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from sage .homology .free_resolution import (FiniteFreeResolution ,
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FiniteFreeResolution_free_module ,
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FiniteFreeResolution_singular )
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- from sage .misc .superseded import deprecated_function_alias
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class GradedFiniteFreeResolution (FiniteFreeResolution ):
@@ -107,7 +106,8 @@ class GradedFiniteFreeResolution(FiniteFreeResolution):
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- ``name`` -- string; name of the base ring
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"""
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- def __init__ (self , module , degrees = None , shifts = None , name = 'S' , ** kwds ):
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+ def __init__ (self , module , degrees = None , shifts = None , name = 'S' ,
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+ ** kwds ) -> None :
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r"""
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Initialize ``self``.
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@@ -162,7 +162,7 @@ def __init__(self, module, degrees=None, shifts=None, name='S', **kwds):
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self ._multigrade = multigrade
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self ._zero_deg = zero_deg
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- def _repr_module (self , i ):
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+ def _repr_module (self , i ) -> str :
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"""
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EXAMPLES::
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@@ -323,7 +323,7 @@ class GradedFiniteFreeResolution_free_module(GradedFiniteFreeResolution, FiniteF
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sage: res = FreeResolution(M, graded=True); res
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S(0)⊕S(0)⊕S(0) <-- S(-3)⊕S(-1) <-- 0
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"""
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- def __init__ (self , module , degrees = None , * args , ** kwds ):
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+ def __init__ (self , module , degrees = None , * args , ** kwds ) -> None :
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"""
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Initialize ``self``.
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@@ -406,7 +406,8 @@ def find_deg(i):
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return [M ]
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- class GradedFiniteFreeResolution_singular (GradedFiniteFreeResolution , FiniteFreeResolution_singular ):
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+ class GradedFiniteFreeResolution_singular (GradedFiniteFreeResolution ,
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+ FiniteFreeResolution_singular ):
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r"""
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Graded free resolutions of submodules and ideals of multivariate
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polynomial rings implemented using Singular.
@@ -469,7 +470,8 @@ class GradedFiniteFreeResolution_singular(GradedFiniteFreeResolution, FiniteFree
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sage: r = I.graded_free_resolution(); r
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S(0) <-- S(-1)⊕S(-2)⊕S(-2) <-- S(-3)⊕S(-3)⊕S(-4) <-- S(-5) <-- 0
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"""
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- def __init__ (self , module , degrees = None , shifts = None , name = 'S' , algorithm = 'heuristic' , ** kwds ):
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+ def __init__ (self , module , degrees = None , shifts = None , name = 'S' ,
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+ algorithm = 'heuristic' , ** kwds ) -> None :
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"""
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Initialize.
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@@ -559,6 +561,3 @@ def _maps(self):
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self ._res_shifts = res_shifts
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return res_mats
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-
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-
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- GradedFreeResolution = deprecated_function_alias (34873 , GradedFiniteFreeResolution_singular )
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