pkoprowski's profile - activity

Bug in quadratic_defect This is not a question but a bug report, but since https://trac.sagemath.org/ is down, I don't k

I don't know how to do it in Sage, but the answer to the second part of your question (i.e. the theory) is in: P. Gianni, B. Trager, G. Zacharias "Groebner bases and primary decomposition of polynomial ideals" JSC 6/1988, 149-167 The same algorithm is AFAIR also in W. Adams, Ph. Loustaunau "Introduction to Groebner Bases"

Returning to the first part of your question - Sage uses Singular internally. I think Singular has an appropriate built-in. Hence, I think you will have to "tunnel" the problem down to Singular and do the work in it.

1) You can easily write matrix "multilined". By default Python joins lines if the first one contains an opening bracket/parenthesis. Hence you can easily write:

ma = matrix([
[25, 5, 1], 
[49, 7, 1], 
[81, 9, 1]])
mb = matrix([
[1121], 
[626],
[967]])

2) In order to display matrix entries as decimals you may convert a matrix base field to RDF like this:

ms = ma^-1 * mb
show(matrix(RDF, ms))

or alternatively:

show(ms.change_ring(RDF))

Thanks for your reply. It indeed solves the problem in two example cases I presented, but... still I sometimes need yet another delimiters around the sage's output (e.g $\langle$ or $\langle\langle$...)

Hi,

how can I output a list in SageTeX without it being enclosed in brackets? Consider for example:

\begin{sagesilent}
A = [ 1, 2, 4 ]
\end{sagesilent}

and in the text

... $A = \{ \sage{A} \}$

produces $A = \{ \left[1, 2, 4\right] \}$ instead of $\{ 1,2,4 \}$. Or a more realistic example:

\begin{sagesilent}
R.<x,y> = PolynomialRing(QQ, 'x,y', order='lex')
I = R.ideal(x^2+1, y*x-y)
\end{sagesilent}

and know somewhere in the text I want to put

The Groebner basis of $I$ is $\{ \sage{I.groebner_basis()} \}$

but the result is: $\{ \left[x^{2} + 1, y\right] \}$ rather then expected $\{ x^{2} + 1, y \}$

Is this a bug in Sage or am I doing something wrong:

q = DiagonalQuadraticForm(QQ, [1,1,-1,-1])
q.is_hyperbolic(2)

The answer should be clearly true, but Sage return false???

I need to find whether a given (often somewhat complicated) dyadic field contains $i$. I tried to use is_square method, but I'm getting error reports.

Consider the following (very simplified) example:

Q2 = Qp(2); Q2(-1).is_square()

As far as good - the answer is False as expected. So try a simple extension:

F.<a> = Qq(2^3); F(-1).is_square()

And... I'm getting an error message:

AttributeError: 'sage.rings.padics.padic_ZZ_pX_CR_element.pAdicZZpXCRElement' object has no attribute 'residue'

Is this a Sage bug or I'm doing something wrong?

I believe this can be easily computed with Macaulay-2, as documented here: http://www.math.uiuc.edu/Macaulay2/do... (BTW, this is yet another reason to integrate Sage with Macaulay by default, not only as a optional package.)