Recent content by GargleBlast42

I'm sorry for bumping this, but I would be really happy about any input.

Hi everyone, I have a severe confusion about the notions of "expanding the theory around a classical vacuum" and "considering small fluctuations around a classical vacuum" which I find in QFT textbooks. My problem is: in the path integral \int D\phi e^{i S[\phi]} one doesn't integrate only...

Hi, given a polynomial ring R=\mathbb{C}[x_1,\ldots,x_n] and an ideal I=\langle f_1, f_2 \rangle, \quad f_1, f_2 \in R, is it always true that R/I \cong (R/\langle f_1 \rangle)/\phi(\langle f_2 \rangle), with \phi: R \rightarrow R/I being the quotient map? That is, is quotienting by I always...

Thanks, your solution works, but it still has a problem - it only seems working when I take the expression in an equation. But I want to simplify solely the expression (b^8 + c^4)/a^8 without putting it into an equation.

Hi everyone, I'm wondering why Mathematica (8.0) can't bring this to the obvious form -1, and leaves the expression as is: Simplify[(b^8 + c^4) /a^8, a^8 + b^8 + c^4 == 0] Is there any nice and elegant way how to achieve that? (I know, that I could take e.g. /.c->(-a^8-b^8)^(1/4), but...

Thank you very much Simon, it solved the problem!

Hi, I'm trying to save (into a file) definitions of some variables which are of the form Subscript[A,1], Subscript[A,2],... where the subscript is used as an index for the variable. When using the Save command I obtain the error Save::sym: Argument A1 at position 2 is expected to be a...

Well, for example, I have this variety in \mathbb{C}^9: x_1^5+x_3^5+x_5^5+x_7^5+x_9^5=0 x_1^4+x_2 x_3^4+x_4 x_5^4+x_6 x_7^4+x_8 x_9^4=0 x_1^3+x_2^2 x_3^3+x_4^2 x_5^3+x_6^2 x_7^3+x_8^2 x_9^3=0 x_1^2+x_2^3 x_3^2+x_4^3 x_5^2+x_6^3 x_7^2+x_8^3 x_9^2=0 x_1+x_2^4 x_3+x_4^4 x_5+x_6^4 x_7+x_8^4 x_9=0...

Hello, I have the following problem: I have an algebraic variety given as a zero locus of a set of polynomials. I know that there are points on this variety, which are singular (i.e. the dimension of the tangent space at these points is bigger than that of the variety). Now fixing one of...

Hello, I was wondering, if there is some good and easy to use computer programm, that, given a set of polynomials, tells me if they generate a radical ideal. Preferably as a Mathematica package.

OK, I will partially answer my own question: The Jacobian is not a reliable indicator of the "number of directions" on an algebraic set. Simple example: the hypersurface in R^3 given by x^2+2xy+y^2, where the Jacobian is vanishing along the surface and so doesn't give the expected dimension...

I have the following problem: I'm studying a system of polynomial equations in R^n and I'm looking at the surface which is the solution set of this system. I'm mainly interested in the dimension of this surface at a given point. Now, naively, one would try to compute the Jacobian (of the m...

Well, that is certainly a solution, but I would like to obtain the most general form. Could one, for example, show that all such solutions have to have the form a_i=\sum_{j\neq i} c_j p_j, with the c_j being some polynomials obeying some further relation (which is obtained by substituting this...

What is the most general solution to an equation of the form: a_1 p_1 + \ldots + a_n p_n =0 where p_i are given polynomials in several (N) variables with no common factor (i.e. their GCD is 1) and a_n are the polynomials we are looking for (again in the same N variables). Of course, I'm asking...

Sorry, I meant of course \delta \psi_+|_{\sigma=0/\pi} = \delta \psi_-|_{\sigma=0/\pi} = 0. With the antiperiodicity - well yes, you couldn't interpret the X's as space-time dimensions, but from the point of view of the 2D Field Theory it would be okay, right?