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Package sage :: Package rings :: Module padic_field :: Class pAdicField |
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Ring
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pAdicField
Method Summary | |
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__init__(self,
p)
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Coerce x into the ring. | |
__cmp__(self,
other)
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__repr__(self)
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The characteristic of the field Qp, which is always 0. | |
This function always returns true, because Qp is a field. | |
name(self)
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prec(self,
n)
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The prime p such that this is the field Qp. | |
If you call print_prec(n), then printing of elements in this p-adic field is truncated at O(p^n). | |
A random integral element of Q_p to precision O(p**prec). | |
The characteristic of the residue class field Qp. | |
The residue class field of the ring Zp of integers of Qp, i.e., the field Z/pZ. | |
series_print(self,
n)
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Inherited from Ring | |
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True if the elements have atomic string representations, in the sense that they print if they print at s, then -s means the negative of s. | |
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Method Details |
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__call__(self,
x,
prec=Infinity)
Coerce x into the ring.
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characteristic(self)The characteristic of the field Qp, which is always 0. >>> K = Qp(7) >>> K.characteristic() 0
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is_field(self)This function always returns true, because Qp is a field. >>> K = Qp(7) >>> K.is_field() True
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prime(self)The prime p such that this is the field Qp. >>> K = Qp(7) >>> K.prime() 7 |
print_prec(self, n=None)If you call print_prec(n), then printing of elements in this p-adic field is truncated at O(p^n). Calling print_prec() with no arguments returns n. This command only affects printing, and does not alter the actual values of elements of this field. |
random(self, prec=10)A random integral element of Q_p to precision O(p**prec). |
residue_characteristic(self)The characteristic of the residue class field Qp. >>> K = Qp(7) >>> K.residue_characteristic() 7 |
residue_class_field(self)The residue class field of the ring Zp of integers of Qp, i.e., the field Z/pZ. >>> K = Qp(3) >>> K.residue_class_field() Z/3Z |
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