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725
bio website cs.ox.ac.uk/people/…
location Oxford, United Kingdom
age 51
visits member for 4 years, 2 months
seen 6 hours ago

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