bio | website | cs.ox.ac.uk/people/… |
---|---|---|
location | Oxford, United Kingdom | |
age | 51 | |
visits | member for | 4 years, 2 months |
seen | 6 hours ago | |
stats | profile views | 1,943 |
Jan 1 |
reviewed | Approve Graded Betti Numbers of a Graded Ideal with Linear Quotients |
Dec 31 |
answered | Polarizations generate the ring of invariants? |
Dec 31 |
comment |
Polarizations generate the ring of invariants?
more precisely, the degree 3 homogeneous component has at least this dimension, $\binom{m-1}{3}$. |
Dec 31 |
comment |
Polarizations generate the ring of invariants?
you might want to check that this will give you enough invariants for $n=3$ (i.e. for the cyclic group of order 3). It is known that you will need $\binom{m-1}{3}$ degree 3 invariants in any generating set. |
Dec 30 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail, this looks way too general for the purpose of "smoothing out" real algebraic and semialgebraic sets. In the computable constructions there one anyway uses only $\epsilon^{p/q}$ for bounded $|p/q|$. |
Dec 30 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail, it could be enough for our purposes, although I never heard about nilpotent infinitesimals. References? |
Dec 30 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail, it's a common place in real algebraic geometry to work over the field of Puiseux series in an infinitesimal $\epsilon$ over $\mathbb{R}$ (or other real closed fields). Cf. e.g. perso.univ-rennes1.fr/marie-francoise.roy/bpr-ed2-posted2.html |
Dec 29 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail : I always found it very tricky to apply the transfer principle in the setting of real algebraic geometry - IMHO it's easier in the setting of univariate calculus... Well, I am no Euler, and I very often got lost. |
Dec 29 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail : don't you need some NSA to make proper sense of Euler's derivation of the infinite product formula for $\sin x$ ? |
Dec 29 |
comment |
Which universities teach true infinitesimal calculus?
@Mikhail: cf. en.wikipedia.org/wiki/Infinitesimal --- as well, I don't think that by "infinitesimal calculus" most people mean non-rigorous Euler-style computations. Call it "Transfer principle-based infinitesimal calculus" if you must. |
Dec 28 |
comment |
Which universities teach true infinitesimal calculus?
perhaps "rigorous" or "axiomatic" would be better word than "true". |
Dec 28 |
revised |
Evaluating products of cyclotomic polynomials at roots of unity
added 38 characters in body |
Dec 26 |
comment |
symmetrizability of generalised cartan matrix
either wikipedia is wrong, or this is by definition: en.wikipedia.org/wiki/Cartan_matrix en.wikipedia.org/wiki/Symmetric_matrix#Symmetrizable_matrix |
Dec 21 |
comment |
Connected components $0-1$ matrices
By definition, the diagonal matrix $I$ is connected. |
Dec 21 |
comment |
Connected components $0-1$ matrices
Conjugation is certainly much harder to deal with. |
Dec 21 |
comment |
Connected components $0-1$ matrices
do you require simultaneous permutations of rows and columns (i.e. conjugation by a permutation matrix)? Or you allow different permutations to permute rows and columns? |
Dec 19 |
comment |
Balanced binary code that “resists” local decoding?
the supports of the codewords either have empty intersection, or intersection of size $2^{k-2}$. So the Hamming distance between any two is $2^{k-1}$ or $2^k$. Thus the minimal distance is $2^{k-1}$. |
Dec 18 |
answered | An optimization problem in complex space |
Dec 18 |
revised |
An optimization problem in complex space
tex corrections |
Dec 18 |
revised |
Balanced binary code that “resists” local decoding?
texify k |