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Package sage :: Package rings :: Module polynomial :: Class Polynomial_rational_dense |
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object
--+ |Element
--+ |Polynomial
--+ | Polynomial_rational_dense
Method Summary | |
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__init__(self,
parent,
x,
check,
is_gen)
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__add__(self,
right)
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__getitem__(self,
n)
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__getslice__(self,
i,
j)
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EXAMPLES: | |
__reduce__(self)
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__setitem__(self,
n,
value)
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The difference self - right. | |
Return a copy of self. | |
Return the degree of this polynomial. | |
discriminant(self)
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list(self)
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resultant(self,
other)
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Inherited from Polynomial | |
Compute value of this polynomial at x. | |
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Division with remainder. | |
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Quotient of division of self by other. | |
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Remainder of division of self by other. | |
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Return the base ring of the parent of self. | |
Returns the complex roots of this polynomial. | |
Return the least common multiple of the denominators of the entries of self, when this makes sense, i.e., when the coefficients have a denominator function. | |
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Return polynomials f1, ..., fn and exponents e1, ..., en such that the gcd fo the coefficients of the fi is 1, and prod fi**ei is equal to a scalar multiple of self. | |
Greatest common divisor of self and polynomial other. | |
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Returns True if this polynomial is monic. | |
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If f = a_r x^r + a_{r+1}x^{r+1} + higher terms ..., with a_r nonzero then the valuation of f is r. | |
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Extended gcd of self and polynomial other. | |
Inherited from object | |
x.__delattr__('name') <==> del x.name | |
x.__getattribute__('name') <==> x.name | |
helper for pickle | |
x.__setattr__('name', value) <==> x.name = value | |
x.__str__() <==> str(x) |
Method Details |
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__mul__(self, right)EXAMPLES:>>> import rings >>> Q = rings.RationalField() >>> x = rings.PolynomialRing(Q).gen() >>> (x - '2/3')*(x**2 - 8*x + 16) x^3 - 26/3*x^2 + 64/3*x - 32/3
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__sub__(self,
right)
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copy(self)Return a copy of self. EXAMPLES: We create the polynomial f=x+3, then set g=f, and change the coefficient of x in g, which also changes the coefficient of x in f. If we instead copy f, then changing the coefficient of x of g does not change f.>>> x = PolynomialRing(IntegerRing()).gen() >>> f = x+3 >>> g = f >>> g[1]=3 >>> f 3*x + 3 >>> g = f.copy() >>> g[1]=5 >>> f 3*x + 3 >>> g 5*x + 3
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degree(self)Return the degree of this polynomial. The zero polynomial has degree -1. EXAMPLES:>>> x = PolynomialRing(IntegerRing()).gen() >>> f = x**93 + 2*x + 1 >>> f.degree() 93 >>> x = PolynomialRing(RationalField(), sparse=True).gen() >>> f = x**100000 >>> f.degree() 100000
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