Represents a JAS polynomial ideal: PolynomialList and Ideal.
Methods for Groebner bases, ideal sum, intersection and others.
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__init__(self,
ring,
polystr="",
list=None)
Ideal constructor. |
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__str__(self)
Create a string representation. |
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__eq__(self,
other)
Test if two ideals are equal. |
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paramideal(self)
Create an ideal in a polynomial ring with parameter coefficients. |
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isGB(self)
Test if this is a Groebner base. |
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iseGB(self)
Test if this is an e-Groebner base. |
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isdGB(self)
Test if this is a d-Groebner base. |
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parNewGB(self,
th)
Compute in parallel a Groebner base. |
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parGB(self,
th)
Compute in parallel a Groebner base. |
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distGB(self,
th=2,
machine="examples/machines.localhost",
port=55711)
Compute on a distributed system a Groebner base. |
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distClient(self,
port=4711)
Client for a distributed computation. |
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distClientStop(self)
Stop client for a distributed computation. |
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eReduction(self,
p)
Compute a e-normal form of p with respect to this ideal. |
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reduction(self,
p)
Compute a normal form of p with respect to this ideal. |
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NF(self,
reducer)
Compute a normal form of this ideal with respect to reducer. |
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lift(self,
p)
Represent p as element of this ideal. |
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intersectRing(self,
ring)
Compute the intersection of this and the given polynomial ring. |
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intersect(self,
id2)
Compute the intersection of this and the given ideal id2. |
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eliminateRing(self,
ring)
Compute the elimination ideal of this and the given polynomial ring. |
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sat(self,
id2)
Compute the saturation of this with respect to given ideal id2. |
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sum(self,
other)
Compute the sum of this and the ideal. |
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univariates(self)
Compute the univariate polynomials in each variable of this ideal. |
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inverse(self,
p)
Compute the inverse polynomial modulo this ideal, if it exists. |
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optimize(self)
Optimize the term order on the variables. |
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realRoots(self)
Compute real roots of 0-dim ideal. |
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realRootsPrint(self)
Print decimal approximation of real roots of 0-dim ideal. |
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radicalDecomp(self)
Compute radical decomposition of this ideal. |
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decomposition(self)
Compute irreducible decomposition of this ideal. |
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complexRoots(self)
Compute complex roots of 0-dim ideal. |
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complexRootsPrint(self)
Print decimal approximation of complex roots of 0-dim ideal. |
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primeDecomp(self)
Compute prime decomposition of this ideal. |
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primaryDecomp(self)
Compute primary decomposition of this ideal. |
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toInteger(self)
Convert rational coefficients to integer coefficients. |
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toModular(self,
mf)
Convert integer coefficients to modular coefficients. |
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csReduction(self,
p)
Compute a normal form of p with respect to this characteristic set. |
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syzygy(self)
Syzygy of generating polynomials. |
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isSyzygy(self,
m)
Test if this is a syzygy of the module in m. |
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