Ideal interpolation: Mourrain's condition vs. D-invariance

C. de Boor. "Ideal interpolation: Mourrain's condition vs. D-invariance." Banach Center Publications 72.1 (2006): 49-55. <http://eudml.org/doc/281736>.

@article{C2006,
abstract = {Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain's characterization requires the polynomial space to be 'connected to 1', a condition that is implied by D-invariance in case the polynomial space is spanned by monomials. We give examples to show that, for more general polynomial spaces, D-invariance and being 'connected at 1' are unrelated, and that Mourrain's characterization need not hold when his condition is replaced by D-invariance.},
author = {C. de Boor},
journal = {Banach Center Publications},
language = {eng},
number = {1},
pages = {49-55},
title = {Ideal interpolation: Mourrain's condition vs. D-invariance},
url = {http://eudml.org/doc/281736},
volume = {72},
year = {2006},
}

TY - JOUR
AU - C. de Boor
TI - Ideal interpolation: Mourrain's condition vs. D-invariance
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 49
EP - 55
AB - Mourrain [Mo] characterizes those linear projectors on a finite-dimensional polynomial space that can be extended to an ideal projector, i.e., a projector on polynomials whose kernel is an ideal. This is important in the construction of normal form algorithms for a polynomial ideal. Mourrain's characterization requires the polynomial space to be 'connected to 1', a condition that is implied by D-invariance in case the polynomial space is spanned by monomials. We give examples to show that, for more general polynomial spaces, D-invariance and being 'connected at 1' are unrelated, and that Mourrain's characterization need not hold when his condition is replaced by D-invariance.
LA - eng
UR - http://eudml.org/doc/281736
ER -