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2022-03-01 09:59:43 +0200 | marked best answer | Writing a polynomial as a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer coefficients, and I know that these factor as product of $t-$ numbers of the form $[k]_t = 1+t+...+t^{k-1}$ . Is there a way to factor the polynomials in sage which readily give the factorization in terms of the $t-$numbers? For example, I have a polynomial $(t^2-t+1)(t^2+t+1)(t+1)^2=(t^5+t^4+t^3+t^2+t+1)(t+1)$. I want the program to return $[6]_t[2]_t$. |

2022-03-01 09:59:14 +0200 | commented answer | Writing a polynomial as a product of t-numbers Thank you, this is very nice. |

2022-02-28 22:10:25 +0200 | edited question | Writing a polynomial as a product of t-numbers Writing polynomial at a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer |

2022-02-28 21:38:21 +0200 | asked a question | Writing a polynomial as a product of t-numbers Writing polynomial at a product of t-numbers I have a function which produces a polynomial in $t$ with positive integer |

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2021-12-13 23:38:12 +0200 | marked best answer | Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say $p(t)$ is unimodal if $a_0 \leq a_1 \leq ... \leq a_k \geq a_{k+1} \geq ... \geq a_n$ i.e, the sequence of coefficients increase at first and then decrease, they don't 'jump around' ; there is no phenomenon like increase then decrease then increase again. Given such a polynomial, how can we check unimodality in sage? |

2021-12-13 23:38:07 +0200 | commented answer | Checking whether a polynomial in unimodal Thank you very much! |

2021-12-13 23:07:17 +0200 | edited answer | Checking whether a polynomial in unimodal From @rburing's answer... slightly modified since taking coefficients in the polynomial ring somehow only gives the non- |

2021-12-13 23:06:40 +0200 | answered a question | Checking whether a polynomial in unimodal From @rburing's answer... slightly modified since taking coefficients in the polynomial ring somehow only gives the non- |

2021-12-13 22:40:00 +0200 | commented answer | Checking whether a polynomial in unimodal No... I meant your earlier program didn't work if there was some internal zeroes |

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2021-12-13 21:48:53 +0200 | commented answer | Checking whether a polynomial in unimodal Actually coeffs don't take into account if some coefficient $a_k=0$ in the middle. So this works fine if there is no int |

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2021-12-13 20:38:46 +0200 | edited question | Checking whether a polynomial in unimodal Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say |

2021-12-13 20:38:05 +0200 | asked a question | Checking whether a polynomial in unimodal Checking whether a polynomial in unimodal Let $p(t)\in \mathbb{Z}_{\geq 0}[t]$. Write $p(t)=\sum_i a_i t^i$. Then we say |

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2021-10-23 20:34:45 +0200 | marked best answer | Non-Symmetric Macdonald expansion I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a linear combination of Non-Symmetric Macdonald polynomials $E_{\alpha}$ where $\alpha$ varies over $\mathbb{Z}^n_{\geq 0}$ with $\sum \alpha_i = k$. Background: We know that these Macdonald polynomials do indeed form a basis of the vector space of homogeneous degree $k$ polynomials in $n$ variables. The Non-Symmetric Macdonald polynomials I am interested in is the type $GL_n$ kind. And their sage implementation can be found here: sage documentation Bottom line is that we have a basis of a vector space already implemented in sage. Now how do we use it to compute coefficients of any vector when written in terms of this basis? |

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2021-10-22 15:24:57 +0200 | commented answer | Non-Symmetric Macdonald expansion Can you explain what is happening in the repM definition please? |

2021-10-21 20:17:54 +0200 | asked a question | Non-Symmetric Macdonald expansion Non-Symmetric Macdonald expansion I want to expand a given polynomial in $n$ variables, homogeneous of degree $k$ as a l |

2021-10-01 19:03:12 +0200 | asked a question | Running a search algorithm Running a search algorithm I want to write a program to check whether a given rational function $f(x,y)$ in two variable |

2021-07-22 18:16:55 +0200 | edited question | Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v |

2021-07-22 18:16:52 +0200 | commented answer | Defining vector partition functions in sage Edited post for clarity... please check. |

2021-07-22 10:58:00 +0200 | commented answer | Defining vector partition functions in sage Understood. I wanted to get all partitions by somehow subtracting one part and knowing the smaller partitions. Do you ha |

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2021-07-21 15:33:26 +0200 | edited question | Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v |

2021-07-21 15:16:53 +0200 | asked a question | Defining vector partition functions in sage Defining vector partition functions in sage I want to define a vector partition function starting from a given list of v |

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2021-06-29 22:30:39 +0200 | marked best answer | Define matrix indexed by partitions I want to define the following matrix in sage: $J$ is of size Partitions(n), and $J_{\lambda, \mu} = 1$ if $\lambda'=\mu$ and $0$ else. Can someone please help? |

2021-06-29 22:30:34 +0200 | commented answer | Define matrix indexed by partitions This was exactly what I was looking for. Thank you so much. |

2021-06-29 21:00:56 +0200 | asked a question | Define matrix indexed by partitions Define matrix indexed by partitions I want to define the following matrix in sage: $J$ is of size Partitions(n), and $J_ |

2021-06-02 18:58:11 +0200 | commented answer | plot not working in windows Thank you. I will try sage 9.1 |

2021-06-02 18:57:39 +0200 | commented question | plot not working in windows Nope. Doesn't work |

2021-06-02 16:03:10 +0200 | asked a question | plot not working in windows plot not working in windows I am using sagemath on windows 10. If I do f(x)=x plot(f) my sagemath complete |

2020-09-19 06:59:12 +0200 | asked a question | Functions in polynomials rings I want to define a function in a polynomial ring in several variables. I am trying to define a function that takes $(i,j)$ to $x_i^j$. I tried This does not work. I tried replacing xi with x[i], that doesn't work. Can someone please tell me what I am doing wrong and how to fix it? If instead of taking 3 variables I take only 1 variable then the method works. |

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2020-09-06 10:42:42 +0200 | commented answer | Derivative in infinite polynomial ring Thanks a lot. |

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2020-09-05 19:50:05 +0200 | asked a question | Derivative in infinite polynomial ring I am defining my ring as R.<x>=InfinitePolynomialRing(QQ), and this should give me ring with variables x[1],x[2],... etc. right? Now I want to differentiate a polynomial with respect to x[1] variable. So I defined f=x[1]^3 (for example). I am trying f.derivative(x[1]) but that does not work. It shows " 'typeerror': argument 'var' has incorrect type (expected sage.rings.polynomial.multi_polynomial_libsingular.MPolynomial_libsingular, got InfinitePolynomial_dense)." Can someone please explain what is wrong and what I should do to fix it? |

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