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2021-12-03 09:18:14 +0200 | commented answer | Symbolic variables in finite-fields Thank you for the idea. I will leave my mistake with the ideal in the question to match your answer. I also tested it wi |

2021-12-03 09:14:27 +0200 | marked best answer | Symbolic variables in finite-fields Hello. I have a finite-field k and its degree n extension E where I perform exponentiation My goal is to track an element in k^n, mapped to E, as the exponentiation in E occurs. Ideally, I would write it as But this leads to "TypeError: positive characteristic not allowed in symbolic computations". I noticed that polynomials could be used instead of symbolic variables (e.g., https://ask.sagemath.org/question/59697), so another idea is to write it as But this leads to "OverflowError: exponent overflow (65536)". It's also slow for larger values of n. The next idea is to reduce $ \alpha_i^q = \alpha_i $ using an ideal It seems to work for values of n = 4, but for anything larger it gets stuck on computing primary decomposition for the ideal. See https://ask.sagemath.org/question/59987 for details. Is there a way to do this in SageMath or, perhaps, using one of the underlying systems, such as Singular, and then move back to SageMath? |

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2021-12-01 22:08:52 +0200 | asked a question | Symbolic variables in finite-fields Symbolic variables in finite-fields Hello. I have a finite-field k and its degree n extension E k = GF(4, 'a') n = 64 E |

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2021-11-29 10:15:02 +0200 | edited question | PolynomialRing appears to hang during construction PolynomialRing appears to hang during construction Hello. I came across a situation which hangs SageMath 9.4: k = GF(4, |

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2021-11-28 01:51:43 +0200 | asked a question | PolynomialRing appears to hang during construction PolynomialRing appears to hang during construction Hello. I came across a situation which hangs SageMath 9.4: k = GF(4, |

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