Ticket #3858: ref.patch
File ref.patch, 8.1 KB (added by , 12 years ago) |
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sage/calculus/calculus.py
# HG changeset patch # User J. H. Palmieri <palmieri@math.washington.edu> # Date 1218748819 25200 # Node ID 6e2afe97a9d8e2e288d21eb826fcf900cd7db2cb # Parent 6946afd933b4f1b19ca2a38f722fc6db15aaa321 fixes in automatic production of reference manual from source diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/calculus/calculus.py
a b 236 236 is different than the one in the interactive interpreter. 237 237 238 238 Check to see that the problem with the variables method mentioned in Trac 239 ticket #3779 is actually fixed:239 ticket \#3779 is actually fixed: 240 240 sage: f = function('F',x) 241 241 sage: diff(f*SR(1),x) 242 242 diff(F(x), x, 1) -
sage/combinat/root_system/dynkin_diagram.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/combinat/root_system/dynkin_diagram.py
a b 210 210 return result 211 211 212 212 def __getitem__(self, i): 213 """213 r""" 214 214 With a tuple (i,j) as argument, returns the scalar product $\langle 215 215 \alpha^\vee_i, \alpha_j\rangle$. 216 216 -
sage/combinat/root_system/root_system.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/combinat/root_system/root_system.py
a b 53 53 sage: space 54 54 Root lattice of the Root system of type ['B', 3] 55 55 56 It is the free \ZZmodule $\bigoplus_i \ZZ.\alpha_i$ spanned by56 It is the free $\ZZ$-module $\bigoplus_i \ZZ.\alpha_i$ spanned by 57 57 the simple roots: 58 58 59 59 sage: space.base_ring() -
sage/combinat/root_system/weyl_characters.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/combinat/root_system/weyl_characters.py
a b 312 312 sage: B3 = WeylCharacterRing(['B',3]) 313 313 sage: B3(1/2,1/2,1/2).mlist() 314 314 [[(1/2, -1/2, -1/2), 1], [(-1/2, 1/2, -1/2), 1], [(1/2, 1/2, 1/2), 1], [(1/2, 1/2, -1/2), 1], [(-1/2, -1/2, 1/2), 1], [(-1/2, -1/2, -1/2), 1], [(1/2, -1/2, 1/2), 1], [(-1/2, 1/2, 1/2), 1]] 315 315 """ 316 316 # Why did the test not pass with the following indentation? 317 317 # [[( 1/2, -1/2, -1/2), 1], 318 318 # [(-1/2, 1/2, -1/2), 1], … … 322 322 # [(-1/2, -1/2, -1/2), 1], 323 323 # [( 1/2, -1/2, 1/2), 1], 324 324 # [(-1/2, 1/2, 1/2), 1]] 325 """326 325 return [[k,m] for k,m in self._mdict.iteritems()] 327 326 328 327 def parent(self): -
sage/matrix/matrix0.pyx
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/matrix/matrix0.pyx
a b 2712 2712 sage: parent(~1) 2713 2713 Rational Field 2714 2714 2715 A matrix with 0 rows and 0 columns is invertible (see trac #3734):2715 A matrix with 0 rows and 0 columns is invertible (see trac \#3734): 2716 2716 sage: M = MatrixSpace(RR,0,0)(0); M 2717 2717 [] 2718 2718 sage: M.determinant() -
sage/matrix/matrix_modn_dense.pyx
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/matrix/matrix_modn_dense.pyx
a b 350 350 351 351 352 352 def _unpickle(self, data, int version): 353 """353 r""" 354 354 TESTS: 355 355 356 356 Test for char-sized modulus: -
sage/modular/congroup.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/modular/congroup.py
a b 476 476 477 477 def lift_to_sl2z(c, d, N): 478 478 """ 479 Given a vector (c, d) in (Z/NZ)^2, this function computes and479 Given a vector (c, d) in $(Z/NZ)^2$, this function computes and 480 480 returns a list [a, b, c', d'] that defines a 2x2 matrix with 481 481 determinant 1 and integer entries, such that c=c'(mod N) and 482 482 d=d'(mod N). … … 1565 1565 1566 1566 1567 1567 def _reduce_coset(self, uu, vv): 1568 """1568 r""" 1569 1569 Compute a canonical form for a given Manin symbol. 1570 1570 1571 1571 INPUT: … … 1604 1604 sage: len(v) 1605 1605 361 1606 1606 1607 This demonstrates the problem underlying trac #1220:1607 This demonstrates the problem underlying trac \#1220: 1608 1608 sage: G = GammaH(99, [67]) 1609 1609 sage: G._reduce_coset(11,-3) 1610 1610 (11, 96) -
sage/modular/modsym/boundary.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/modular/modsym/boundary.py
a b 6 6 form $[P, u/v]$, where $u/v$ is a cusp for our group $G$. The group of 7 7 boundary modular symbols naturally embeds into a vector space $B_k(G)$ 8 8 (see Stein, section 8.4, or Merel, section 1.4, where this space is 9 called $\ mathbb{C}[\Gamma \\ \mathbb{Q}]_k$, for a definition), which10 is a finite dimensional $\ mathbb{Q}$ vector space of dimension equal9 called $\CC[\Gamma \\ \QQ]_k$, for a definition), which 10 is a finite dimensional $\QQ$ vector space of dimension equal 11 11 to the number of cusps for $G$. The embedding takes $[P, u/v]$ to 12 12 $P(u,v)\cdot [(u,v)]$. We represent the basis vectors by pairs [(u,v)] 13 13 with u, v coprime. On $B_k(G)$, we have the relations 14 14 \[ [\gamma \cdot (u,v)] = [(u,v)] \] 15 15 for all $\gamma \in G$ and 16 16 \[ [(\lambda u, \lambda v)] = \operatorname{sign}(\lambda)^k [(u,v)] \] 17 for all $\lambda \in \ mathbb{Q}^\times$.17 for all $\lambda \in \QQ^\times$. 18 18 19 19 It's possible for these relations to kill a class, i.e., for a pair 20 20 [(u,v)] to be 0. For example, when N=4, u=1, v=2 and k=3 then (-1,-2) -
sage/modular/modsym/modsym.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/modular/modsym/modsym.py
a b 1 """1 r""" 2 2 Creation of modular symbols spaces 3 3 4 4 EXAMPLES: … … 40 40 sage: t2*t5 - t5*t2 == 0 41 41 True 42 42 43 This tests the bug reported in trac #1220:43 This tests the bug reported in trac \#1220: 44 44 sage: G = GammaH(36, [13, 19]) 45 45 sage: G.modular_symbols() 46 46 Modular Symbols space of dimension 13 for Congruence Subgroup Gamma_H(36) with H generated by [13, 19] of weight 2 with sign 0 and over Rational Field -
sage/modules/free_module.py
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/modules/free_module.py
a b 852 852 853 853 854 854 def __len__(self): 855 """855 r""" 856 856 Return the cardinality of the free module. 857 857 858 N.B. Currently len(QQ) gives a TypeError, hence so does len(QQ ^3).858 N.B. Currently len(QQ) gives a TypeError, hence so does len(QQ\^{}3). 859 859 860 860 EXAMPLES: 861 861 sage: k.<a> = FiniteField(9) … … 2122 2122 User basis matrix: 2123 2123 [2 4 0] 2124 2124 2125 The following module isn't in the ambient module ZZ^3but is2126 contained in the ambient vector space QQ^3:2125 The following module isn't in the ambient module $ZZ^3$ but is 2126 contained in the ambient vector space $QQ^3$: 2127 2127 2128 2128 sage: V = M.ambient_vector_space() 2129 2129 sage: W.span_of_basis([ V([1/5,2/5,0]), V([1/7,1/7,0]) ]) -
sage/rings/real_mpfi.pyx
diff -r 6946afd933b4 -r 6e2afe97a9d8 sage/rings/real_mpfi.pyx
a b 1010 1010 1011 1011 Then the interval is contained in the interval: 1012 1012 1013 mantissa*b^exponent - error*b^k .. mantissa*b^exponent + error*b^k 1013 $\text{mantissa}*b^{\text{exponent}} - \text{error}*b^k .. 1014 \text{mantissa}*b^{\text{exponent}} + \text{error}*b^k$ 1014 1015 1015 1016 To control the printing, we can specify a maximum number of 1016 1017 error digits. The default is 0, which means that we do not print … … 2931 2931 return x 2932 2932 2933 2933 def is_int(self): 2934 """2934 r""" 2935 2935 OUTPUT: 2936 2936 bool -- True or False 2937 2937 n -- an integer