Changeset 2338:efd19da829d4
- Timestamp:
- 01/11/07 17:41:32 (6 years ago)
- Branch:
- default
- Location:
- sage
- Files:
-
- 4 edited
-
calculus/calculus.py (modified) (2 diffs)
-
functions/piecewise.py (modified) (1 diff)
-
modular/modsym/ambient.py (modified) (1 diff)
-
modular/modsym/subspace.py (modified) (1 diff)
Legend:
- Unmodified
- Added
- Removed
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sage/calculus/calculus.py
r2331 r2338 1 """nodoctest""" 2 1 3 from sage.rings.all import (CommutativeRing, RealField, is_Polynomial, 2 4 is_RealNumber, is_ComplexNumber, RR, … … 80 82 SymbolicExpressionRing = SymbolicExpressionRing_class() 81 83 SER = SymbolicExpressionRing 84 # conversions is the dict of the form system:command 82 85 83 86 class SymbolicExpression(RingElement): 84 r"""85 A Symbolic Expression in acoordance with SEP #1.86 87 87 """ 88 # conversions is the dict of the form system:command 88 A Symbolic Expression. 89 """ 89 90 def __init__(self, conversions={}): 90 91 RingElement.__init__(self, SymbolicExpressionRing) -
sage/functions/piecewise.py
r2278 r2338 727 727 sage: f = Piecewise([[(-pi,pi),f]]) 728 728 sage: float(f.fourier_series_cosine_coefficient(2,pi)) 729 0.99999999976227982729 1.0 730 730 sage: f1 = lambda x:-1 731 731 sage: f2 = lambda x:2 -
sage/modular/modsym/ambient.py
r2337 r2338 760 760 the $S^e$ as a module over the \emph{anemic} Hecke algebra 761 761 adjoin the star involution. 762 763 EXAMPLES: 764 sage: M = ModularSymbols(Gamma0(22), 2); M 765 Modular Symbols space of dimension 7 for Gamma_0(22) of weight 2 with sign 0 over Rational Field 766 sage: M.factorization(): 767 ... print b.dimension(), b.level(), e 768 1 11 2 769 1 11 2770 1 11 2771 1 22 1 772 773 An example with sign 1: 774 sage: M = ModularSymbols(Gamma0(22), 2, sign=1); M 775 Modular Symbols space of dimension 5 for Gamma_0(22) of weight 2 with sign 1 over Rational Field 776 sage: for b, e in M.factorization(): 777 ... print b.dimension(), b.level(), e 778 1 11 2 779 1 11 2780 1 22 1 781 782 An example for Gamma1: 783 sage: M = ModularSymbols(Gamma1(26), 2, sign=1); M 784 Modular Symbols space of dimension 33 for Gamma_1(26) of weight 2 with sign 1 and over Rational Field 785 sage: for b, e in M.factorization(): 786 ... print b.dimension(), b.level(), e 787 1 13 2 788 1 13 2789 1 13 2790 213 2791 2 13 2792 2 13 2793 2 13 2794 2 13 2795 1 26 1 796 1 26 1797 1 26 1798 226 1799 2 26 1800 801 An example with level divisible by a square: 802 sage: M = ModularSymbols(Gamma0(2*9),2); M 803 ??? 804 sage: for b, e in M.factorization(): 805 ... print b.dimension(), b.level(), e 806 ??? 807 """ 762 """ 763 764 ## EXAMPLES: 765 ## sage: M = ModularSymbols(Gamma0(22), 2); M 766 ## Modular Symbols space of dimension 7 for Gamma_0(22) of weight 2 with sign 0 over Rational Field 767 ## sage: M.factorization(): 768 ## ... print b.dimension(), b.level(), e 769 ## 1 11 2 770 ## 1 11 2 771 ## 1 11 2 772 ## 1 22 1 773 774 ## An example with sign 1: 775 ## sage: M = ModularSymbols(Gamma0(22), 2, sign=1); M 776 ## Modular Symbols space of dimension 5 for Gamma_0(22) of weight 2 with sign 1 over Rational Field 777 ## sage: for b, e in M.factorization(): 778 ## ... print b.dimension(), b.level(), e 779 ## 1 11 2 780 ## 1 11 2 781 ## 1 22 1 782 783 ## An example for Gamma1: 784 ## sage: M = ModularSymbols(Gamma1(26), 2, sign=1); M 785 ## Modular Symbols space of dimension 33 for Gamma_1(26) of weight 2 with sign 1 and over Rational Field 786 ## sage: for b, e in M.factorization(): 787 ## ... print b.dimension(), b.level(), e 788 ## 1 13 2 789 ## 1 13 2 790 ## 1 13 2 791 ## 2 13 2 792 ## 2 13 2 793 ## 2 13 2 794 ## 2 13 2 795 ## 2 13 2 796 ## 1 26 1 797 ## 1 26 1 798 ## 1 26 1 799 ## 2 26 1 800 ## 2 26 1 801 802 ## An example with level divisible by a square: 803 ## sage: M = ModularSymbols(Gamma0(2*9),2); M 804 ## ??? 805 ## sage: for b, e in M.factorization(): 806 ## ... print b.dimension(), b.level(), e 807 ## ??? 808 808 try: 809 809 return self._factorization -
sage/modular/modsym/subspace.py
r2288 r2338 142 142 (Modular Symbols subspace of dimension 1 of Modular Symbols space of dimension 3 for Gamma_0(11) of weight 2 with sign 0 over Rational Field) 143 143 sage: [A.T(2).matrix() for A, _ in D] 144 [[ 3], [-2], [-2]]144 [[-2], [-2], [3]] 145 145 sage: [A.star_eigenvalues() for A, _ in D] 146 [[1], [ 1], [-1]]146 [[1], [-1], [1]] 147 147 148 148 In this example there is one old factor squared.
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