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2017-06-30 13:22:19 -0500 | asked a question | Integrating complicated expression with two variables I am trying to compute a double integral with respect to variables x and y. I first compute the integral with respect to the variable x: which gives me as an output : instead of an expression now only depending on the second variables y. Then, when I try to integrate with respect to the second variable y by writing I get the following output: finally if I try to write (to get the numerical value) I get the error message I have tried integrating the same type of function when there is only one variable and the integration works fine, so I am thinking something goes wrong in the double integration but I can't figure out what! Thanks. |

2017-06-29 13:23:21 -0500 | asked a question | Absolute value of a polynomial How can I generate a random polynomial with two variables x, y of fix degree which is not of type : I would like to compute the absolute value of this polynomial, but when I generate it using :
for example, I get : What would be a good alternative to get |F(x,y)| ? Thanks |

2017-06-29 10:19:51 -0500 | commented question | Double-integration and logs Thanks again for your answer. I have added an absolute value to my polynomial, so now I am integrating log(abs(F)). I thought this would solve the issue of having the log of a negative value, but it doesn't seem to change..... I need to fix the f =0 case. |

2017-06-28 09:47:54 -0500 | commented question | Double-integration and logs This is an example for which the double integration of log(F) never ends: F = -2 |

2017-06-28 09:17:35 -0500 | commented question | Double-integration and logs Thank you. I tried copying your example and I run into the error : ValueError: Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation |

2017-06-27 16:18:40 -0500 | asked a question | Double-integration and logs I am running into various odd problems while trying to compute a double integral. My code is as follows: Problems: 1) If I use the random polynomial F generated by .random_element, the integration generates the following error : TypeError: integral() takes exactly one argument (3 given). However, if I use the other one I manually generate, then it integrates okay. If I copy from the terminal the .random_element() polynomial and explicitly write it in my code, then it will also work. Why not directly from the .random_element() function then ? 2) If I set f = F or even f = F Any idea what might cause these weird bugs ? Thanks! |

2017-06-27 16:16:14 -0500 | asked a question | Bugs with double-integration and logs I am running into various odd problems while trying to compute a double integral. My code is as follows: Problems: 1) If I use the random polynomial F generated by .random_element, the integration generates the following error : TypeError: integral() takes exactly one argument (3 given). However, if I use the other one I manually generate, then it integrates okay. If I copy from the terminal the .random_element() polynomial and explicitly write it in my code, then it will also work. Why not directly from the .random_element() function then ? 2) If I set f = F or even f = F Any idea what might cause these weird bugs ? Thanks! |

2017-04-21 08:01:22 -0500 | commented answer | Ideals and commutative rings My matrix is slightly different and has many zeros. Maybe this causes the ring R to be non-commutative. I will have a look. Thanks for your answer! |

2017-04-21 07:18:51 -0500 | asked a question | Ideals and commutative rings I consider a matrix $M$ which I transform into a system of equations similar as this (but with a different $M$) sage: M=matrix(3,3,[1,2,3,4,5,6,7,8,9]) sage: P=PolynomialRing(GF(p),M.nrows(),names="x") sage: (vector(P.gen(i) for i in range(3))*M).list() [x0 + 4 (Example taken from another equation where $p$ is a prime). When I try to create the ideal generated by this system, I get the following error : TypeError: R must be a commutative ring. Any idea how I can fix this? |

2017-04-06 09:42:03 -0500 | asked a question | Mapping a list to some variables for a system of equations I have a list of integers $(a, b, c, d)$ and a system of equations, where each equation has two unknowns. My system looks like $(x0+x4, x1+x4, x2+x4, x3+x4).$ I am trying to evaluate the system in $(a,b,c,d)$. If I write $system(x0=1, x1=2, x3=1, x4=1)$, the system correctly outputs the result of each equation. Now, I would like to do something like $system(x0=a, x1=b, x3=c, x4=d)$ but without having to manually put the variables in. I have tried writing $system(list)$ but the number of variables and unknown doesn't match. Is there any way I can achieve this ? |

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2017-04-05 16:42:45 -0500 | asked a question | Convert a Free Module Element into a vector I have an element $v$ of type 'sage.modules.free_module_element.FreeModuleElement_generic_dense', concretely I have $(x0, x1, 1)$, which I would like to multiply by a matrix $M$, i.e., have $M*v.$ \ I am trying to convert this element into a vector, but the naive attempt to do $vector(v)$ fails to give me a valid multiplication (TypeError: unsupported operand parent(s) for '*': 'Full MatrixSpace of 2 by 2 dense matrices over Integer Ring' and 'Ambient free module of rank 3 over the integral domain Multivariate Polynomial Ring in x0, x1 over Rational Field'). Is there any way I can do this multiplication ? thanks! |

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2017-04-04 03:58:58 -0500 | commented answer | Transforming a matrix into a system of equations thank you ! I have two additional questions. It seems that your solution gives the column coefficient to a polynomial (and not the rows). Would it be possible to have the row coefficients? One way would be to simple transpose the matrix beforehand. I have tried using M.ncolumns() but it seems to generate an error. Also, is there anyway the last coefficient could be a constant variable (1) (in order to have $ax+by+c$ for example) ? |

2017-04-03 22:21:45 -0500 | asked a question | Transforming a matrix into a system of equations I have a $n \times n$ matrix that I would like to transform into a system of $n$ equations (for $n$ disctinct variables). I am not sure how to proceed (the end goal being to solve the system eventually). The number of variables is not fixed. Should I consider every row of the lattice and map each coefficient $c_{ij}$ to a string that I write as $"c_{11}x_1 + .....+ c_{1n-1}x_n + c_{1n}$. I am hoping there exists a more direct solution. Thanks! |

2017-04-03 17:21:15 -0500 | asked a question | Groebner basis to solve linear system of equations I am trying to solve a linear system of equation modulo some prime $p$. I have a matrix which gives me the coefficients of the polynomials (i.e., first row would be ($a, c, b, d$) for $ax+by+cz+d =0$). I would usually use solve_right(), writing my system as $Ax=b$ mod $p$, but I am intrigued by the use of Groebner basis. I have read about their implementation but I am confused at the notion of ideal to define before solving the system. I would like to solve the system in the ring $Z/pZ$. Also, can I feed a matrix to the function or should I first convert the matrix in a bunch of equations ? Any clarification would be welcome ! |

2017-04-02 20:05:23 -0500 | commented answer | Solving modular systems of equation great, thanks. I'll try the last option. |

2017-04-02 13:52:46 -0500 | asked a question | Solving modular systems of equation I am trying to solve a system of equations mod $p$, for $p$ prime. I have build matrices $A$ and $b$ and I am using the function solve_right() to solve $Ax = b$. But I need to solve $Ax = b$ mod $p$. Is there any functions that could do that ? thanks ! |

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