ReductionSeq
edu.jas.ps

Class ReductionSeq<C extends RingElem<C>>

• Type Parameters:
`C` - coefficient type

`public class ReductionSeq<C extends RingElem<C>>extends Object`
Multivariate power series reduction sequential use algorithm. Implements Mora normal-form algorithm.
• Constructor Summary

Constructors
Constructor and Description
`ReductionSeq()`
Constructor.
• Method Summary

Methods
Modifier and TypeMethod and Description
`boolean``contains(List<MultiVarPowerSeries<C>> S, List<MultiVarPowerSeries<C>> B)`
Ideal containment.
`boolean``criterion4(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B, ExpVector e)`
GB criterion 4.
`boolean``isTopReducible(List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A)`
Is top reducible.
`boolean``moduleCriterion(int modv, ExpVector ei, ExpVector ej)`
Module criterion.
`boolean``moduleCriterion(int modv, MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B)`
Module criterium.
`MultiVarPowerSeries<C>``normalform(List<MultiVarPowerSeries<C>> Pp, MultiVarPowerSeries<C> Ap)`
Top normal-form with Mora's algorithm.
`MultiVarPowerSeries<C>``SPolynomial(MultiVarPowerSeries<C> A, MultiVarPowerSeries<C> B)`
S-Power-series, S-polynomial.
`List<MultiVarPowerSeries<C>>``totalNormalform(List<MultiVarPowerSeries<C>> P)`
Total reduced normalform with Mora's algorithm.
`MultiVarPowerSeries<C>``totalNormalform(List<MultiVarPowerSeries<C>> P, MultiVarPowerSeries<C> A)`
Total reduced normal-form with Mora's algorithm.
• Methods inherited from class java.lang.Object

`equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• Constructor Detail

• ReductionSeq

`public ReductionSeq()`
Constructor.
• Method Detail

• moduleCriterion

`public boolean moduleCriterion(int modv,                      MultiVarPowerSeries<C> A,                      MultiVarPowerSeries<C> B)`
Module criterium.
Parameters:
`modv` - number of module variables.
`A` - power series.
`B` - power series.
Returns:
true if the module S-power-series(i,j) is required.
• moduleCriterion

`public boolean moduleCriterion(int modv,                      ExpVector ei,                      ExpVector ej)`
Module criterion.
Parameters:
`modv` - number of module variables.
`ei` - ExpVector.
`ej` - ExpVector.
Returns:
true if the module S-power-series(i,j) is required.
• criterion4

`public boolean criterion4(MultiVarPowerSeries<C> A,                 MultiVarPowerSeries<C> B,                 ExpVector e)`
GB criterion 4. Use only for commutative power series rings.
Parameters:
`A` - power series.
`B` - power series.
`e` - = lcm(ht(A),ht(B))
Returns:
true if the S-power-series(i,j) is required, else false.
• SPolynomial

`public MultiVarPowerSeries<C> SPolynomial(MultiVarPowerSeries<C> A,                                 MultiVarPowerSeries<C> B)`
S-Power-series, S-polynomial.
Parameters:
`A` - power series.
`B` - power series.
Returns:
spol(A,B) the S-power-series of A and B.
• normalform

`public MultiVarPowerSeries<C> normalform(List<MultiVarPowerSeries<C>> Pp,                                MultiVarPowerSeries<C> Ap)`
Top normal-form with Mora's algorithm.
Parameters:
`Ap` - power series.
`Pp` - power series list.
Returns:
top-nf(Ap) with respect to Pp.
• totalNormalform

`public MultiVarPowerSeries<C> totalNormalform(List<MultiVarPowerSeries<C>> P,                                     MultiVarPowerSeries<C> A)`
Total reduced normal-form with Mora's algorithm.
Parameters:
`A` - power series.
`P` - power series list.
Returns:
total-nf(A) with respect to P.
• totalNormalform

`public List<MultiVarPowerSeries<C>> totalNormalform(List<MultiVarPowerSeries<C>> P)`
Total reduced normalform with Mora's algorithm.
Parameters:
`P` - power series list.
Returns:
total-nf(p) for p with respect to P\{p}.
• isTopReducible

`public boolean isTopReducible(List<MultiVarPowerSeries<C>> P,                     MultiVarPowerSeries<C> A)`
Is top reducible.
Parameters:
`A` - power series.
`P` - power series list.
Returns:
true if A is top reducible with respect to P.
• contains

`public boolean contains(List<MultiVarPowerSeries<C>> S,               List<MultiVarPowerSeries<C>> B)`
Ideal containment. Test if each b in B is contained in ideal S.
Parameters:
`S` - standard base.
`B` - list of power series
Returns:
true, if each b in B is contained in ideal(S), else false