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The ring of sparse polynomials |
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Sparse polynomials are represented as an ordered list of monomials. The corresponding type is Polynomial MonomialSparseRing C, where C is the type of coefficients. Here we describe the main functionnalities available for these polynomials.
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use "realroot"
1.Constructors
1.1.Ring constructors
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R := ZZ[x,y]
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ring (ZZ,'x,'y,'z)
1.2.Polynomial constructors
Construction of a polynomial from variables from the ring:
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x:= R[0]; p := 215*x^4+10*x-3232231
Construction of a polynomial from a string:
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p:= R<<"215*x^4+10*x-3232231"
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q := polynomial(R,"3*x^3*z-x^2*y+2")
An equivalent construction with variables
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y:=R[1], z:= R[2]; q := 3*x^3*z-x^2*y+2
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2.Functions
2.1.Aritmetic operations
Arithmetic operations inherited from the coefficient ring are available:
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p+33455552
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q+=p
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r:=q*p
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2.2.Coefficients
Coefficients with respect to variable 
(the
results is a list of multivariate polynomials):
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coefficients(r,0)
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coefficients r
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2.3.Differentiation
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diff(r,'x)
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diff(r,0)
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2.4.Homogeneization
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homogenize(q,R<<'w)
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