Book a Demo!
CoCalc Logo Icon
StoreFeaturesDocsShareSupportNewsAboutPoliciesSign UpSign In
Download
241852 views
Tweet
Share
Share
1
r"""

2
A functor creating rings of orthogonal modular forms.

3


4
AUTHOR :

5
    -- Martin Raum (2009 - 07 - 30) Initial version

6
"""

7


8
#===============================================================================

9
# 

10
# Copyright (C) 2009 Martin Raum

11
# 

12
# This program is free software; you can redistribute it and/or

13
# modify it under the terms of the GNU General Public License

14
# as published by the Free Software Foundation; either version 3

15
# of the License, or (at your option) any later version.

16
# 

17
# This program is distributed in the hope that it will be useful, 

18
# but WITHOUT ANY WARRANTY; without even the implied warranty of

19
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU

20
# General Public License for more details.

21
# 

22
# You should have received a copy of the GNU General Public License

23
# along with this program; if not, see <http://www.gnu.org/licenses/>.

24
#

25
#===============================================================================

26


27
from sage.categories.rings import Rings

28
from sage.categories.pushout import ConstructionFunctor

29


30
class ModularFormsFunctor ( ConstructionFunctor ) :

31
    

32
    rank = 10

33
    

34
    def __init__(self, type, precision) :

35
        """

36
        A functor constructing a ring or module of modular forms.

37
        

38
        INPUT:

39
            - ``type``      -- A type of modular forms.

40
            - ``precision`` -- A precision.

41
        

42
        NOTE:

43
            This does not respect keyword and has to be extended as soon as subclasses of

44
            ModularFormsAmbient_abstract demand for it.

45
        

46
        TESTS::

47
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import *

48
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *

49
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *

50
            sage: F = ModularFormsFunctor( ModularFormTestType_scalar(), NNFilter(5) )

51
        """

52
        self.__type = type

53
        self.__precision = precision

54
        

55
        ConstructionFunctor.__init__(self, Rings(), Rings())

56


57
    def __call__(self, A) :

58
        """

59
        INPUT:

60
            - `A` -- A ring.

61
        

62
        TESTS::

63
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import *

64
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *

65
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *

66
            sage: F = ModularFormsFunctor( ModularFormTestType_scalar(), NNFilter(5) )

67
            sage: F(QQ)

68
            Graded expansion ring with generators g1, g2, g3, g4, g5

69
        """

70
        from modularform_ambient import ModularFormsAmbient

71


72
        return ModularFormsAmbient(A, self.__type, self.__precision)

73
        

74
    def merge(self, other) :

75
        """

76
        TESTS::

77
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_functor import *

78
            sage: from psage.modform.fourier_expansion_framework.modularforms.modularform_testtype import *

79
            sage: from psage.modform.fourier_expansion_framework.monoidpowerseries.monoidpowerseries_basicmonoids import *

80
            sage: F = ModularFormsFunctor( ModularFormTestType_scalar(), NNFilter(5) )

81
            sage: G = ModularFormsFunctor( ModularFormTestType_vectorvalued(), NNFilter(5) )

82
            sage: F.merge(F) is F

83
            True

84
            sage: F.merge(G) is None

85
            True

86
            sage: G.merge(F) is G 

87
            True

88
        """

89
        if type(other) != type(self) :

90
            return None

91
        

92
        if self.__type == other.__type and \

93
           self.__precision == other.__precision :

94
            return self

95
        else :

96
            try :

97
                if other.__type.vector_valued() == self.__type and \

98
                   self.__precision == other.__precision :

99
                    return self

100
            except AttributeError, NotImplementedError :

101
                return None 

102
    

103
        return None

104


105