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Computes a representation of a term in other terms if it exists.
SB.TermRepr(Term:POLY,TermList:LIST of POLY):LIST of INT
SB.TermRepr(Term:POLY,TermList:LIST of POLY,ReprType:INT):LIST of INT
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This functions tries to compute a term representation of the given term
Term in terms of the list
TermList. If it is not possible to get such a representation NULL will be returned. If a representation exists a list of integers will be returned which gives the exponents of the power product of the term in the other terms, e.g. for the term
Term=x^2y and the list of terms
TermList=[x,y] the function will return
[2,1] as the representation.
With the optional parameter
ReprType it is possible to choose between different ways of getting a possible representation.
- @param Term A term in the current ring.
- @param TermList A list of terms in the current ring.
- @return A list of integers, which gives the representation, or NULL.
The following parameter is optional:
- @param ReprType Either 0,1 or 2. With this parameter it is possible to choose between different ways of getting the representation: By ReprType=0 a toric ideal is used to compute the representation. This is also the default value. By ReprType=1 algebra homomorphisms are used, by ReprType=2 a system of diophantine equations is used to compute the representation.
Use R::=QQ[x,y];
SB.TermRepr(x^2y^2,[x,y]);
SB.TermRepr(x^2y^2,[xy^2,x,y]);
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-- output:
[2, 2]
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[1, 1, 0]
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-- Done.
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Use R::=QQ[x,y,z];
L:=[x^2y^4z^8,xy^3,z^5];
SB.TermRepr(xy^4z,L); -- for xy^4z no representation is existing
T:=L[1]^3L[3]^2; -- T = (x^2y^4z^8)^3 * (xy^3)^0 * (z^5)^2
T;
SB.TermRepr(T,L);
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-- output:
NULL
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x^6y^12z^34
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[3, 0, 2]
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-- Done.
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