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Package sage :: Package modular :: Module cusps :: Class Cusp |
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The set of cusps.
A cusp is either a rational number of infinity, i.e., an element of P1(Q). A Cusp is stored as a pair (a,b), where gcd(a,b)=1 and a,b are of type sage.rings.integers.Integer.Method Summary | |
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Create the cusp a/b in P^1(Q), where if b=0 it is the point at infinity. | |
__neg__(self)
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__repr__(self)
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Return the denominator of the cusp a/b. | |
is_chi_equiv(self,
other,
chi)
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Return whether self and other are equivalent modulo Gamma_0(N). | |
is_gamma1_equiv(self,
other,
N)
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Return the numerator of the cusp a/b. |
Method Details |
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__init__(self,
a,
b=1)
Create the cusp a/b in P^1(Q), where if b=0 it is the point at
infinity.
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denominator(self)Return the denominator of the cusp a/b.>>> x=Cusp(6,9); x 2/3 >>> x.denominator() 3 |
is_gamma0_equiv(self, other, N)Return whether self and other are equivalent modulo Gamma_0(N). Keyword arguments: other -- a cusp N -- an integer (specifies the group Gamma_0(N)) Return True and an integer a if this cusp is equivalent to other modulo the action of Gamma_0(N). Here a is the upper left entry of a matrix in Gamma_0(N) that sends self to other (or is it other way around??). If the two cusps self and other are not congruent, then return (False, None). |
numerator(self)Return the numerator of the cusp a/b.>>> x=Cusp(6,9); x 2/3 >>> x.numerator() 2 |
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