2020-05-30 03:58:26 -0500 | commented question | Are there fast(er) ways to compute inverses of Hermitian matrices? "How symbolic" are they? What do the entries look like? Polynomials? Rational functions? Worse? You might benefit from changing the ring. Also, inverting is usually best avoided. Are you sure it's necessary? In any case, an example would help. |

2020-05-27 06:00:58 -0500 | answered a question | extract coefficients from products and sums of descending products If you don't mind I will just focus on the example of This is almost a rational function in To simplify our job, use the fraction field of a polynomial ring rather than the symbolic ring: To get the (actual) exponents of Output: You can also collect terms according to |

2020-05-27 04:42:53 -0500 | answered a question | Warning against a deprecated function You are implicitly treating the expression You should be more explicit about it, e.g. replacing it by Note that it would be more efficient to compute To be explicit: or, alternatively e.g. |

2020-05-26 11:35:47 -0500 | answered a question | How do i solve a 2 variable polynomial over 1 variable The polynomial Alternatively: |

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2020-05-18 12:57:15 -0500 | commented question | Elliptic Curve over Tower of Finite Field Why do you want to use |

2020-05-18 06:43:30 -0500 | answered a question | Navigation inside a notebook You can use Markdown and HTML. For example, if you add a Markdown cell (Cell → Cell Type → Markdown) then you can add headings which will render approximately like this:
but the Jupyter notebook also adds links which you can see by hovering over the headings. Then you can link to these headings in a Markdown cell using the link syntax: By using HTML you can also link to places which are not headings, e.g. if you make a then you can link to it by |

2020-05-14 05:23:43 -0500 | commented question | How can I find the points on the hyperelliptic curve? Over what field? |

2020-05-12 01:05:25 -0500 | commented question | Latex and SageMath Well, yes, but there are many ways to typeset matrices in LaTeX. Can you give some example(s) which you want to convert? |

2020-05-09 12:34:31 -0500 | answered a question | Implicitization by symmetric polynomials As suggested in my comment: you can eliminate $x_1,…,x_t$ from the ideal $$I = \langle y_i - e_i(p_1(x_1,\ldots,x_t),\ldots,p_m(x_1,\ldots,x_t)) : i = 1,\ldots, m \rangle$$ in the ring $\mathbb{Q}[x_1,\ldots,x_t,y_1,\ldots,y_m]$, where $e_i$ are the elementary symmetric polynomials in m variables. For efficiency reasons we compute the elimination ideal $I \cap \mathbb{Q}[y_1,\ldots,y_m]$ manually, using a Groebner basis $G$ of $I$ with respect to a block ordering where the $x$'s are the greatest and the $y$'s have a weighted degrevlex ordering where $y_k$ has degree $k$ (simulating the degree of $e_k$), so that substituting $y_i = e_i(x_1,\ldots,x_t)$ into the polynomials in $G \cap \mathbb{Q}[y_1,\ldots,y_m]$ yields symmetric dependencies of minimal degree. Example: It seems to be slightly faster than your function on this example. |

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2020-05-09 04:53:41 -0500 | commented question | Implicitization by symmetric polynomials Can you add your code and a sample case? Maybe naive idea: eliminate $x_1,\ldots,x_t$ from $\langle y_i - e_i(p_1(x_1,\ldots,x_t),\ldots,p_m(x_1,\ldots,x_t)) \rangle$ where $e_i$ are the elementary symmetric polynomials in $m$ variables. |

2020-05-08 09:39:34 -0500 | answered a question | Polynomial ring over the ring of integers modulo 3 The most literal interpretation is to build the quotient ring $(\mathbb{Z}/3\mathbb{Z})[x]/(x^p - x - 1)$: Since $3$ is prime you can also replace If $x^p - x - 1$ is irreducible (for example for $p=3$) then it is a modulus for the field with $3^p$ elements: |

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2020-05-04 11:35:16 -0500 | answered a question | Escape characters for LaTeX How about this? |

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2020-04-30 09:41:47 -0500 | commented question | RuntimeError Groebner basis for a Boolean system What is happening is: an ideal with generators $x_i^2 + x_i$ etc. plus your generators is created in the polynomial ring over |

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2020-04-30 06:45:05 -0500 | answered a question | Find expansion of polynomial in an ideal You can do this with the |

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2020-04-25 11:01:27 -0500 | commented answer | How to correctly plot x^(1/3) To get the real cube root of $-x$ (where $x>0$) you just have to add a minus sign in front of the real cube root of $x$; that's what this does. |

2020-04-25 10:57:42 -0500 | commented answer | How to correctly plot x^(1/3) |

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2020-04-25 09:18:15 -0500 | answered a question | How to correctly plot x^(1/3) SageMath sometimes chooses complex cube roots, which explains this behavior. There's not much you can do about this internal choice. But you can do this: |

2020-04-25 07:31:05 -0500 | commented question | How to correctly plot x^(1/3) What do you expect to get instead? |

2020-04-24 00:09:54 -0500 | commented question | Unexpected error in a notebook It says you cannot subtract a graphics object from an integer. Look for subtraction (with |

2020-04-23 10:01:44 -0500 | commented question | graphics not save from one cell to the other It should work. What do you mean by "doesn't work"? What happens exactly? |

2020-04-23 05:49:45 -0500 | commented answer | Choosing the way a function is displayed Yes, if you need irrational coefficients you should change |

2020-04-23 05:29:11 -0500 | answered a question | Choosing the way a function is displayed Yes. I guess you have it as a symbolic expression, like this: You can consider it as an element of the ring $\mathbb{Q}(p,D,w_0)[x]$, and then get the coefficients: You might want to convert these back to symbolic expressions again: Or avoid symbolic expressions entirely, by defining etc. |

2020-04-13 08:04:14 -0500 | commented question | product of functions A symbolic product in SageMath is currently not implemented, but you could take a logarithm and use a symbolic sum. |

2020-04-11 10:45:10 -0500 | commented question | I'm looking for a program in Sage which allows me to know if two seidel matrices from a graph are similar by a signed permutation matrix There is already an answer to this question here: how to test if two matrices are similar by a signed permutation matrix |

2020-04-11 08:55:57 -0500 | commented question | Definition of symbolic functions on path algebra Do I understand correctly that you want a "generic" derivation $d$, not any particular one? (A particular one would be easier.) I'm not an expert on path algebras, but: for an element |

2020-04-11 06:45:13 -0500 | commented question | Definition of symbolic functions on path algebra It seems SageMath only has an implementation for derivations over commutative rings. I guess you could do something yourself though. Which derivations do you want to create, and what do you want to do with them? |

2020-04-11 03:12:57 -0500 | commented question | Definition of symbolic functions on path algebra What do you actually want to achieve? Symbolic functions are probably not the answer. |

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2020-04-09 07:41:52 -0500 | answered a question | Compute dimension of vector subspace Take the block matrix over $\mathbb{Q}$ defined by and divide its rank by P.S. To get random matrices of lower rank you can use e.g. |

2020-04-07 12:46:26 -0500 | commented question | Compute dimension of vector subspace How about this matrix? |

2020-04-06 13:47:31 -0500 | commented answer | Random errors when using Singular via Sage You're welcome. When using Sage, I find it easiest to use the Sage interface. Mostly for the ease of writing code (which should not be forgotten), but also because the runtime cost compared to using the programs/interfaces directly is often negligible. For example here the most time is probably spent on things like the GTZ algorithm and computing a Gröbner basis (as part of |

2020-04-06 12:33:54 -0500 | answered a question | Random errors when using Singular via Sage The answer is that the output of Singular's |

2020-04-06 11:58:34 -0500 | commented question | Random errors when using Singular via Sage I'll have a look, but in the meantime note that everything you are doing can be done in ordinary |

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