Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues
Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1301-1318
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Two methods for computing the integrals of rational functions over $\mathbb R^n$ are considered. The first is applicable to differentials with rational antiderivatives and uses the interpretation of $\mathbb R^n$ as a chain of integration in some toric compactification. The second method is based on the theory of multidimensional residues and the multidimensional version of the Sokhotskii formula for the jump of an integral.
@article{SM_1996_187_9_a2,
author = {T. O. Ermolaeva and A. K. Tsikh},
title = {Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues},
journal = {Sbornik. Mathematics},
pages = {1301--1318},
publisher = {mathdoc},
volume = {187},
number = {9},
year = {1996},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1996_187_9_a2/}
}
TY - JOUR AU - T. O. Ermolaeva AU - A. K. Tsikh TI - Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues JO - Sbornik. Mathematics PY - 1996 SP - 1301 EP - 1318 VL - 187 IS - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_1996_187_9_a2/ LA - en ID - SM_1996_187_9_a2 ER -
%0 Journal Article %A T. O. Ermolaeva %A A. K. Tsikh %T Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues %J Sbornik. Mathematics %D 1996 %P 1301-1318 %V 187 %N 9 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_1996_187_9_a2/ %G en %F SM_1996_187_9_a2
T. O. Ermolaeva; A. K. Tsikh. Integration of rational functions over $\mathbb R^n$ by means of toric compactifications and multidimensional residues. Sbornik. Mathematics, Tome 187 (1996) no. 9, pp. 1301-1318. http://geodesic.mathdoc.fr/item/SM_1996_187_9_a2/