Markiyan Hirnyk

Markiyan Hirnyk

7163 Reputation

25 Badges

11 years, 162 days

MaplePrimes Activity


These are questions asked by Markiyan Hirnyk

What is the total number of the characters in "Vanity Fair" by William Thackeray?
How to determine it with Maple, making use of StringTools and EssayTools? I think an electronic version of this novel is free. 
AFAIK, there are about 600 personages in "And Quiet Flows the Don" by Mikhail Sholokhov.

PS. It happened to me to collaborate with Dr. I. Kulchytskyi on text analysis, but the asked problem is new for me.

PPS. Here is a link to the plain text.

Import("http://www.gutenberg.org/cache/epub/599/pg599.txt");

 

How to find the integral of (x+y)/(x+y+z) over the part of the unit ball  centered at the origin which lies in the positive octant { x>=0 , y>=0, z>=0 } ? Numeric calculations suggest Pi/9.

How to find the double integral of sin(x^2)*cos(y^2) over the disk of radius R which is centered at the origin? 

Here is my try 

restart; evalf(VectorCalculus:-int(sin(x^2)*cos(y^2), [x, y] = Circle(`<,>`(0, 0), 1), inert), 15);
                       0.722091449378409
identify(%);
                       0.722091449378409

 

It is suggested  

hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)) = 1/z

if z > 1. Here is my try to prove that with Maple:


 

a := `assuming`([convert(hypergeom([1/3, 2/3], [3/2], (27/4)*z^2*(1-z)), elementary)], [z > 1])

-(1/((1/2)*(27*z^3-27*z^2+4)^(1/2)+(3/2)*z*(3*z-3)^(1/2))^(1/3)-1/((1/2)*(27*z^3-27*z^2+4)^(1/2)-(3/2)*z*(3*z-3)^(1/2))^(1/3))/(z*(3*z-3)^(1/2))

(1)

b := `assuming`([simplify(a, symbolic)], [z >= 1])

2*(-(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)+(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3))/((3*z-3)^(1/2)*(12*(3*z+1)^(1/2)*z+12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*(12*(3*z+1)^(1/2)*z-12*z*(3*z-3)^(1/2)-8*(3*z+1)^(1/2))^(1/3)*z)

(2)

plot(1/b, z = 1 .. 10)

 

simplify(diff(1/b, z), symbolic)

-48*(((3*z-2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2))*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)+((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3)*((-3*z+2)*(3*z+1)^(1/2)+z*(3*z-3)^(1/2)))/((3*z+1)^(1/2)*(3*z-3)^(1/2)*((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(2/3)*((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(2/3)*(((12*z-8)*(3*z+1)^(1/2)-12*z*(3*z-3)^(1/2))^(1/3)-((12*z-8)*(3*z+1)^(1/2)+12*z*(3*z-3)^(1/2))^(1/3))^2)

(3)

``


 

Download simplification.mw

Can somebody execute this code on a powerful comp and report the result in MaplePrimes? That would be kind of her/him.


 

RealDomain:-solve(a^2+b^2+c^2+a*b+a*c+b*c-  (a+b-c)*sqrt(2*a*b+a*c+b*c)-(a+c-b)*sqrt(a*b+2*a*c+b*c)-(b+c-a)*sqrt(a*b+a*c+2*b*c));

Error, (in assuming) when calling '`resultant/modular2`'. Received: 'Maple was unable to allocate enough memory to complete this computation.  Please see ?alloc'

 

``


 

Download want_for_execution.mw

1 2 3 4 5 6 7 Last Page 1 of 34