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2024-04-04 05:47:08 +0200 | marked best answer | Solutions to Matrix Equation which are elements of a polynomial ring. I'm VERY new to SageMath, and I'm having trouble understanding how polynomial rings work in this language... I have the following code: I'm trying to find solutions to the following matrix equation: Now here is the caveat: I want the solutions of rstructure to only be elements of the quotient ring I've defined as S. If you've gotten this far, I'll boil down my main questions below: (1) What are x=F.gen() and a=S.gen() doing? (2) I want to see all the possible solutions of r_i, d_i that satisfy the matrix equation with the condition that they are elements of S (the quotient ring that I've defined earlier). (3) If it is not clear, "rstructure" is an element of (F_3[x]/< x^2 >)^3. What I'm particularly interested in are solutions in (F_p[x])^3. Is computing this even possible for a given prime p? Thanks for taking the time to read this! Hope to figure this out soon. |
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2024-04-04 02:38:31 +0200 | commented answer | Solutions to Matrix Equation which are elements of a polynomial ring. That's very cool! Unfortunately, I'm starting to realize there are consequences to finding solutions over quotient rings |
2024-04-01 12:28:40 +0200 | asked a question | Solutions to Matrix Equation which are elements of a polynomial ring. Solutions to Matrix Equation which are elements of a polynomial ring. I'm VERY new to SageMath, and I'm having trouble u |