diff -r 88a01948450d -r d33698326409 using_sage/questions.rst --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/using_sage/questions.rst Wed Dec 01 16:51:35 2010 +0530 @@ -0,0 +1,99 @@ +Objective +--------- + +1. How do you find the limit of the function ``x/sin(x)`` as ``x`` tends to + ``0`` from the negative side. + + Answer: lim(x/sin(x), x=0, dir="below") + +#. Find the third differential of the function ``exp(sin(x)*cos(x^2))`` + + Answer: diff(exp(sin(x)*cos(x^2), x, 3) + +#. Solve the system of linear equations:: + + x-2y+3z = 7 + 2x+3y-z = 5 + x+2y+4z = 9 + + Answer:: + + A = Matrix([[1, -2, 3], + [2, 3, -1], + [1, 2, 4]]) + + b = vector([7, 5, 9]) + + solve_right(A, b) + +#. How do you get the factorized form of ``x^4 - 4x^2 + x^3 + 2x + 7`` + + Answer:: + + factor( x^4 + x^3 - 4*x^2 + 2*x + 7 ) + +#. list all the primes between 2009 and 2900 + + Answer: prime_range(2009, 2901) + +#. Which function is used to check primality + + a. isPrime + #. isprime + #. is_prime + #. prime + + Answer: is_prime + +#. How do you list all the combinations of ``[1, 2, 3, 4]`` + + + Answer:: + + c1 = Combinations([1, 2, 3, 4]) + c1.list() + +#. How do you list all the permutations of ``[1, 3, 2, 3]`` + + Answer:: + + p1 = Permutations([1, 3, 2, 3]) + p2.list() + + +Programming +----------- + +1. Obtain the sum of primes between 1 million and 2 million. + + Answer:: + + prime_sum = 0 + for i in range(1000001, 2000000, 2): + if is_prime(i): + prime_sum += i + + prime_sum + + OR + :: + + sum(prime_range(1000000, 2000000)) + +2. ``graphs.WorldMap()`` gives the world map in the form of a + graph. :: + + G = graphs.WorldMap() + G.vertices() + + + Suppose, I wish to go from India to France by Road, find out the + least number of Visas that I'll have to obtain. + + Answer:: + + G.distance("India", "France") + + + +