Karl's profile - activity

Given a Groebner basis $G=\lbrace f_1,\dots,f_s \rbrace$ and $g$, how can I get the quotients of $g$ on division by $G$ ? I know that when considering the quotients, the ordering we use to list the divisors $f_1,\dots,f_s$ matters. I also know the command p.reduce(I) for remainders. I would appreciate any help with this situation.

Excuse me for my silly question.

"3.3. Using Sage" in https://wiki.sagemath.org/SageApplian... says that after the virtual machine has finished booting, I should see the following window:

But what I encounter is the following window: http://imgur.com/HBchZXo

I have tried entering the first two folders and opening the "notebook-browser" but I still do not know how to launch the Sage Notebook. Could anyone help me? I would appreciate any help with this situation.

I am a newcomer to Sage. The PREP Tutorials(http://doc.sagemath.org/html/en/prep/Intro-Tutorial.html#help-inside-sage) introduce two applications of “tab completion”:

1. If you aren’t one hundred percent sure of the name of a command.
2. Use this to see what you can do to an expression or mathematical object.

I tried some examples of the first type in SageMathCell and succeeded. But, in SageMathCell, when I tried some second type examples that the tutorials provide, I didn't see a list pop up. Is there something wrong? I would appreciate any help with this situation.

I am a newcomer to Sage. I learn Sage to compute Gröbner bases.

Concerning polynomial ring, if I type:

R = PolynomialRing(QQ, 't')
R

I get:

Univariate Polynomial Ring in t over Rational Field

But if I type:

R = PolynomialRing(RR, 't')
R

I get:

Univariate Polynomial Ring in t over Real Field with 53 bits of precision

What does "with 53 bits of precision" mean? If I don't know its meaning, will it matter when I compute Gröbner bases? I would appreciate any help with this situation.