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

Banach Center Publications (2006)

- Volume: 72, Issue: 1, page 49-55
- ISSN: 0137-6934

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topC. 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 -

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