Opened 9 years ago

Closed 7 years ago

# extend partial_fraction_decomposition() to work on ratios of multivariate polynomials

Reported by: Owned by: araichev major sage-duplicate/invalid/wontfix categories partial fraction decomposition multivariate polynomial ring robertwb, malb Alex Raichev N/A

### Description

Code to the compute a partial fraction decomposition of any elements of a fraction field of a multivariate polynomial rings over a field. Extends the existing sage.categories.quotient_fields function partial_fraction_decomposition().

### comment:1 Changed 9 years ago by araichev

Imports fail in decompose_via_algebraic_dependence().

### comment:2 Changed 9 years ago by malb

```diff --git a/sage/categories/quotient_fields.py b/sage/categories/quotient_fields.py
--- a/sage/categories/quotient_fields.py
+++ b/sage/categories/quotient_fields.py
@@ -1052,8 +1052,8 @@

- Alex Raichev (2011-01-10)
"""
-        from sage.structure.sequence import *
-        from sage.rings.polynomial.polynomial_ring_constructor import *
+        from sage.structure.sequence import Sequence
+        from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

parts = REFDSum([])
R = self.base_ring()
@@ -1195,4 +1195,4 @@
if done_decomposing:
return parts
else:
-            return parts.decompose_via_nullstellensatz()
\ No newline at end of file
+            return parts.decompose_via_nullstellensatz()
diff --git a/sage/rings/polynomial/multi_polynomial_sequence.py b/sage/rings/polynomial/multi_polynomial_sequence.py
--- a/sage/rings/polynomial/multi_polynomial_sequence.py
+++ b/sage/rings/polynomial/multi_polynomial_sequence.py
@@ -159,6 +159,7 @@
from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
from sage.rings.polynomial.multi_polynomial import is_MPolynomial
from sage.structure.sequence import Sequence_generic
+from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing

from sage.interfaces.singular import singular
```

gets you further. There was indeed an import missing, I wonder why we didn't catch this before?

### Changed 9 years ago by araichev

Tested on Sage 4.8

### comment:4 Changed 9 years ago by araichev

• Status changed from new to needs_review

### Changed 9 years ago by araichev

Tested on Sage 5.0.1

### comment:5 in reply to: ↑ description Changed 9 years ago by araichev

Also posted notes at http://arxiv.org/abs/1206.4740 about the mathematical background of the multivariate partial fraction decompositions involved. These are referenced in the patch.

Last edited 9 years ago by araichev (previous) (diff)

### comment:6 Changed 9 years ago by araichev

• Owner changed from nthiery to (none)

I'd like to discard this ticket, because the patch's functionality has been subsumed by the patch for http://trac.sagemath.org/sage_trac/ticket/10519.

### comment:7 Changed 8 years ago by jdemeyer

• Milestone changed from sage-5.11 to sage-5.12

### comment:8 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.1 to sage-6.2

### comment:9 Changed 7 years ago by vbraun_spam

• Milestone changed from sage-6.2 to sage-6.3

### comment:10 Changed 7 years ago by rws

• Milestone changed from sage-6.3 to sage-duplicate/invalid/wontfix
• Status changed from needs_review to positive_review

abandoned, see comment:6

### comment:11 Changed 7 years ago by vbraun

• Resolution set to duplicate
• Status changed from positive_review to closed
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