L_POLYADD

=L_POLYADD(a, b, [drop_leading_zeros])
=L_POLYSUB(a, b, [drop_leading_zeros])

Description

Adding and subtracting polynomials is trivial when the vectors of coefficients are the same size. But, it requires a bit of logic to match up the correct terms when the polynomials are different degrees.

L_POLYADD(a,b) adds polynomial a and polynomial b, resulting in polynomial c which is a row vector the same length as the longest of the two original vectors. Leading zero terms are not removed from the polynomial, unless you use drop_leading_zeros=TRUE.

L_POLYSUB(a,b) subtracts polynomial b from polynomial a, and is based on L_POLYADD:

L_POLYSUB(a,b) = L_POLYADD(a,-b)

For these polynomial functions, the polynomial is defined as p(x) = β_n*x_n + β_n-1*x_n-1 + … + β₂*x₂ + β₁*x₁ + β₀, and the coefficients should be defined as a row vector: {β_n,β_n-1,...,β₁,β₀}.

If the resulting polynomial c is a zero vector and you have set drop_leading_zeros to TRUE, the function will return a #N/A error.

Lambda Formula

This code for using L_POLYADD in Excel is provided under the License as part of the LAMBDA Library, but to use just this function, you may copy the following code directly into your spreadsheet.

/**
* Add two polynomials a + b = c
*/
L_POLYADD = LAMBDA(a,b,[drop_leading_zeros],
LET(doc,"https://www.vertex42.com/lambda/polyadd.html",
    na,COLUMNS(a),
    nb,COLUMNS(b),
    c,IF(na=nb,a+b,
    IF(na>nb,a+HSTACK(SEQUENCE(1,na-nb,0,0),b),
        b+HSTACK(SEQUENCE(1,nb-na,0,0),a)
    )),
    IF(drop_leading_zeros=TRUE,DROP(c,0,MATCH(TRUE,c<>0,0)-1),c)
));
/**
* Subtract polynomial b from polynomial a: a - b = c
*/
L_POLYSUB = LAMBDA(a,b,[drop_leading_zeros],
LET(doc,"https://www.vertex42.com/lambda/polyadd.html",
    L_POLYADD(a,-b,drop_leading_zeros)
));

Name: L_POLYADD
Description: Add two polynomials: a + b = c
Arguments: a, b
Function:
[in the works]

L_POLYADD Examples

Test: Copy and Paste this LET function into a cell
=LET(
    a, {1,2,0,4,5},
    b, {-3,0,3},
    L_POLYADD(a,b)
)

Result: {1,2,-3,4,8}

=LET(
    a, {1,2,4},
    b, {1,0,1},
    L_POLYSUB(a,b, TRUE)
)

Result: {2,3}

=LET(
    a, {0,0,1,2,3},
    L_POLYADD(a, 0*a, TRUE)
)

Result: {1,2,3}