Changeset 4077:96ed94d32305

Timestamp:

04/23/07 01:50:08 (6 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Children:

4078:3cee4b64bf26, 4079:0f2ffefcfa13, 4099:543dba25c40e, 4103:bf0311ec7662, 4136:1578cb90808d, 4804:2c23e747fbb7, 4806:3bf6690d9871

Message:

Martin's patch.

Location:

sage

Files:

• ext/interactive_constructors_c.pyx (modified) (1 diff)
• rings/groebner_fan.py (modified) (2 diffs)
• rings/ideal.py (modified) (3 diffs)
• rings/morphism.py (modified) (1 diff)
• rings/multi_polynomial_element.py (modified) (1 diff)
• rings/multi_polynomial_ideal.py (modified) (5 diffs)
• rings/number_field/number_field_ideal.py (modified) (1 diff)
• rings/quotient_ring.py (modified) (2 diffs)
• rings/quotient_ring_element.py (modified) (1 diff)
• rings/ring.pyx (modified) (3 diffs)
• schemes/generic/divisor.py (modified) (5 diffs)

sage/ext/interactive_constructors_c.pyx

@@ -194 +194 @@
         sage: S = quo(R, (x^3, x^2 + y^2), 'a,b')
         sage: S
-        Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y^2 + x^2, x^3)
+        Quotient of Polynomial Ring in x, y over Rational Field by the ideal (x^3, y^2 + x^2)
         sage: a^2
         -1*b^2

sage/rings/groebner_fan.py

@@ -105 +105 @@
             sage: G = I.groebner_fan(); G
             Groebner fan of the ideal:
-            Ideal (y^2*z - x, -1*y + x*z^2, -1*z + x^2*y) of Polynomial Ring in x, y, z over Rational Field
+            Ideal (-1*z + x^2*y, y^2*z - x, -1*y + x*z^2) of Polynomial Ring in x, y, z over Rational Field
         """
         self.__is_groebner_basis = is_groebner_basis
@@ -206 +206 @@
             sage: G = R.ideal([x^2*y - z, y^2*z - x, z^2*x - y]).groebner_fan()
             sage: G._gfan_ideal()
-            '{-1*b + a*c^2, b^2*c - a, -1*c + a^2*b}'
+            '{-1*c + a^2*b, b^2*c - a, -1*b + a*c^2}'
         """
         try:

sage/rings/ideal.py

@@ -60 +60 @@
         sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
         sage: I
-        Ideal (x^2 + 1, x^2 + 3*x + 4) of Univariate Polynomial Ring in x over Integer Ring
+        Ideal (x^2 + 3*x + 4, x^2 + 1) of Univariate Polynomial Ring in x over Integer Ring
         sage: Ideal(R, [4 + 3*x + x^2, 1 + x^2])
-        Ideal (x^2 + 1, x^2 + 3*x + 4) of Univariate Polynomial Ring in x over Integer Ring
+        Ideal (x^2 + 3*x + 4, x^2 + 1) of Univariate Polynomial Ring in x over Integer Ring
         sage: Ideal((4 + 3*x + x^2, 1 + x^2))
-        Ideal (x^2 + 1, x^2 + 3*x + 4) of Univariate Polynomial Ring in x over Integer Ring
+        Ideal (x^2 + 3*x + 4, x^2 + 1) of Univariate Polynomial Ring in x over Integer Ring
         
         sage: ideal(x^2-2*x+1, x^2-1)
-        Ideal (x^2 - 2*x + 1, x^2 - 1) of Univariate Polynomial Ring in x over Integer Ring
+        Ideal (x^2 - 1, x^2 - 2*x + 1) of Univariate Polynomial Ring in x over Integer Ring
         sage: ideal([x^2-2*x+1, x^2-1])
-        Ideal (x^2 - 2*x + 1, x^2 - 1) of Univariate Polynomial Ring in x over Integer Ring
-        sage: ideal(x^2-2*x+1, x^2-1)
-        Ideal (x^2 - 2*x + 1, x^2 - 1) of Univariate Polynomial Ring in x over Integer Ring
-        sage: ideal([x^2-2*x+1, x^2-1])
-        Ideal (x^2 - 2*x + 1, x^2 - 1) of Univariate Polynomial Ring in x over Integer Ring
+        Ideal (x^2 - 1, x^2 - 2*x + 1) of Univariate Polynomial Ring in x over Integer Ring
+
 
     This example illustrates how SAGE finds a common ambient ring for the ideal, even though
@@ -80 +77 @@
         sage: i = ideal(1,t,t^2)
         sage: i
-        Ideal (1, t, t^2) of Univariate Polynomial Ring in t over Integer Ring
+        Ideal (t, 1, t^2) of Univariate Polynomial Ring in t over Integer Ring
         sage: i = ideal(1/2,t,t^2)
         Traceback (most recent call last):
@@ -164 +161 @@
         if coerce:
             gens = [ring(x) for x in gens]
-        gens = list(set(gens))
-        
-        # Regarding the "important" comment below: Otherwise the
-        # generators will be in a completely random order, given the
-        # code that comes before that line.  A basic design choice in
-        # SAGE is that as much as possible lists of objects (e.g.,
-        # list(R), where R is finite), should not be in a random
-        # order.  Feel free to add this as a comment.  It would be
-        # fine to replace the sort by something else, if it yields the
-        # same answer.  However, I don't think randomizing the orders
-        # of things, e.g., lists of generators, for no reason, is a
-        # good idea in SAGE.  This is another "rule of thumb" for the
-        # programmer's guide.
-        gens.sort()    # important!
+
         self.__gens = tuple(gens)
         MonoidElement.__init__(self, ring.ideal_monoid())

sage/rings/morphism.py

@@ -345 +345 @@
         sage: S.lift()
         Set-theoretic ring morphism:
-          From: Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y, y^2 + x^2)
+          From: Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y^2 + x^2, y)
           To:   Polynomial Ring in x, y over Rational Field
           Defn: Choice of lifting map

sage/rings/multi_polynomial_element.py

@@ -1111 +1111 @@
             sage: M = f.lift(I)
             sage: M
-            [y^4 + x*y^5 + x^2*y^3 + x^3*y^4 + x^4*y^2 + x^5*y^3 + x^6*y + x^7*y^2 + x^8, y^7]
+            [y^7, y^4 + x*y^5 + x^2*y^3 + x^3*y^4 + x^4*y^2 + x^5*y^3 + x^6*y + x^7*y^2 + x^8]
             sage: sum( map( mul , zip( M, I.gens() ) ) ) == f
             True

sage/rings/multi_polynomial_ideal.py

@@ -177 +177 @@
             sage: S = I._singular_()
             sage: S
-            y,
-            x^3+y
+            x^3+y,
+            y
         """
         if singular is None: singular = singular_default
@@ -439 +439 @@
             Ideal (y^2, x*y, x^2) of Polynomial Ring in x, y over Rational Field
             sage: IJ = I*J; IJ
-            Ideal (y^3, x*y, x^2*y^2, x^3) of Polynomial Ring in x, y over Rational Field
+            Ideal (x^2*y^2, x^3, y^3, x*y) of Polynomial Ring in x, y over Rational Field
             sage: IJ == K
             False
@@ -463 +463 @@
             sage: I = (p*q^2, y-z^2)*R
             sage: I.minimal_associated_primes ()
-            [Ideal (-1*z^2 + y, 2 + z^3) of Polynomial Ring in x, y, z over Rational Field, Ideal (-1*z^2 + y, 1 + z^2) of Polynomial Ring in x, y, z over Rational Field]
+            [Ideal (2 + z^3, -1*z^2 + y) of Polynomial Ring in x, y, z over Rational Field, Ideal (1 + z^2, -1*z^2 + y) of Polynomial Ring in x, y, z over Rational Field]
         
         ALGORITHM: Uses Singular.
@@ -531 +531 @@
             sage: I = ideal([x^2,x*y^4,y^5])
             sage: I.integral_closure()
-            [x^2, y^5, x*y^3]
+            [x^2, y^5, -1*x*y^3]
 
         ALGORITHM: Use Singular
@@ -830 +830 @@
             sage: R.<x,y> = PolynomialRing(IntegerRing(), 2, order='lex')
             sage: R.ideal([x, y])
-            Ideal (y, x) of Polynomial Ring in x, y over Integer Ring
+            Ideal (x, y) of Polynomial Ring in x, y over Integer Ring
             sage: R.<x0,x1> = GF(3)[]
             sage: R.ideal([x0^2, x1^3])

sage/rings/number_field/number_field_ideal.py

@@ -235 +235 @@
             sage: J = K.ideal([i+1, 2])
             sage: J.gens()
-            (2, i + 1)
+            (i + 1, 2)
             sage: J.gens_reduced()
             (i + 1,)

sage/rings/quotient_ring.py

@@ -69 +69 @@
         sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2])
         sage: S = R.quotient_ring(I); S
-        Quotient of Univariate Polynomial Ring in x over Integer Ring by the ideal (x^2 + 1, x^2 + 3*x + 4)
+        Quotient of Univariate Polynomial Ring in x over Integer Ring by the ideal (x^2 + 3*x + 4, x^2 + 1)
 
         sage: R.<x,y> = PolynomialRing(QQ)
@@ -135 +135 @@
             sage: l = pi.lift(); l
             Set-theoretic ring morphism:
-              From: Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y^2, x^2)
+              From: Quotient of Polynomial Ring in x, y over Rational Field by the ideal (x^2, y^2)
               To:   Polynomial Ring in x, y over Rational Field
               Defn: Choice of lifting map

sage/rings/quotient_ring_element.py

@@ -38 +38 @@
         sage: R.<x> = PolynomialRing(ZZ)
         sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S
-        Quotient of Univariate Polynomial Ring in x over Integer Ring by the ideal (x^2 + 1, x^2 + 3*x + 4)
+        Quotient of Univariate Polynomial Ring in x over Integer Ring by the ideal (x^2 + 3*x + 4, x^2 + 1)
         sage: v = S.gens(); v
         (xbar,)

sage/rings/ring.pyx

@@ -164 +164 @@
             sage: R.<x,y> = QQ[]
             sage: R.ideal((x,y))
-            Ideal (y, x) of Polynomial Ring in x, y over Rational Field
+            Ideal (x, y) of Polynomial Ring in x, y over Rational Field
             sage: R.ideal(x+y^2)
             Ideal (y^2 + x) of Polynomial Ring in x, y over Rational Field
@@ -671 +671 @@
             sage: S.<a,b> = R.quotient((x^2, y))
             sage: S
-            Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y, x^2)
+            Quotient of Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
             sage: S.gens()
             (a, 0)
@@ -694 +694 @@
             sage: S.<a,b> = R.quo((x^2, y))
             sage: S
-            Quotient of Polynomial Ring in x, y over Rational Field by the ideal (y, x^2)
+            Quotient of Polynomial Ring in x, y over Rational Field by the ideal (x^2, y)
             sage: S.gens()
             (a, 0)

sage/schemes/generic/divisor.py

@@ -18 +18 @@
     True
     sage: D = D1 - D2 + D3; D
-    10*(z + y, 2*z + x) + 3*(y, x) - (z, x)
+    10*(2*z + x, z + y) + 3*(x, y) - (x, z)
     sage: D[1][0]
     3
     sage: D[1][1]
-    Ideal (y, x) of Polynomial Ring in x, y, z over Finite Field of size 5
+    Ideal (x, y) of Polynomial Ring in x, y, z over Finite Field of size 5
     sage: C.divisor([(3, pts[0]), (-1, pts[1]), (10,pts[5])])
-    10*(z + y, 2*z + x) + 3*(y, x) - (z, x)
+    10*(2*z + x, z + y) + 3*(x, y) - (x, z)
 """
 #*******************************************************************************
@@ -99 +99 @@
             [(0, 0), (2, 2), (2, 3), (3, 1), (3, 4)]
             sage: D = C.divisor(pts[0])*3 - C.divisor(pts[1]); D
-            -(3 + y, 3 + x) + 3*(y, x)
+            -(3 + x, 3 + y) + 3*(x, y)
             sage: D.scheme()
             Affine Curve over Finite Field of size 5 defined by y^2 + 4*x + 4*x^9
@@ -130 +130 @@
         sage: D = E.divisor(P)
         sage: D
-        (y, x)
+        (x, y)
         sage: 10*D
-        10*(y, x)
+        10*(x, y)
         sage: E.divisor([P, P])
-        2*(y, x)
+        2*(x, y)
         sage: E.divisor([(3,P), (-4,5*P)])
-        -4*(5/8*z + y, -1/4*z + x) + 3*(y, x)
+        -4*(-1/4*z + x, 5/8*z + y) + 3*(x, y)
     """
     def __init__(self, v, check=True, reduce=True, parent=None):
@@ -222 +222 @@
             [(0, 0), (2, 2), (2, 3), (3, 1), (3, 4)]
             sage: D = C.divisor([(3,pts[0]), (-1, pts[1])]); D
-            -(3 + y, 3 + x) + 3*(y, x)
+            -(3 + x, 3 + y) + 3*(x, y)
             sage: D.support()
             [(0, 0), (2, 2)]
@@ -248 +248 @@
             1
             sage: D = C.divisor([(3,pts[0]), (-1,pts[1])]); D
-            -(3 + y, 3 + x) + 3*(y, x)
+            -(3 + x, 3 + y) + 3*(x, y)
             sage: D.coeff(pts[0])
             3