The dual of the polynomial ring |
The dual polynomials are represented as an ordered list of monomials, which define the inverse system associated to the polynomial ring. The corresponding type is Polynomial MonomialDualRing 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.Ring constructors
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R := ZZ['x,'y]
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D := dual R
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Dual polynomial constructors |
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Construction of dual elements from strings:
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l1 := D<<"215*x^4+10*x-3232231"
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l2 := polynomial(D,"3*x^3*z-x^2*y+2")
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Arithmetic operations |
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Arithmetic operations inherited from the coefficient ring are available:
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l1+33455552
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l1+=l2
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l1*l2
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Functions |
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Coefficients with respect to variable
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coefficients(l1,0)
Coefficients of all the monomials:
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coefficients(l1)
Differentiation with respect to variable
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:
Dead
External product with polynomials |
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p := R<<"x^2-x*z+y^3-1"
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l1*p
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p*l1
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