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2020-02-29 04:21:11 +0200 asked a question How to compose two functions

Suppose I have a function f(x)=x^2+1

What is the command to compose it with itself twice or thrice?

I was using:

f= (x^2+1)

g= lambda t: (t^2+1)

f(*g)

or

sage: g = lambda t: (t^2+1) sage: f = lambda x: (x^+1) sage: f(*g(t))

or

sage: x = var('x')

sage: f=x^2+1

sage: compose(f, 3, x)

Nothing works! Also, I don't know how to use the Dynamical system code in this case here.

Also, it would be of great help if you can give me one example command for the composition of two different functions e.g f(x)=x^2+1 and g(x)=x^3+2 if it is not obvious from the answer of the composition of the same function twice.

2019-08-08 19:04:50 +0200 commented answer Define the affine variety $X = V (y − x^2, y − x + 1)$.

The question is this: "Define the affine variety (a) $X = V (y − x^2, y − x + 1)$. (b) Find all the rational points on X."

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2019-08-08 01:14:35 +0200 asked a question Define the affine variety $X = V (y − x^2, y − x + 1)$.

Define the affine variety (a) $X = V (y − x^2, y − x + 1)$. (b) Find all the rational points on X.

What I got in the examples is that we can use the code

sage: x,y,z = PolynomialRing(GF(5), 3, 'xyz').gens()

sage: C = Curve(y^2z^7 - x^9 - xz^8); C

sage: C.rational_points()

To get rational points over Finite Field of size 5. To calculate over rational we can replace $GF(5)$ by QQ but to get a finite result we have to have the intersection.

Later I also used:

sage: R.<x,y> = PolynomialRing(QQ)

sage: R

sage: I = R.ideal(y-x^2,y-x+1)

sage: I.variety()

But didn't get my result.

2019-07-28 18:36:06 +0200 asked a question Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root.

Sage question: Define the polynomial ring $\Bbb Q[c][x]$.Find the $c$ values where $x^2 + x + c + 1$ has a double root. Sage code I have found.

K.<c>=QQ['c']

R.<x>=K[]

f=x^2+x+c+1

f

How do I find the code for the $c$ values where $x^2 + x + c + 1$ has a double root. Also, can you give some examples so that I can construct some programming code in sage?