2024-01-20 09:06:08 +0100 commented question Evaluate polynomial over extension ring thanks a lot! 2024-01-20 09:05:42 +0100 marked best answer Evaluate polynomial over extension ring Given a ring and polynomial like: _. = RR[] K. = RR.extension(I^2 + 1) L. = K[] f = a + i*b  then I would expect that f(i=0) would give me a. But instead it just returns the same value again. Any ideas how to do this? Thanks 2024-01-20 09:05:38 +0100 commented answer Evaluate polynomial over extension ring thanks a lot! Gives me a load of stuff to look into now. Good day 2024-01-19 09:53:01 +0100 edited question Evaluate polynomial over extension ring Evaluate polynomial over extension ring Given a ring and polynomial like: _. = RR[] K. = RR.extension 2024-01-19 09:52:40 +0100 asked a question Evaluate polynomial over extension ring Evaluate polynomial over extension ring Given a ring and polynomial like: _. = RR[] K. = RR.extension 2023-12-03 10:05:51 +0100 answered a question Sage convert SymbolicRing equation to symbolic expression Here's my solution in the end: Convert equation to symbolic form. Make it homogenous. Then use the expr.coefficient(), 2023-12-03 09:37:05 +0100 edited question Sage convert SymbolicRing equation to symbolic expression Sage convert SymbolicRing equation to symbolic expression Often I want to group terms in different ways. Say for example 2023-12-03 08:58:57 +0100 edited question Sage convert SymbolicRing equation to symbolic expression Sage convert SymbolicRing equation to symbolic expression Often I want to group terms in different ways. Say for example 2023-12-03 08:58:23 +0100 asked a question Sage convert SymbolicRing equation to symbolic expression Sage convert SymbolicRing equation to symbolic expression Often I want to group terms in different ways. Say for example 2023-02-11 22:57:39 +0100 marked best answer Manually grouping symbolic terms Given a symbolic expression like: sage: var("a b c x y") (a, b, c, x, y) sage: a*x^2 + a*y^2 + b*y^2 + c*y^2 + (2*a*y + b*y)*x  How can I manually collect terms together? I want to represent this equation in the form: $$Ax^2 + Bxy + Cy^2$$ Where $A = a, B = 2a + b, C = a + b + c$. Desired output should be: a*x^2 + (2*a + b)*x*y + (a + b + c)*y^2  And then is there any way to read off these coefficients? Thanks 2023-02-01 09:03:56 +0100 asked a question Manually grouping symbolic terms Manually grouping symbolic terms Given a symbolic expression like: sage: var("a b c x y") (a, b, c, x, y) sage: a*x^2 + 2023-01-15 17:15:53 +0100 asked a question Assumptions giving wrong boolean answer for simple expression Assumptions giving wrong boolean answer for simple expression Let $a, b \in \mathbb{Z}$ with $a < 0$, then we can pla 2022-08-25 19:33:16 +0100 received badge ● Self-Learner (source) 2022-08-25 19:33:16 +0100 received badge ● Teacher (source) 2022-08-25 16:08:03 +0100 answered a question Polynomial is in ideal of a coordinate ring This works: sage: K. = QQ[] sage: I = Ideal(y^2 - x^3 - x) sage: L. = K.quotient(I) sage: I = I 2022-08-25 15:57:19 +0100 asked a question Polynomial is in ideal of a coordinate ring Polynomial is in ideal of a coordinate ring I am getting an error with the code below. Please advise how I can do this. 2022-08-25 15:55:02 +0100 answered a question how to import a function in another file For importing sage files, try the functions load() and attach() 2022-08-04 08:59:44 +0100 received badge ● Supporter (source) 2022-08-04 08:58:30 +0100 marked best answer Evaluation map and ideal from polynomial ring K[X] -> K How can I define a localized evaluation map $\phi_{a_1, \dots, a_n} : K[x_1, \dots, x_n] \rightarrow K$ by $\phi_{a_1, \dots, a_n}(p(x_1, \dots, x_n)) = p(a_1, \dots, a_n)$? K = GF(47) R. = K[] H = R.hom_eval(K(10), K(20)) assert H((x - 10)*(y - 20)) == 0  And also how can I construct the ideal of this map? 2022-08-01 09:37:43 +0100 edited question Evaluation map and ideal from polynomial ring K[X] -> K Evaluation map and ideal from polynomial ring K[X] -> K How can I define a localized evaluation map $\phi_{a_1, \dots 2022-08-01 09:37:05 +0100 edited question Evaluation map and ideal from polynomial ring K[X] -> K Evaluation map and ideal from polynomial ring K[X] -> K How can I define a localized evaluation map$\phi_{a_1, \dots 2022-08-01 09:35:35 +0100 asked a question Evaluation map and ideal from polynomial ring K[X] -> K Evaluation map and ideal from polynomial ring K[X] -> K How can I define a localized evaluation map $\phi_{a_1, \dots 2022-08-01 08:12:51 +0100 answered a question Construct local ring of function field variety https://math.stackexchange.com/questions/294644/basis-for-the-riemann-roch-space-lkp-on-a-curve?rq=1 2022-07-31 07:44:58 +0100 commented question Construct local ring of function field variety Maybe I should have excluded the part about the ideal. I just want to construct the local ring, which is$K[V]_P$aka th 2022-07-30 08:24:34 +0100 asked a question Construct local ring of function field variety Construct local ring of function field variety Hello sage community, I want to localize a variety's field at a certain 2022-07-30 07:45:56 +0100 marked best answer How to test element is in multivariate function field's ideal I'm trying to calculate the valuation of a function in a the function field of a coordinate ring$K(V) = { f / g : f, g \in K[V] }$. My first attempt is to construct the coordinate ring$K[V] = K[x, y] / \langle C(x, y) \rangle$sage: K. = Integers(11)[] sage: S = K.quotient(y^2 - x^3 - 4*x) sage: S Quotient of Multivariate Polynomial Ring in x, y over Ring of integers modulo 11 by the ideal (10*x^3 + y^2 + 7*x)  Now I want to see if a function$f = y - 2x$lies in the ideal$I = \langle u \rangle$where$u = x - 2$. sage: I = S.ideal(x - 2) sage: S(y - 2*x) in I False  But sage is wrong.$y - 2x \in \langle x - 2 \rangle$as shown by the following code: sage: f1 = S(y - 2*x) sage: f1 9*xbar + ybar sage: f2 = S( ....: (x - 2) * ( ....: (x - 2)^2*(y + 4) - 5*(x - 2)*(y + 4) - 2*((x - 2)^3 - 5*(x - 2)^2 + 5*(x - 2) ....: ))) / S((y + 4)^2) sage: f2 9*xbar + ybar sage: bool(f1 == f2) True  As plainly visible, f2 has the factor$(x - 2)\$. How can I calculate this in sage without having to factor the polynomial myself? I assume this is because we need an actual function field in sage, but I get singular errors when I attempt to turn S into a fraction field. sage: K. = Integers(11)[] sage: S = K.quotient(y^2 - x^3 - 4*x) sage: R = FractionField(S) # ... RuntimeError: error in Singular function call 'primdecSY': ASSUME failed: ASSUME(0, hasFieldCoefficient(basering) ); error occurred in or before primdec.lib::primdecSY_i line 5983:  return (attrib(rng,"ring_cf")==0); leaving primdec.lib::primdecSY_i (5983)  Is there a way to construct local rings and maximal ideals? Or a way to calculate valuations (order of vanishing for poles and zeros) on elliptic curves? Thanks 2022-07-30 07:45:56 +0100 received badge ● Scholar (source) 2022-07-30 07:33:26 +0100 commented answer How to test element is in multivariate function field's ideal For example: sage: K. = GF(11)[] sage: S = K.quotient(y^2 - x^3 - 4*x) sage: I = S.ideal(x - 2) sage: I Ide 2022-07-29 18:23:32 +0100 commented answer How to test element is in multivariate function field's ideal But why now does it say True for all powers of the ideal? The valuation of this function on the curve is 2, so the outpu 2022-07-28 10:54:23 +0100 received badge ● Student (source) 2022-07-28 08:05:29 +0100 edited question How to test element is in multivariate function field's ideal How to test element is in multivariate function field's ideal I'm trying to calculate the valuation of a function in a t 2022-07-28 08:04:37 +0100 edited question How to test element is in multivariate function field's ideal How to test element is in multivariate function field's ideal I'm trying to calculate the valuation of a function in a t 2022-07-28 07:27:10 +0100 edited question How to test element is in multivariate function field's ideal How to test element is in multivariate function field's ideal I'm trying to calculate the valuation of a function in a t 2022-07-28 07:26:37 +0100 edited question How to test element is in multivariate function field's ideal How to test element is in multivariate function field's ideal I'm trying to calculate the valuation of a function in a t 2022-07-28 07:24:20 +0100 edited question How to test element is in multivariate function field's ideal Incorrect result for x in ideal. Sage reports false, but I provide a correct factorization I'm trying to calculate the v 2022-07-28 07:24:14 +0100 received badge ● Editor (source) 2022-07-28 07:24:14 +0100 edited question How to test element is in multivariate function field's ideal Incorrect result for x in ideal. Sage reports false, but I provide a correct factorization I'm trying to calculate the v 2022-07-28 07:20:00 +0100 asked a question How to test element is in multivariate function field's ideal Incorrect result for x in ideal. Sage reports false, but I provide a correct factorization I'm trying to calculate the v 2022-07-14 11:48:04 +0100 asked a question Elliptic Curve divisor from polynomial and vice versa Elliptic Curve divisor from polynomial and vice versa I want to construct the Picard group of an elliptic or hyperellipt