Changeset 7381:031ff38df952

Timestamp:

11/17/07 09:48:17 (6 years ago)

Author:

Martin Albrecht <malb@…>

Branch:

default

Message:

added doctest for #991

File:

• sage/rings/polynomial/multi_polynomial_ideal.py (modified) (2 diffs)

sage/rings/polynomial/multi_polynomial_ideal.py

@@ -377 +377 @@
             [Ideal (a - 1, b - 1, c - 1, d^2 + 3*d + 1, e + d + 3) of
             Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a - 1, b - 1, c^2 + 3*c + 1, d + c + 3, e - 1) of
+            Rational Field, Ideal (a - 1, b - 1, c^2 + 3*c + 1, d + c
+            + 3, e - 1) of Multivariate Polynomial Ring in e, d, c, b,
+            a over Rational Field, Ideal (a - 1, b^4 + b^3 + b^2 + b +
+            1, c - b^2, d - b^3, e + b^3 + b^2 + b + 1) of
             Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a - 1, b^4 + b^3 + b^2 + b + 1, c - b^2, d - b^3, e
-            + b^3 + b^2 + b + 1) of Multivariate Polynomial Ring in e,
-            d, c, b, a over Rational Field,
-            Ideal (a - 1, b^2 + 3*b + 1, c + b + 3, d - 1, e - 1) of
+            Rational Field, Ideal (a - 1, b^2 + 3*b + 1, c + b + 3, d
+            - 1, e - 1) of Multivariate Polynomial Ring in e, d, c, b,
+            a over Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1, b -
+            1, c + a^3 + a^2 + a + 1, d - a^3, e - a^2) of
             Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a^4 + a^3 + a^2 + a + 1, b - 1, c + a^3 + a^2 + a +
-            1, d - a^3, e - a^2) of Multivariate Polynomial Ring in e,
-            d, c, b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a
-            + 1, b - a, c - a, d^2 + 3*d*a + a^2, e + d + 3*a) of
-            Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
+            Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1, b - a, c -
+            a, d^2 + 3*d*a + a^2, e + d + 3*a) of Multivariate
+            Polynomial Ring in e, d, c, b, a over Rational Field,
             Ideal (a^4 + a^3 + a^2 + a + 1, b - a, c^2 + 3*c*a + a^2,
             d + c + 3*a, e - a) of Multivariate Polynomial Ring in e,
-            d, c, b, a over Rational Field,
-            Ideal (a^4 + a^3 + a^2 + a + 1, b^3 + b^2*a + b^2 + b*a^2
-            + b*a + b + a^3 + a^2 + a + 1, c + b^2*a^3 + b^2*a^2 +
-            b^2*a + b^2, d - b^2*a^2 - b^2*a - b^2 - b*a^2 - b*a -
-            a^2, e - b^2*a^3 + b*a^2 + b*a + b + a^2 + a) of
+            d, c, b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a
+            + 1, b^3 + b^2*a + b^2 + b*a^2 + b*a + b + a^3 + a^2 + a +
+            1, c + b^2*a^3 + b^2*a^2 + b^2*a + b^2, d - b^2*a^2 -
+            b^2*a - b^2 - b*a^2 - b*a - a^2, e - b^2*a^3 + b*a^2 + b*a
+            + b + a^2 + a) of Multivariate Polynomial Ring in e, d, c,
+            b, a over Rational Field, Ideal (a^4 + a^3 + a^2 + a + 1,
+            b^2 + 3*b*a + a^2, c + b + 3*a, d - a, e - a) of
             Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a^4 + a^3 + a^2 + a + 1, b^2 + 3*b*a + a^2, c + b +
-            3*a, d - a, e - a) of Multivariate Polynomial Ring in e,
-            d, c, b, a over Rational Field,
-            Ideal (a^4 + a^3 + 6*a^2 - 4*a + 1, 11*b^2 - 6*b*a^3 -
-            10*b*a^2 - 39*b*a - 2*b - 16*a^3 - 23*a^2 - 104*a + 24,
-            11*c + 3*a^3 + 5*a^2 + 25*a + 1, 11*d + 3*a^3 + 5*a^2 +
-            25*a + 1, 11*e + 11*b - 6*a^3 - 10*a^2 - 39*a - 2) of
-            Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a^4 - 4*a^3 + 6*a^2 + a + 1, 11*b^2 - 6*b*a^3 +
-            26*b*a^2 - 41*b*a + 4*b + 8*a^3 - 31*a^2 + 40*a + 24, 11*c
-            + 3*a^3 - 13*a^2 + 26*a - 2, 11*d + 3*a^3 - 13*a^2 + 26*a
-            - 2, 11*e + 11*b - 6*a^3 + 26*a^2 - 41*a + 4) of
-            Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field,
-            Ideal (a^2 + 3*a + 1, b - 1, c - 1, d - 1, e + a + 3) of
-            Multivariate Polynomial Ring in e, d, c, b, a over
-            Rational Field, Ideal (a^2 + 3*a + 1, b + a + 3, c - 1, d
-            - 1, e - 1) of Multivariate Polynomial Ring in e, d, c, b,
-            a over Rational Field]
+            Rational Field, Ideal (a^4 - 4*a^3 + 6*a^2 + a + 1, 11*b^2
+            - 6*b*a^3 + 26*b*a^2 - 41*b*a + 4*b + 8*a^3 - 31*a^2 +
+            40*a + 24, 11*c + 3*a^3 - 13*a^2 + 26*a - 2, 11*d + 3*a^3
+            - 13*a^2 + 26*a - 2, 11*e + 11*b - 6*a^3 + 26*a^2 - 41*a +
+            4) of Multivariate Polynomial Ring in e, d, c, b, a over
+            Rational Field, Ideal (a^4 + a^3 + 6*a^2 - 4*a + 1, 11*b^2
+            - 6*b*a^3 - 10*b*a^2 - 39*b*a - 2*b - 16*a^3 - 23*a^2 -
+            104*a + 24, 11*c + 3*a^3 + 5*a^2 + 25*a + 1, 11*d + 3*a^3
+            + 5*a^2 + 25*a + 1, 11*e + 11*b - 6*a^3 - 10*a^2 - 39*a -
+            2) of Multivariate Polynomial Ring in e, d, c, b, a over
+            Rational Field, Ideal (a^2 + 3*a + 1, b - 1, c - 1, d - 1,
+            e + a + 3) of Multivariate Polynomial Ring in e, d, c, b,
+            a over Rational Field, Ideal (a^2 + 3*a + 1, b + a + 3, c
+            - 1, d - 1, e - 1) of Multivariate Polynomial Ring in e,
+            d, c, b, a over Rational Field]
             """
 
@@ -1088 +1081 @@
             48
 
+        TESTS:
+            sage: K.<w> = GF(27)
+            sage: P.<x, y> = PolynomialRing(K, 2, order='lex')
+            sage: I = Ideal([ x^8 + y + 2, y^6 + x*y^5 + x^2 ])
+
+            Testing the robustness of the Singular interface
+            
+            sage: T = I.triangular_decomposition('singular:triangLfak')
+            sage: I.variety()
+            [{y: w^2 + 2, x: 2*w}, {y: w^2 + w, x: 2*w + 1}, {y: w^2 + 2*w, x: 2*w + 2}]
+
         ALGORITHM: Uses triangular decomposition.
         """