Extracting coefficients from sum
Extracting coefficients from sum
I'm having the hardest time working if I have a sum of products, with coefficients out the front, like
expr = 1 + 2 a[0] b[1] + 2 a[0] b[1] c[3] + c[6] + 5 d[3, 4]
How do I get a list of terms with their coefficients, like
1, 1, 2, a[0] b[1], 2, a[0] b[1] c[3], 1, c[6], 5, d[3,4] ?
or even
1, 1, 2, a[0], b[1], 2, a[0],b[1],c[3] , 1, c[6], 5, d[3,4]?
I've tried:
Table[Coefficient[expr, i], i, i, Variables[expr]]
(* 2 b[1] + 2 b[1] c[3], a[0], 2 a[0] + 2 a[0] c[3], b[1], 2 a[0] b[1], c[3], 1, c[6], 5, d[3, 4] *)
But this returns coefficients for the "individual" variables a[0], b[1], c[1], c[3], d[3,4], not the variables as they are grouped in the sum.
a[0]
b[1]
c[1]
c[3]
d[3,4]
I also tried manually picking through the sum, without much success
expr[[2,1]], expr[[2,2;;-1]] (* want 2, a[0] b[1] *)
(* 2, a[0],b[1] *) (* YAY! *)
expr[[4,1]], expr[[4,2;;-1]] (* want 1, c[6] *)
(* 6, c *) (* Oh no... *)
2 Answers
2
You can use a combination of MonomialList and FactorTermsList. MonomialList gives a list of the monomials (including coefficients) and FactorTermsList gives a 2 element list with the overall numerical factor and the rest of the monomial:
MonomialList
FactorTermsList
MonomialList
FactorTermsList
expr = 1 + 2 a[0] b[1] + 2 a[0] b[1] c[3] + c[6] + 5 d[3, 4];
FactorTermsList /@ MonomialList[expr]
2, a[0] b[1] c[3], 2, a[0] b[1], 1, c[6], 5, d[3, 4], 1, 1
Update: In version 9, there is System`ReduceUtilsDump`MonomialCoefficients which (when Transposed) gives the desired result.
System`ReduceUtilsDump`MonomialCoefficients
Transpose
Transpose @ System`ReduceUtilsDump`MonomialCoefficients @ expr
1, 1, 2, a[0] b[1], 2, a[0] b[1] c[3], 1, c[6], 5, d[3, 4]
It seems that this function is no longer available in version 11. The following
implementation is a variation of the code behind System`ReduceUtilsDump`MonomialCoefficients:
System`ReduceUtilsDump`MonomialCoefficients
ClearAll[coefList]
coefList[a_Times] := Select[a, #] & /@ NumericQ, Not@*NumericQ
coefList[a_Plus] := coefList/@(List @@ a)
coefList[a_] := 1, a
coefList @ expr
1, 1, 2, a[0] b[1], 2, a[0] b[1] c[3], 1, c[6], 5, d[3, 4]
Original answer:
Using Replace:
Replace
Replace[List @@ expr, c_. t__ :> c, 1 t, 1]
1, 1, 2, a[0] b[1], 2, a[0] b[1] c[3], 1, c[6], 5, d[3, 4]
Replace[List @@ expr, c_. t__ :> c, t, 1]
1, 1, 2, a[0], b[1], 2, a[0], b[1], c[3], 1, c[6], 5, d[3, 4]
If you wish you can Flatten the first sublist:
Flatten
FlattenAt[%, 1, 2]
1, 1, 2, a[0], b[1], 2, a[0], b[1], c[3], 1, c[6], 5, d[3, 4]
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