2020-06-14 16:26:02 +0100 | asked a question | Count GF(q) arithmetics Hi, I was trying to count the number of basic arithmetics happened in a GF(q)[x] or GF(q)[x].quo(irr) operation. I turned to define a wrapper class However, I turns out that GF(q) in sage is not a class. Instead it is some sort of factory object. Is there any way to count the number of arithmetics happened to an element? |

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2020-06-01 13:12:27 +0100 | asked a question | Lifting an Isogeny without Starting All Over So I was computing isogeny over finite field in different extension degrees. Let's suppose I have obtained an isogeny $\phi$ over $\mathbb{F}_q$ and an embedding . $\iota:\mathbb{F}_{q}\to\mathbb{F}_{q^k}$. How do I lift $\phi$ to a larger field $\mathbb{F}_{q^k}$ by $\iota$? What I did for now is to extract the kernel polynomial $\phi_x\in\mathbb{F_q}[x]$; componentwisely lift its coefficient to $\mathbb{F}_{q^k}$ and obtain $\tilde\phi_x=\iota(\phi_x)$, then using Kohel's formula to compute the lifted isogeny $\tilde\phi:E\to E[\tilde\phi_x]$. However, this costs too much computational resources to recompute the whole isogeny from scratch. In theory, since we have already computed $\phi$ before hand, one reasonable approach is to simply lift the rational coefficients of $\phi$ by $\iota$ componentwise. But I'm not quite sure how we could do this within Sage because I can't find a constructor to construct an isogeny object without specifying its kernel. Any ideas? |

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2020-05-20 11:54:38 +0100 | answered a question | Elliptic Curve over Tower of Finite Field It seems my question didn't raise enough attention. I would answer my own question, though. To embed a curve into a larger field, simply use |

2020-05-20 11:48:23 +0100 | commented question | Elliptic Curve over Tower of Finite Field @rburing It's because I would need to do some arithmetics in these different field and I couldn't priori decide the larger ring. |

2020-05-17 21:44:34 +0100 | commented question | Elliptic Curve over Tower of Finite Field I've added runnable codes. |

2020-05-17 16:29:30 +0100 | commented question | Elliptic Curve over Tower of Finite Field @tmonteil I have edit and include the codes |

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2020-05-17 12:27:09 +0100 | asked a question | Elliptic Curve over Tower of Finite Field So I was trying to construct a curve and compute arithmetics on different hierachy of extensions.
The problem is, since in my application the characteristic $p$ is so large that the regular On another hand, if I simply specify the relative extension Is there any way to get around this? |

2020-05-17 12:17:01 +0100 | asked a question | Elliptic Curve on Tower of Finite Field So I was trying to construct a curve and compute arithmetics on different hierachy of extensions.
The problem is, since in my application the characteristic $p$ is so large that the regular On another hand, if I simply specify the relative extension Is there any way to get around this? |

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2020-02-16 20:05:43 +0100 | asked a question | Isogeny from Two Curves Hi, I was wondering given two curves $E_1,E_2$ $\ell$-isogeneous where $\ell$ is some prime. Do we have anything in Sage that help us compute its itermediate isogeny? |

2020-02-16 20:05:43 +0100 | asked a question | Isogeny from Two Curves Hi, I was wondering given two curves $E_1,E_2$ $\ell$-isogeneous where $\ell$ is some prime. Do we have anything in Sage that help us compute its itermediate isogeny? |

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