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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-3,
author = {C. de Boor},
title = {Ideal interpolation: Mourrain's condition vs. D-invariance},
journal = {Banach Center Publications},
volume = {72},
year = {2006},
pages = {49-55},
zbl = {05082646},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-3}
}
C. de Boor. Ideal interpolation: Mourrain's condition vs. D-invariance. Banach Center Publications, Tome 72 (2006) pp. 49-55. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-3/