ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 11 Nov 2017 13:54:16 +0100composition of functionhttps://ask.sagemath.org/question/39482/composition-of-function/f(z1z2) , g(z1)
z1 and z2 are two points on elliptic curve so z1=(z+3*a+4) and z2=(z+3*a)
z1 and z2 addition of two points and z1 is doubling point function
p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])
#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P # select Random point P on elliptic Curve
Q =E(0,2)Fri, 10 Nov 2017 16:09:22 +0100https://ask.sagemath.org/question/39482/composition-of-function/Comment by tmonteil for <p>f(z1z2) , g(z1)</p>
<p>z1 and z2 are two points on elliptic curve so z1=(z+3<em>a+4) and z2=(z+3</em>a)
z1 and z2 addition of two points and z1 is doubling point function</p>
<pre><code>p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])
#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P # select Random point P on elliptic Curve
Q =E(0,2)
</code></pre>
https://ask.sagemath.org/question/39482/composition-of-function/?comment=39483#post-id-39483What is your question ?Fri, 10 Nov 2017 16:42:26 +0100https://ask.sagemath.org/question/39482/composition-of-function/?comment=39483#post-id-39483Comment by dan_fulea for <p>f(z1z2) , g(z1)</p>
<p>z1 and z2 are two points on elliptic curve so z1=(z+3<em>a+4) and z2=(z+3</em>a)
z1 and z2 addition of two points and z1 is doubling point function</p>
<pre><code>p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])
#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P # select Random point P on elliptic Curve
Q =E(0,2)
</code></pre>
https://ask.sagemath.org/question/39482/composition-of-function/?comment=39486#post-id-39486This seems to be intrinsically related to
[https://ask.sagemath.org/question/33127/elliptic-curve-point/](https://ask.sagemath.org/question/33127/elliptic-curve-point/)Fri, 10 Nov 2017 19:27:11 +0100https://ask.sagemath.org/question/39482/composition-of-function/?comment=39486#post-id-39486Comment by santoshi for <p>f(z1z2) , g(z1)</p>
<p>z1 and z2 are two points on elliptic curve so z1=(z+3<em>a+4) and z2=(z+3</em>a)
z1 and z2 addition of two points and z1 is doubling point function</p>
<pre><code>p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])
#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P # select Random point P on elliptic Curve
Q =E(0,2)
</code></pre>
https://ask.sagemath.org/question/39482/composition-of-function/?comment=39493#post-id-39493i want to find out function f(g(z) and g(f(z))Sat, 11 Nov 2017 10:03:04 +0100https://ask.sagemath.org/question/39482/composition-of-function/?comment=39493#post-id-39493Comment by dan_fulea for <p>f(z1z2) , g(z1)</p>
<p>z1 and z2 are two points on elliptic curve so z1=(z+3<em>a+4) and z2=(z+3</em>a)
z1 and z2 addition of two points and z1 is doubling point function</p>
<pre><code>p=5
A=4
B=4
K.<a>=GF(p^2);K.modulus()
#R.<z>=PolynomialRing(K);
R.<z> = PolynomialRing( K, sparse=True )
E = EllipticCurve(GF(p),[0,0,0,A,B]);
#print"EC=",E
#print (E.points()[:4])
#print "\n Take Two point on Elliptic curve "
P =E(1,2)
print"point1=",P # select Random point P on elliptic Curve
Q =E(0,2)
</code></pre>
https://ask.sagemath.org/question/39482/composition-of-function/?comment=39498#post-id-39498Please give a mathematical description of the functions $f$ and $g$, including their (co)domains. If code is given, then try to find minimal shapes for it that introduce the framework of the problem in a clear way. Above, as in the other post, nothing, really nothing can be understood, not even guessed. For instance, the given curve E is defined simply as
E = EllipticCurve( GF(5), [ 0,0,0,4,4 ] ) # or just [4,4] as coefficients input
And there is no connection to the **polynomial ring** $K[z]$ in a new variable $z$, that cannot be used in the context. Here, $K$ is the field with $25$ elements, generated by $a$ over F=`GF(5)`, and we neither use (properly) a, nor K, nor R. A point on the curve has **two components**. And E is defined / F - not even over K. So z is forbidden in `E`!Sat, 11 Nov 2017 13:54:16 +0100https://ask.sagemath.org/question/39482/composition-of-function/?comment=39498#post-id-39498