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FactorTermsList

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

FactorTermsList[poly]
    gives a list in which the first element is the overall numerical factor in poly, and the second element is the polynomial with the overall factor removed.
FactorTermsList[poly, {x1, x2, ...}]
    gives a list of factors of poly. The first element in the list is the overall numerical factor. The second element is a factor that does not depend on any of the xi. Subsequent elements are factors which depend on progressively more of the xi.

Examples

No verified examples yet for this function.

Implementation notes

Algorithm. builtin_factortermslist (in src/poly/facpoly_factorterms.inc) is the list-returning sibling of FactorTerms. It calls the same engine ft_compute_list but returns the factor List directly instead of multiplying it out: {c_0, c_1, …, c_k, residue}, where c_0 is the numerical content, c_1..c_k are the contents extracted with respect to progressively smaller subsets of the requested variables, and residue is the remaining polynomial part. Unlike FactorTerms it does not auto-thread (its result shape is already a list). See FactorTerms for the content-extraction algorithm.

Data structures. Expr* factors gathered into a single List; content computation uses the recursive multivariate-GCD helper ft_content_wrt_set.

  • Protected.
  • The product of the returned list always reproduces the input (after

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= FactorTermsList[6 x^2 + 4 x]
Out[1]= {2, 2 x + 3 x^2}

In[2]:= FactorTermsList[2 x^2 + 4 x + 2]
Out[2]= {2, 1 + 2 x + x^2}

In[1]:= FactorTermsList[a b x^2 + a b c x, {x}]
Out[1]= {1, a b, c x + x^2}

In[1]:= FactorTermsList[12 x^3 y + 18 x^2 y, {x, y}]
Out[1]= {6, 1, y, 3 x^2 + 2 x^3}

Notes

FactorTermsList[poly] returns {overall numerical factor, polynomial with that factor removed}. The numerical content (here 2) is pulled out, leaving the primitive part; it does not factor the remaining polynomial further. Given a variable list {x1, ..., xn}, it stratifies the polynomial: the first element is the numeric content, the second is the factor depending on none of the variables, and the later elements depend on progressively more of them. In the last example 12 x^3 y + 18 x^2 y separates as 6 · 1 · y · (3 x^2 + 2 x^3), isolating the variable-free numeric content 6, the y-only factor, and finally the x-dependent remainder.