10 | | - sage/categories/pushout.py : line 2393 |
11 | | - sage/categories/rings.py : lines 446, 482, 522 |
12 | | - sage/structure/category_object.pyx : line 473 |
13 | | - sage/rings/quotient_ring_element.py : lines 56, 98, 208 |
14 | | - sage/rings/morphism.pyx : line 465 |
15 | | - sage/rings/ring.pyx: lines 409, 708, 792 |
| 10 | - sage/categories/pushout.py : |
| 11 | - QuotientFunctor.__cmp__ |
| 12 | {{{ |
| 13 | sage: P.<x> = QQ[] |
| 14 | sage: F = P.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] |
| 15 | sage: F == loads(dumps(F)) |
| 16 | True |
| 17 | sage: P2.<x,y> = QQ[] |
| 18 | sage: F == P2.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] |
| 19 | False |
| 20 | sage: P3.<x> = ZZ[] |
| 21 | sage: F == P3.quo([(x^2+1)^2*(x^2-3),(x^2+1)^2*(x^5+3)]).construction()[0] |
| 22 | True |
| 23 | }}} |
| 24 | |
| 25 | |
| 26 | - sage/categories/rings.py : |
| 27 | - Rings.quotient |
| 28 | {{{ |
| 29 | sage: F.<x,y,z> = FreeAlgebra(QQ, 3) |
| 30 | sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F |
| 31 | sage: Q = Rings().parent_class.quotient(F,I); Q |
| 32 | }}} |
| 33 | - Rings.quo |
| 34 | {{{ |
| 35 | sage: MS = MatrixSpace(QQ,2) |
| 36 | sage: MS.full_category_initialisation() |
| 37 | sage: I = MS*MS.gens()*MS |
| 38 | sage: MS.quo(I,names = ['a','b','c','d']) |
| 39 | }}} |
| 40 | - Rings.quotient_ring |
| 41 | {{{ |
| 42 | sage: MS = MatrixSpace(QQ,2) |
| 43 | sage: I = MS*MS.gens()*MS |
| 44 | sage: MS.quotient_ring(I,names = ['a','b','c','d']) |
| 45 | }}} |
| 46 | - sage/structure/category_object.pyx : |
| 47 | - CategoryObject.__temporarily_change_names |
| 48 | {{{ |
| 49 | sage: MS = MatrixSpace(GF(5),2,2) |
| 50 | sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS |
| 51 | sage: Q.<a,b,c,d> = MS.quo(I) |
| 52 | }}} |
| 53 | |
| 54 | - sage/rings/quotient_ring_element.py : |
| 55 | - QuotientRingElement |
| 56 | {{{ |
| 57 | sage: R.<x> = PolynomialRing(ZZ) |
| 58 | sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S |
| 59 | }}} |
| 60 | - QuotientRingElement.__init__ |
| 61 | {{{ |
| 62 | sage: R.<x> = PolynomialRing(ZZ) |
| 63 | sage: S.<xbar> = R.quo((4 + 3*x + x^2, 1 + x^2)); S |
| 64 | }}} |
| 65 | - QuotientRingElement._repr_ |
| 66 | {{{ |
| 67 | sage: S = SteenrodAlgebra(2) |
| 68 | sage: I = S*[S.0+S.1]*S |
| 69 | sage: Q = S.quo(I) |
| 70 | }}} |
| 71 | |
| 72 | - sage/rings/morphism.pyx : |
| 73 | - RingMap_lift |
| 74 | {{{ |
| 75 | sage: MS = MatrixSpace(GF(5),2,2) |
| 76 | sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS |
| 77 | sage: Q = MS.quo(I) |
| 78 | }}} |
| 79 | - sage/rings/ring.pyx: |
| 80 | - Ring.ideal_monoid |
| 81 | {{{ |
| 82 | sage: F.<x,y,z> = FreeAlgebra(ZZ, 3) |
| 83 | sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F |
| 84 | sage: Q = sage.rings.ring.Ring.quotient(F,I) |
| 85 | }}} |
| 86 | - Ring.quotient |
| 87 | {{{ |
| 88 | sage: R.<x> = PolynomialRing(ZZ) |
| 89 | sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) |
| 90 | sage: S = R.quotient(I, 'a') |
| 91 | }}} |
| 92 | - Ring.quotient_ring |
| 93 | {{{ |
| 94 | sage: R.<x> = PolynomialRing(ZZ) |
| 95 | sage: I = R.ideal([4 + 3*x + x^2, 1 + x^2]) |
| 96 | sage: S = R.quotient_ring(I, 'a') |
| 97 | sage: S.gens() |
| 98 | }}} |