*a)*sqrt(a)-1) I have another question. I can transform this.(log(1-sqrt(2))-log(-1))/2;
logcontract(%),logconcoeffp:lambda([ex],true); But I can not transform this. Please tell me that reason.(log(1-sqrt(2))-log(-1));
logcontract(%),logconcoeffp:lambda([ex],true); Date: Fri, 5 Apr 2013 18:35:57 -0400
Subject: Re: [Maxima] integrate(sqrt(x^2+y^2),x,0,1)$ integrate(%,y,0,1)$
From: macrakis at alum.mit.edu
To: shinabe.munehiro at hotmail.co.jp
CC: maxima at math.utexas.edu
Thank you for the interesting example.
Unfortunately, it looks as though it's rather messy to simplify the form 'integrate' gives. Here is one way. (I've written out the steps individually and labelled them to make it easy to see what's going on.)
qq: integrate(integrate(sqrt(x^2+y^2),x,0,1),y,0,1);
qq1: logarc(qq); /* transform asinh to log */
qq2: logcontract(qq1),logconcoeffp:lambda([ex],true);
qq3: expand(qq2);
qq4: logcontract(qq3),logconcoeffp:lambda([ex],true);qq5: part(qq4,1,1); /* need to isolate this part to work on it */load(sqdnst)$
qq6: sqrtdenest(qq5);qq7: sqrtdenest(qq6);
qq8: sqrtdenest(qq7); /* yes, three times */qq9: subst(qq8,qq5,qq4); /* substitute back simplified result */qq10: factor(qq9);
I don't see how a new user could ever come up with this sequence of simplifications.
Is there a simpler way?
The kernel of the issue is basically simplifying log((sqrt(2)+1)*(sqrt(2)-1)^3)/2, which requires knowing about logconcoeffp and sqrtdenest, which are pretty obscure. The human simplifier would notice that
((sqrt(2)+1)*(sqrt(2)-1)^3)^(1/2)= ((sqrt(2)+1)*(sqrt(2)-1)*(sqrt(2)-1)^2) ^ (1/2)= (1 * (sqrt(2)-1)^2) ^ (1/2)= sqrt(2)-1
Here's a somewhat harder related challenge: how can you transform this:
((sqrt(a)+1)*(sqrt(a)-1)^3)^(1/2)
or sqrt(a^2-2*a^(3/2)+2*sqrt(a)-1)
to
sqrt(a-1)*(sqrt(a)-1)
(Possibly with some abs's in there.)
-s
On Fri, Apr 5, 2013 at 10:44 AM, Part Marty <shinabe.munehiro at hotmail.co.jp> wrote:
Please teach me the modification method of the following formula.
integrate(sqrt(x^2+y^2),x,0,1)$
integrate(%,y,0,1)$
It leads to the following formula.
1/3*(sqrt(2)+log(sqrt(2)+1))
kill(all)$
algebraic:true$
lognegint:true$
assume(y>0)$
integrate(sqrt(x^2+y^2),x,0,1)$
integrate(%,y,0,1)$
logcontract(%);
(%06)(log(-(sqrt(2)-1)/(sqrt(2)+1))+10*asinh(1)-%i*%pi+2^(7/2))/24
_______________________________________________
Maxima mailing list
Maxima at math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima